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z_mat_manual - Z-set

1. prefix size description default dT V gradient of temperature yes q V heat flux yes temperature S the temperature at the Gauss point yes Example Two examples of thermal behavior follow behavior thermal conductivity isotropic k 48 822 coefficient capacity 4 8168e6 return behavior thermal conductivity isotropic k temperature 0 1 0 0 0 6 500 0 return Z set Non li amp structure an behavior variable friction behavior variable friction Description This behavior is used to specify a variable friction in certain contact models see the com mand contact zone variable_friction in the Z set user manual The behavior specifies a friction coefficient y that may depend on the current total relative sliding us of the contact surfaces and or the cumulative relative sliding Ucum This is analogous to the role played by the current inelastic deformation and the cumulative plastic deformation in isotropic and kinematic hardening in conventional material models The analogy is as follows the total friction coefficient yu is written as u Ho UR Ucum Hx Ucum Us Where uo plays the role analogous to the elastic limit upr to the isotropic hardening and ux to the kinematic hardening Syntax k kbehavior variable_friction isotropic constant linear nonlinear fricl uo fric3 Q bl bi J betai 6 kinematic linear nonlinear fric2 C L b b
2. State coupling is given through symmetric interaction matrices M H Msj h extensions which change the e variable will be given in the next release of Z BuLoN exceptions are available Z set Non linear material amp structure analysis suite 10 13 behavior gen_evp 10 14 Syntax The material file structure for the gen_evp model consists of an elasticity object an optional thermal strain object an optional arbitrary number of potentials without restriction on types and a number of optional interaction objects behavior gen_evp modifier x elasticity lt ELASTICITY gt global_output damage lt DAMAGE gt localization lt LOCALIZATION gt global_function lt GLOBAL_FUNCTION gt thermal_strain lt THERMAL_STRAIN gt conductivity lt CONDUCTIVITY gt potential lt POTENTIAL gt name interaction lt INTERACTION gt The compatibility of objects with the other objects and with the integration method will be investigated during the running of the problem Because of the dynamic nature of these models however it is often difficult to make any verification as to the physical meaning of a particular model combination It is therefore strongly advised to observe the material behavior on a single element This allows experimentation of the integration method and selection of the output variables without performing costly full scale calculations
3. criterion anisotropic orthotropic c11 44667 c22 c44 0 c55 c12 18 c23 T1 orthotropic cil 1266667 c22 c44 0 c55 c12 101 c23 T2 orthotropic c11 1021667 c22 c44 0 c55 c12 1205 c23 g_function anisotropic orthotropic c11 3 346000 c22 c44 0 c55 58 c33 666 1 7 c66 0 4 c31 26667 338 c33 666 66 c66 0 439 c31 2276667 3235 c33 6666666 1 c66 O 444 c31 2226667 3 346 c33 666 1 375 c66 0 c12 3 012667 c23 333333 c31 3333333 recovery_flow hyperbolic K 331 69 n 3 569 eps0 0 00000019831932773108 00354 11900 2 0 3 0 model_coef p 11900 0 p1 1656 0 p2 325 5 return 13 79 lt POTENTIAL gt lt POTENTIAL gt crystal Description The crystal potential type is rather a group of similar potential classes for modeling dif ferent monocrystalline slip systems To construct a single crystal it is normally required to add several different potentials For instance a FCC crystal is often constructed with the octahedral and cubic planes modeled in two potentials The model includes a localization step where the stress is resolved into a scalar 7 acting along the slip direction in the slip plane i this is the resolved shear stress The localization depends on the precise orientation of slip planes and slip directions as described in the section lt CRYSTAL_ORIENTATION gt on page 13 31 E The yield criterion depends on a number of scalar kinematic back st
4. continuedExample An example with multiple load segments and cycles follows Note that the second load segment uses a time variable offset by the ending of the first segment simulate test biaxe load segment time sigil sig22 sig33 sigi2 0 0 0 0 0 0 0 0 0 0 1 O 100 0 0 0 kload cycle 4 segment time sig11 sig22 sig33 eto12 0 0 0 0 100 0 0 0 0 0 1 0 0 0 100 0 0 0 0 02 3 0 0 0 100 0 0 0 0 02 4 0 0 0 100 0 0 0 0 0 model file biaxe sim integration runge_kutta 1 e 3 1 e 3 output time eto22 sig22 eto12 sigi2 evcum return The second example imposes an external parameter temperature which can be used in the behavior through variable coefficients or a parametric strain definition simulate test genevp_variable_temp load segment time sigil sig22 sig33 sigi2 param temperature 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 210 0 0 0 0 0 0 2 0 0 0 210 0 0 0 0 100 0 model file genevp_variable_temp sim integration runge_kutta 1 e 2 output time eto22 epcum sig22 temperature RO C sig mises return continuedAnother useful loading employes the rate form to convienantly give a pre loading followed by an anternating strain rate simulate test rate_loading load segment 5 time sig11 eto22 sig33 sigi2 0 0 O O O O 1000 O 0 01 O kload cycle 8 segment rate 5 time sigl1 eto22 sig33 sigi2 4 O 0 004 0 O set Non linear structure analysis suite Zi 8
5. porous_criterion zhang niemi coefficients Example A simple example from a test case is given below porous_criterion zhang _niemi lambda0 chi_c fs 13 72 Z set No amp structure lt POTENTIAL gt lt POTENTIAL gt Description The potential object classes define the dissipation potentials within a gen_evp behavior assem bly Each potential given describes an inelastic strain mechanism along with the hardening variables which affect its evolution We can generally combine an arbitrary number and mix of the potentials in order to create complex behaviors This combination is however not ver ified for physical compatibility so a particular assembly should be extensively studied under simple volume element loadings Syntax potential potential type name The types and number of sub options is dependent on the potential type and is thus left to be described with the potential types The types available are summarized below CODE DESCRIPTION gen_evp classical plasticity using un coupled isotropic and kinematic hardening non associated need info delobelle special kinematic hardening evolution with multiple ten sor variables gen_evp2 modified gen_evp with different hardening variables coupled_recovery kinematic recovery which couples the back stresses associated completely associated version of classical plasticity z6_gen_evp un associated interactions compatible with Z6 mises_2m1c Compl
6. 15 11 x simulate kx test load 400 O 0 004 0 O model file rate_loading sim integration runge_kutta 5 e 2 output time eto22 sig22 return 15 12 Z set Non linear material amp structure analysis suite x x simulate xtest x model model Description This command defines the model to be simulated in the current test Syntax One specifies the simulation one time per test using the following syntax model type coefficients coef list constant file name integration INTEGRATION initial_value var_name value If the optional model name type is given after the model command the model will be of the generalized simulation type not fem compatible In this case the model coefficients will be read below the coefficients command or in a file with the coefficients command in it terminated with return Otherwise the file command must be used to specify the external file name with the fem compatible behavior standard behavior file as described in the chapter Material File file gives the file name for a behavior type model This can be one of the standard finite element behaviors or a custom ZebFront behavior Note that the filename may be the same as the input file name including the suffix The file will be scanned for the behavior keyword We normally suggest putting the behavior definition at the end of the input file integration defines the integr
7. 3CJ3 FI o where C and F are the coefficients named C and F and which can depend notably on the porosity variable f As stated above the J2 will be as supplied by the shear anisotropy default standard Jz measure and the J is calculated by p11 02 T 033 and p q and r are coefficients not depending on state variables Syntax The syntax follows the typical porous potential format with the 5 coefficients C F p q and r to be entered Again only C and F can depend on the porosity porous_criterion elliptic coefficients continued Z set Non linear material amp structure analysis suite lt POROUS_CRITERION gt Example An example test is in Sam_test INP in the input files elliptica and ellaniso inp behavior porous_plastic kelasticity orthotropic y1111 464 y2222 239 y3333 239 y1212 105 y2323 105 y3131 105 y1122 172 y2233 142 y3311 172 porous_potential porous_criterion elliptic_aniso Cc 1 F 1 839926000000000e 03 p 1 q 2 061266000000000e 01 r 2 330418000000000e 01 shear_anisotropy hill hilla 4 172356995000000e 01 hillb 2 066054000000000e 00 hillc 1 992586000000000e 00 hilld 1 hillf 1 hille 1 flow norton pseudo rate independant K 0 001 n 10 plasticity with these coefs isotropic_hardening nonlinear_double RO 4 500000000000000e 01 Q1 3 729991000000000e 01 b1 3 276424000000000e 02 Q2 8 166423000000000e 03 b2 0 001 return
8. AETI aE lag_mult_stepxg i 1 m vO max A t 0 where AS is the lagrange multiplier of the ith constraint at the kth iteration and g is the value of the ith constraint of the best solution known so far The larger lag_mult_step the quicker the lagrange multipliers will change Default value is 0 1 16 34 Z set Non linear material amp structure analysis suite x xoptimize augmented lagrangian optimize augmented lagrangian Description This optimizer is a basic implementation of the classic augmented lagrangian method for constrained optimization For problems of the form 10 i 1 m TER a dual method is used to find a saddle point of the augmented lagrangian function L a A r Maz w iA r Maz Min L x A r A ER where L x A r is defined by Li r fa Ea i gula r SE gia with A the lagrange multipliers and r a penalty parameter that insure the differentiability of the dual function A r near the optimum A The penalty parameter r must then be chosen large enough to improve convergence of the dual problem but not too large because the lagrange function L A r can become ill conditioned in this case For each value of the lagrange multiplier A the unconstrained problem Min L z A r is solved by a BFGS method At each iteration of the BFGS method an economic line search procedure based upon the Goldstein rule has been implemented Syntax The following a
9. L betak Bj Possible choices are isotropic constant takes one parameter uo isotropic linear takes two parameters uo and Q to give UR Queum xisotropic nonlinear takes four parameters uo Q b and 6 to give ur Q 1 exp b1 ucum kinematic linear takes one parameter C to give ux Clusl kinematic nonlinear takes three parameters C b and BP to give ux C 1 exp bucum el Here Umax S Currently the behavior parameters cannot depend on any external parameter such as temperature Also note that not all contact models support a variable friction coefficient If so it is indicated in the description of each contact model Example this behavior is Z set specific and therefore does not apply for Z mat for other codes 12 17 x behavior variable friction x behavior variable_friction kinematic nonlinear fric2 3 b 4 e 2 betak 1 8 isotropic nonlinear frici 0 18 fric3 3 bi 5 e 2 return 12 18 Z set Non linear material amp structure analysis suite Chapter 13 Material Components 13 1 Z set Non linear material 13 2 amp structure analysis suite lt ANISOTROPIC_DAMAGE gt lt ANISOTROPIC_DAMAGE gt Description These behavior objects are specific to the elastic and viscoplastic anisotropic damage models They allow different types of damage variable to be used easily and in combination All the coefficients and functions
10. Model Simulation Model Simulation Description As part of the Z set package there is a model simulation mode which can be applied to any differential model as supplied by the user or used to simulate material behavior for a volume element based on one of the standard behaviors or a ZebFront behavior see the developers handbook for a description of the latter To allow rapid prototyping of models ZebFront modes are available in either a pure model definition or with small additions to user behaviors defined in this manner For mechanical material behaviors some special functionality is provided This includes generalized mixed mode loading and the visualization of yield surfaces Note that curve out put of a finite element calculation may be obtained using the curve command in Zebulon and then fed into the simulator for loading to obtain more detailed output or yield surface visualization Syntax Zrun S problem More Information For more information on simulations please refer to the following manual sections and ex ample files e Tests in the directory Z7PATH test Simulator_test where there are many examples of input files exercising all the simulator options e Examples handbook and corresponding example files There is some information show ing basic use the Simulation chapter and many more examples in the Material Behaviors chapter In fact most of the behavior outputs are generated with the sim
11. Multi potential models are primarily used for cases of time independent plasticity in combi nation with viscoplastic deformation or to assemble multiple crystalline deformation systems By default there is no thermal strain no inelastic deformation or any interactions The optional names name given after each potential type are used as a means to specify individual potentials for interactions and in construction of the output variable names Normally it is advised to use ep for a plastic potential s name and ev for a viscoplastic one Unless the option global_output is given the internal variables are stored in their local material frame instead of the global one Stored Variables The stored variables for this model are the following prefix size description default eto T 2 total small deformation strain yes sig T 2 Cauchy stress yes eel T 2 elastic strain no ein T 2 total inelastic strain tensor yes enmi T 2 potential named nm inelastic strain yes tensor The variable ein is only stored in the event of multiple potentials The separate inelastic strain tensors for each potential and their hardening variable names will be given for each separate potential type Because the behavior does not know any specifics of the potentials or the user supplied names and the applications of the same potential object may differ according to the rest of the behavior options the variable names are vaguely specified at this
12. e One may use the Lagrangian modifiers described on page 14 5 to transform the behavior into finite strain when the conditions for calculating the deformation gradient ina UMAT have been met see ABAQUS user manual 25 2 26 e For use with ABAQUS Explicit one must add the material modifier explicit Mrom version 5 6 handbook Z set Non linear material 2 9 amp structure analysis suite E Interface files debug debug Description This command indicates that debug output will be included during the run This is primarily for user defined functions and behavior models using the prn set of C functions The command will also print out the active list of auto load keywords so one may verify if a particular function is loaded with the Z mat ABAQUS link Output from the debug statements will be in a file named OUT located in the given directory full path If no path is given and the library is unable to determine the problem directory the full path of the output file is tmp OUT This path sometimes helps to get around the problem copying to a scratch directory by ABAQUS Syntax x debug path local_debug ele gp flags flags limit_debug_time st end where path is the path to use for storing the OUT debug file local_debug localize the debug output to a given element number and a given Gauss point number flags Set flags for the internal int DeBuG This is used control what gets prin
13. parameter variables which do not have associated forces and hardening variables which do have associated forces The distinction concerns the form of interaction which is possible The total variables may therefore be envisioned as eet p1h1 p2hz Pran where the first bracketed term represents the global model variables and each additional represents the potential mechanisms chosen The first term is noted to assume a linear elastic small deformation law Again the p and h variables are defined by the chosen potentials The model additionally stores auxiliary variables used as secondary output data These variables take the following form The first bracketed term is again for the global auxiliary variables and the following brack eted terms indicates each potential s variables In the event of more than one potential the first total inelastic strain will be stored in addition to each inelastic deformation component If interactions are present the hardening variable evolutions will take the form h A m o vi H w H where A is the plasticity or viscoplasticity multiplier for the i th potential v is the cumulated inelastic strain equivalent and H are the associated forces for the potential 7 Note that the evolution equations will normally only be written in terms of the associated force and thus one can immediately extend these models to include state coupling
14. the option of having simply a ratio of f over R which could be used to apply the isotropic hardening law as a viscosity hardening The default value of L is 1 and the user should note that only values of 1 and 0 make sense Example The following example is from rate_crit02 inp in test Volume_test INP behavior gen_evp xelasticity isotropic young 2 e9 poisson 0 4 potential gen_evp ev criterion ratio L 1 0 flow norton A 1000 n 2 isotropic by_point sigeg evcum 60 e6 0 1 e8 2 1 e8 200 return Z set Non amp structure an 13 25 13 26 lt CRITERION gt lt CRITERION gt tensile mises Description This is a criterion which acts as a von Mises yield if the trace of the effective stress e g J X is greater than zero If it is less than zero the criterion will never yield 0 5 Ter Ki l R 0 fer Tr a gt 0 otherwise 6 Z set Non linear material amp structure analysis suite lt CRITERION gt lt CRITERION gt tresca Description The plasticity threshold in Tresca criterion is linked to the maximum shear stress and is given by 1 a 93 The complete equation of the criterion can be written as f max lo oj os 0 Aj Z set Non linear material amp structure analysis suite 13 27 lt CRITERION gt 13 28 lt CRITERION gt unsym Description This criterion models the equivalent stress and deformation
15. 1 1 1 1 0 1 1 1 1 3 0 1 1 1 1 1 1 1 0 1 1 176 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1311 O 1 1 1 1 1 0 1 1 1 1 O 1 1 1 1 0 1 1 3 HCP basal slip systems with 2 hardening coefficients 1 2 1 0 L0 0 0 1 2 1 1 0 0 0 0 1 1 1 2 0 0 00 1 prismatic 3 HCP second order prismatic systems with 2 hardening coefficients 1 0 1 0 1 2 1 0 0 1 1 0 2 1 1 0 1 1 00 CL1 1 2 0 ES rrr EA pyramidal0 6 pyramidal systems requires c_over_a to be entered 1 0 1 1 1 2 1 0 CO 1 1 1 2 1 1 0 1 1 O 1 1 1 2 0 1 O 1 1 1 2 1 0 9 1 1 1 2 1 1 0 1 1 0 1 1 1 2 0 continued Z set Non linear material amp structure analysis suite lt CRYSTAL_ORIENTATION gt 12 additional pyramidal systems requires c_over_a to be entered pyramidal1 1 2 1 1 3 1 3 1 1 C 1 1 1 1 1 1 2 1 2 1 1 1 i 0 0 1 1 1 1 0 0 1 1 2 3 1 2 3 2 1 3 2 1 3 1 Co Co 6 1 0 0 1 1 1 1 0 0 1 3 1 3 2 3 2 3 1 3 1 3 1 1 i i 1 1 1 1 1 1 1 0 1 1 1 2 0 1 1 1 2 1 1 1 2 1 1 3 1 1 pyramidalPil o 1 1 2 1 O 1 1 1 o 1 2 0 1 2 1 1 1 gt 3 1 1 1 0 Co oi 0 1 3 1 2 1 0 1 1 0 1 o 1 2 0 1 2 1 1 1 1 0 1 1 1 pyramidalPi2 2 1 3
16. Secondary Models 11 1 11 2 Z set Non linear material amp structure analysis suite behavior aging behavior aging Description This behavior is a viscoplastic model intended for modeling the thermally activated aging behavior of aluminum for applications such as cast Al cylinder heads in TMF loading The model includes classical combined nonlinear isotropic kinematic hardening only 2 kinematic terms are now allowed The model is programmed for both Runge Kutta and theta method implicit integration and for both general FEA and simulation modes The model has a standard additive strain decomposition with elastic viscoplastic and thermal strain parts Eel Eto Eth Eup The stress is computed from linear elasticity depending on the elastic matrix component selected rom Der e There is an integrated aging parameter which will cause aging effects on the hardening This parameter evolves from 0 unaged to 1 fully aged with a saturating nonlinear form ice and the coefficient 7 is the time constant for saturation of the aging We expect that the two coefficients C and 7 are functions of temperature to be able to handle overheating effects The hardening parameters are computed with aging effects as follows X Cia Xo 1 3C20 R Ro QQ e 0 0R The remainder of the model is classical viscoplasticity f J s X X2 R nol gt F q a Evp n Qi
17. fe f fe B n 1 a Bm ab o Ba AA Rate equations ea to An th OF 1 m P 0 1 gt b o ar boog p f A 1 f 1 n a B Syntax In the porous_plastic behavior f is calculated from f using the coefficient mechanism Z set Non linear material amp structure analysis suite xkkbehavior becker_needleman behavior becker_needleman modifier kelasticity lt ELASTICITY gt thermal_strain lt THERMAL_STRAIN gt x model_coef coefs qi q2 f_c ff e_dotO b sig0 m eps0 C Example Here is an example using coefficients from the original paper x behavior becker_needleman kelasticity isotropic young 1865 67 poisson 0 3 xmodel_coef ql 2 38 q2 0 748 eps0 0 0125 e_dotO 1 e 3 same as loading rate sig0 1 0 b 1 0 1 isotropic 0 kinematic TC 0 15 fot 0 25 m 0 02 0 002 C 1 return Z set Non amp structure a behavior cast_iron behavior cast iron Description This behavior is a combined damage viscoplasticity model to simulate the nonlinear and fatigue behavior of cast iron materials It allows significant flexibility in terms of the combi nation of damage and plastic mechanisms hardening models and driving force for damage There are quite a number of coefficients to manipulate however A description of how to attack this problem is given in the Theory manual This model uses a scalar damage v
18. integration rotation initialize_variable The sub commands for material pertain to the behavior defined in the current ma terial file only Note that the function of this command is somewhat different than the equivalently named command used in the Z set inp file A last comment Always Verify Your Materials The behaviors supplied in the Z mat library are compatible with the simulation program so there is no excuse to not validate the material behavior with a given set of coefficients Z set Non linear material amp structure analysis suite Interface files x material integration integration Description This option determines the local integration method for a material behavior Syntax integration method params The allowable methods are summarized in the table below CODE DESCRIPTION runge_kutta explicit Runge Kutta integration with automatic time step ping based on integration error theta_method_a implicit generalized midpoint integration this method nor mally supplies the best tangent matrix theta_auto_a automatic time stepping in the implicit 06 method runge kutta The Runge Kutta method implements a second order explicit integration with automatic time stepping Variables are normalized to allow varied variable magnitudes in stiff sets of equations The method takes two real parameters These are the convergence criteria followed by a minimum value for n
19. ulation module e Developer handbook to see how to make simulation compatible models including ZebFront Z set Non amp structure an 15 3 x simulate 15 4 simulate Description This command marks the beginning of a simulator calculation definition The Z set program in simulation mode S switch will search this command and interpret all the sub commands until the next level command is reached More than one simulation block may be included in the input file which are accessed using the N lt num gt command line option Syntax The simulation accepts the following syntax for the problem definition x x x simulate test test_name x x model model definition solver solver type_name solver options return The definition of a test is used to specify particular tests to simulate The tests will be run through in the order of their appearance using the default output file prefix of test_name The test test_name is required In each test different loading conditions output models etc may be defined See the following pages for these commands and their syntax Options model and solver are available as a means to change the default model definition and the default solver method It can be a great convenience to define these at the x x level in simulations where there are many tests of the same material The command syntax for model is the same as in the test secti
20. xm c xh xm Y 9 i o o t replace xh by xe replace xh by xr replace all x s replace xh by xc t Syntax The nelder mead optimizer has a number of adjustable parameters which can be set in the xxxconvergence section These are summarized below tolerance Minimal relative difference between the highest and lowest vertex for conver gence This is exclusive with min The algorithm stops when the last change in objective function is fractionally smaller than tolerance It is the default stopping criterion with a value of 1 e 9 size_optimum Minimal value of the objective function below which the search stops This is exclusive with tolerance It is not the default stopping criterion Default value is 1 e 5 size_degeneration Minimal relative value below which simplex is considered as degener ate ie vertices are no more linearly independent Default value is 1 e 6 16 28 Z set Non linear material g amp structure analysis suite xoptimize nelder mead length Initial perturbation magnitude as a factor times the initial value It is the charac teristic length scale It is used to construct the initial simplex from one starting point Default value is 1 It is a rather sensitive parameter and one should play with it if the simplex does not start the search properly iter Maximum function evaluations before terminating Default value is 100 max_restart
21. Example There is an example file in the test database directory ZebFront_test INP named aging inp These tests are normally deprecated compared to the equivalent but more general capa bility in the tests Simulator test INP aging tmf Z set Non li amp structure an Description behavior aniso damage behavior aniso_ damage This model implements an anisotropic damage model for fibrous ceramic composites The damage is described by a number of scalar and tensorial variables as input by the user The effect of closure strains and non symmetric tension compression behavior is handled as well The stress is calculated using the following definition of effective modulus o Cp Y CP e e where Co is the undamaged elasticity tensor CW is the damage modification of the elasticity and is a user loadable closure strain Each scalar and tensorial variable will contribute a term to the summation of CF Syntax behavior aniso_damage modifier CQ ELASTICITY thermal_strain THERMAL_STRAIN damage ANISOTROPIC_DAMAGE closure tl t6 scalar_interaction full identity Stored Variables prefix size description default eto T 2 strain tensor yes sig T 2 Cauchy stress yes d i S scalar damage variables yes D T 2 tensor damage variable yes Example The following example shows the input format for a material with two scalar variables behavior aniso
22. If the name is the base name of a tensorial or vector set of variables the limit will be placed on all the components of that variable e g if sig is given all the stress components will be used vall real value for the limit of the last given variable name Limit names values must be given in pairs Example Here is a small typical use for viscoplasticity type problems The time step will be limited both in the increment of viscoplastic strain evcum to changes less than 0 1 and stress component changes to less that 15 MPa All components of the stress tensor will be checked to be within the limits x x automatic_time limit evcum 1 e 3 sig 15 divergence 2 0 security 1 2 Z set Non linear material amp structure analysis suite Interface files x behavior behavior Description This command is more fully described in the chapter Material Models and Material Compo nents This command lets the user include in line a material definition in the Z mat interface file If this command is not used the material file will be sought using the file or standard sub commands of material Be aware of the following items when defining a Z mat behavior e Behavior definitions have the external parameter value temperature available always for coefficient definitions thermal strains and similar coefficient taking material objects With ABAQUS additional field variables can be defined using the field options
23. J C Nagtegaal On the Implementation of Inelastic Constitutive Equations with Special Reference to Large Deformation Problems Comp Meth Applied Mech Eng 33 469 484 1982 J A Nelder and R Mead A simplex method for function minimization Computer Journal 7 308 313 1965 P Pilvin The Contribution of Micromechanical Approaches to the Modelling of Inelastic Behavior of Polycrystals Fourth International Conference on Biaxial Multiaxial Fatigue May 31 June 3 Paris France 1994 P Pilvin Sidolo2 3 Manuel utilisateur Centre des Mat riaux Ecole des Mines de Paris France 1996 J C Simo and T J R Hughes Computational Inelasticity Springer Verlag New York 1998 K Schittkowski QLD A FORTRAN Code for Quadratic Programming User s Guide Mathematisches Institut Universit at Bayreuth Germany 1986 J L Zhou C Lawrence and A L Tits User s Guide for CFSQP Version 2 5 Inst for System Research T R 94 16r1 Univ of Maryland College Park MD 20742 1997 Z set Non linear material amp structure analysis suite Z set Non linear material amp structure analysis suite Chapter 19 Index 19 1 Z set Non linear material 19 2 amp structure analysis suite Index optimize compare 16 10 compare i_file_file 16 14 compare i_func_file 16 15 compare t_file_file 16 12 compare g_file_file 16 13 comparison constraint 16 17 const
24. Z set Non li 13 86 amp structure an lt POTENTIAL gt lt POTENTIAL gt suvic Description This is the SUVIC model which applies well to ductile rock material such as sodium chloride materials over long term creep loading There are isotropic and kinematic hardenings with static recovery as well as evolution in the creep law and changing saturation values for the hardening variables cs fe B H E i a K Ko An n ae B J B BIN ai ifa 3i ae cali 2 tale ey i i1 E PS NIE iii E B AQ M C A1 42 2 R Agr M C A3 A4 K Ask Mg C A5 A6 BL Bp 0 09 R R In A w0 KW J 0 n A v0 _ Bl R A A n 13 Z set Non linear material amp structure analysis suite 13 87 lt POTENTIAL gt Example behavior gen_evp xelasticity isotropic young 18900 poisson 0 25 potential salt ev criterion mises flow norton_k_variable n 4 0 kinematic nonlinear short range A1 6400 0 Bp equivalence Bpa0v kinematic nonlinear long range A1 40 0 Bp Bpalv isotropic non_linear_recovery A 1800 0 RO 0 0 Rp Rp K non_linear_recovery RO 0 04 A 260 0 Rp Kp parameters A 6 00e 7 N 4 0 must be duplicated vdot0 1 e 13 sig0 4 63 RO 1 38 BO1 0 83 B02 1 25 m 0 81 return 13 88 Z set N amp structur lt POTENTIAL gt lt POTENTIAL gt 2M1C Description The potential of type mises_2m1c exists
25. min 1 max 50 c 9 16 25 xoptimize shell 16 26 shell Description The shell option allows to declare external system commands to be executed before the evaluation of the function to be optimized These jobs are done using a posix system call Use the zrun command if the job is a Z set calculation using Zrun because it will not launch a whole new executable Example xkkshell Zmat fg testi gt amp dev null abaqus post job test1 input test1 jnl gt amp dev null awk print 3 4 100 0 testi test gt result One can also make up a script with the shell commands for a bit more flexibility x shell RUN From EXAMPLES ZBB Inverse aba thermal Levenberg RUN bin sh Zmat fg nt4xx28c PLT nt4xx28c 2 gt amp 1 gt dev null cat nt4xx28c test exit 0 x xoptimize ZTrun run Description The zrun option runs a sub process of Z set to simulate some part of the model s as part of the optimzation comparison scheme All zrun statements will be run after all the shel1 entries Example Note that for simulation running with Q suppresses the screen output of the simulation so one can watch just the optimization progression zrun Zrun S Q testl Z set Non linear material amp structure analysis suite 16 27 optimize nelder mead optimize nelder_mead Description The nelder mead or simplex method Neld65 is an order 0
26. objects criterion flow kinematics and an isotropic hardening This behavior actually allows for more than one potential instance so very complex behaviors are possible behavior gen_evp kelasticity isotropic young 260000 poisson 0 3 potential associated ev criterion mises flow norton n 7 0 K 400 kinematic linear C 15000 0 kinematic nonlinear C 6000 0 D 100 0 isotropic nonlinear RO 130 0 Q 20 0 b 500 0 kkretUIN Another important thing to notice here is the coefficient C is entered after each kinematic entry These coefficients are distinct in the behavior because they belong strictly to the kinematic objects This totally illuminates the possible conflicts inherent with hard coding the model to have for example C1 and C2 9 4 Z set Non linear material amp structure analysis suite Grad Flux Grad Flux The compatibility of material behaviors with the element is determined dynamically based on their gradient or primal and flux dual variables These can also be thought of as the material input output combination These variables are also observable state variables and observable associated forces Some of the primal dual variable combinations in Z mat are as follows CODE DESCRIPTION eto sig small deformation e a F sig updated Lagrangian large strain F o dT q thermal analysis dc J diffusion analysis The process relative to element integration is shown schematically be
27. structure an erial e 11 13 kkkbehavior finite strain crystal 11 14 Syntax x behavior finite_strain_crystal kelasticity lt ELASTICITY gt f low isotropic korientati x model_coe C COEFFICI D COEFFICI lt FLOW gt lt ISOTROPIC_HARDENING gt on lt CRYSTAL_ORIENTATION gt f ENT ENT Stored Variables prefix size description default F UT 2 deformation gradient yes sig T 2 total Cauchy stress yes Fp UT 2 plastic deformation gradient yes gamma V resolved shear strains yes alpha V back strains on slip system yes crss V current resolved shear stress yes xkkbehavior matmod behavior matmod Description This model is an implementation of the MATMOD equations due to Miller Mil176 The model accounts for isotropic kinematic hardening and presents a particular form of temperature dependence in the material coefficients Me AN V3 s R An D 2 J o R O exp ozer In 85m i for T lt 0 6Tm 0 exp Q kT for T gt 0 6T Em BO sn R H in B0 sinh A R E D Hal Ein Co IR 42 41 D H2Co BO sinh A2D Syntax kkbehavior matmod thermal_strain lt THERMAL_STRAIN gt elasticity lt ELASTICITY gt x model_coef Stored Variables prefix size description default eto T 2 total strain yes sig T 2 Cauchy stress yes ein T 2 inelastic strain tensor yes D S isotropic d
28. the yield function has 16 parameters To ensure convexity and derivability the following conditions are required a gt 1 and b gt 2 No restriction applies to the ES coefficients in particular they can be negative The particular case where L L and a b b corresponds to the yield function of Karafillis and Boyce 1993 and the case where a 1 corresponds to the yield function of Barlat et al 1991 Finally when a 1 and c 1 it amounts to von Mises yield function if bt 2 or 4 and to Tresca yield function if b 1 or 00 If c 1 the resulting yield function is isotropic as it only depends on the eigenvalues of g Example porous_potential porous_criterion modified_rousselier isotropic function flow plasticity shear_anisotropy bron a 2 2 alpha 0 60 bi 10 3 c11 0 58 c12 1 35 c13 1 14 c14 1 23 c15 1 35 c16 1 57 b2 13 1 c21 2 07 c22 0 20 c23 0 33 c24 0 85 c25 1 31 c26 0 59 13 16 Z set Non linear material d amp structure analysis suite lt CRITERION gt lt CRITERION gt cast_iron Description This criterion provides assymetric tension compression behavior which is suggested for cast iron modeling Hjel94 Jose95 In general this model would be used with behavior gen_evp potential gen_evp2 and includes one or more non_symmetric kinematic hardening terms and possibly others as well You can have either isotropic hardening scaling both the compressive and tensile behavior wit
29. 0 n 10 0 kinematic nonlinear_phi C 50000 0 D 1000 0 phi 0 0 delta 0 0 Xbar 6 0 isotropic nonlinear RO 382 0 Z set Non linear material 13 81 amp structure analysis suite lt POTENTIAL gt Q 5 6 b 2429 0 interaction slip hi 1 0 h2 1 2 h3 1 1 interaction iso ev cu h 0 2 return 13 82 Z set Non linear material amp structure analysis suite lt POTENTIAL gt lt POTENTIAL gt gen evp Description The potential object of type gen_evp serves as the basic type for classical plasticity and viscoplasticity models with both isotropic variable and an arbitrary number of kinematic hardening variables c f Lema85 The potential will accept a wide variety of criterion types associated and non associated as well as a variety of flow rules plastic and viscoplastic The dissipation potential for this model is written generally Q fer p o Xy O R 200 X If there are hardening variables they will be stored in the following order h i a2 an r where the tensorial variables are the kinematic internal variables analogue to an offset strain and r is an internal variable modeling the isotropic expansion or contraction of the yield domain analogue to an equivalent strain Syntax The syntax understood by this potential is summarized below potential gen_evp name flow lt FLOW gt criterion lt CRITERION gt kinematic lt KINEMATIC
30. 0 D 100 0 isotropic constant RO 100 e 00 return For this material file the output of the Zpreload program shows the material variables and their associated ABAQUS output variables Flux Name Z set Non linea aterial 3 17 amp structure analysis suite Example Sigil sig22 sig33 sigi2 sig23 sig31 Grad Name etol1l eto22 eto33 etol2 eto23 eto31 var_int Name eel11 sdv1 eel22 sdv2 eel33 sdv3 eel12 sdv4 ee123 sdv5 eel31 sdv6 evcum sdv7 al111 sdv8 al122 sdv9 al133 sdv10 al112 sdv11 al123 sdv12 al131 sdv13 var_aux Name evil1 sdv14 evi22 sdv15 evi33 sdv16 evil2 sdvi7 evi23 sdv18 evi31 sdv19 amp structure a 3 18 Z set Non lin Post calculations Post calculations Description With version 8 3 all the Z set post computations can be used with ABAQUS results files and are in fact used for each of the Z mat validation examples It is sufficient to use the data_source selection to choose an import format for the results files The post processing environment contains a large number of very convenient curve extraction routines which can be used to automate analysis post processing There are also a large number of both global and local post computations which can be applied for failure analysis etc The post computations are now part of the Z mat bundle Example An example from the Z mat tests follows generating an ASCII datafile with the stress strain behavior as com
31. 0 and O otherwise Hx Heaviside of its parameter times its parameter Equal to x for x gt 0 and 0 otherwise Example function load_tab sin 6 28319 time kkelasticity young function 2 e6 100 temperature 2 temperature 2 poisson 0 3 Z set Non amp structure an Functions Z set Non linear material 17 4 amp structure analysis suite Environment Variables Environment Variables The environment variables are used to personalize the Z set program for individual users and maintain a self contained project structure The function extends as well to manage multi architecture sites thereby allowing the transparent use of the program over a diverse network The currently used environment variables are summarized as CODE DESCRIPTION Z7PATH path to the head Z set s directory structure Z7_MAX_NB_DOF number of DOFs above which disk storage is used Z7_TMP_DIR path for the temporary files if needed Z7_LICENSE path to a license file if not stored in Z7PATH 1ib Zebulon License Z7PATH variable which indicates the location of the Z set distribution This variable allows easy switching to different distributions It also is a cause of much difficulty with users if not configured correctly cd usr local Z8 Sept 1999 setenv Z7PATH pwd source lib Z7_cshrc Z7MAX_NB_DOF This sets the maximum number of degrees of freedom before the global matrix is stored on disk Because disk storage is not expen
32. 2 2 1 1 3 2 1 2 1 1 2 1 1 1 2 3 1 2 2 1 1 1 3 1 3 2 3 2 L 1 2 2 2 2 2 1 1 1 1 1 2 2 1 1 1 1 twinning 6 twinning systems in hexagonal crystals requires c_over_a to be entered 2 O 1 1 1 0 0 1 1 1 1 1 1 0 1 2 0 2 1 Co 1 o 1 1 1 1 1 1 0 2 1 1 1 2 0 2 1 1 0 1 O 1 1 1 0 1 1 1 continued 13 33 Non linear material amp structure analysis suite Z set lt CRYSTAL_ORIENTATION gt bec112 12 additional slip systems for bcc crystals These also apply to Shockley partial dislocations in fcc crystals MOS E IO TE AE MES ES ES NOS IO ERES Rh RNRRFRANPPRPRNBRR SSN climb_cfc 1 1 1 1 2 1 1 1 1 4 Ey EY AY AY Y Y LY Y d Y L 4 climb directions on octahedral planes 1 1 J 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 climb_cubic 3 climb directions on cubic planes ES OA O 1 0 0 0 0 1 L y Ey climb_cubic1 The first of the cubic climb directions 1 o 0 L1 0 0 climb_cubic2 The second of the cubic climb directions Co 1 OF O 1 0 climb_cubic3 The third of the cubic climb directions Co o 1 L0 O 1 plane Enter in a single slip system The first system in octahedral could be entered in as kpotential plane 1 1 1 1 0 1 13 34 Z set Non linear material amp structure a
33. 2 33 3 23 4 31 5 12 6 Voigt For instance a Voigt coefficient ceg becomes c44 or y1212 in Zmat Zebulon The matrix forms are given below isotropic The isotropic model allows several methods of entering the coefficients for convenience The primary method gives the Young s modulus E and Poisson coefficient v which correspond to the names young and poisson respectively E P vE 1 v 1 2v 1 v Dij ij An alternate definition defines the shear modulus G or u and the bulk modulus K or K These correspond to the coefficient names G or mu and K or kappa Z set Non linear material 13 9 amp structure analysis suite lt COEFFICIENT_MATRIX gt transverse Transverse isotropy has two directions which are equivalent There are two ways to specify transverse elasticity parameters Elasticity modules Direction 1 is the longitudinal one and directions 2 and 3 are the two transverse ones The elasticity is specified with 5 classical parameters El Et nult nutt and Git They define the Hooke relation such as en a et et o o 0 fon E22 7 nuit 0 0 0 022 E33 H 0 0 0 033 E23 7 Hut 0 0 023 E13 sym JCH 0 013 E12 aah 012 An old parameter named glt instead of Git is defined as 012 glt 12 whereas Git is defined as 0129 2 Glt 12 This old parameter is still available for compatibility with old data sets Matrix coefficients The program allows the user to specify which terms
34. 4 Z set No amp structure Zsamcef interface point of the FE mesh which will result in huge ouput files and may dramatically slow down the calculation automatic_time This command may be used in conjunction with the SAMCEF auto matic time step procedure based upon material integration error To enable this option the following parameters must be given as arguments of the SUB command in the SAMCEF input file SUB VISC 1 activates material automatic time step PRCV 1 material allowable error note that default value of 0 1 is not compatible with the Z mat mechanism SREF 1 material ref norm default value limit namei vmaxi This command indicates that during a loading increment the increase of the namei material variable should not be greater than a given value of vmaxi Several limit commands acting on different material variables may be added if necessary The material error returned by Z mat to SAMCEF will be calculated as follows ERRLOC max en 1 UMALi where Av is the increase of variable number 7 and the max is taken over all material variables v specified by a limit command This ERRLOC value will then be compared by SAMCEF to the PRCV parameter of the SUB command in order to estimate the appropriate time step size Note that PRCV should always be set to 1 0 in this particular context save_tensor tname save_scalar sname Output of user behavior material variables to the SAMCEF r
35. 4 may be more conservative fmin minimum function value for convergence Default is 0 0001 gmin minimum norm of the gradient of the objective function for convergence Default is l e 8 stepmini minimum step at each iteration Default is 0 00001 There is a possible false stopping of the optimizer if lambda is taken very large and stepmini very small because lambda acts as a move limit on the parameter change Example This following is a complete optimization input using this method x optimize levenberg_marquardt files plast sim shell Zrun S plast3 2 gt amp 1 gt dev null values cl 1000 min 200 max 15000 cnl 140000 min 50000 max 200000 dnl 100 min 50 max 2000 ro 260 min 50 max 500 q 200 min 20 max 500 b 5 min 2 max 20 Z set Non linear material amp structure analysis suite optimize levenberg mar convergence perturb 0 005 lambda0 5 lambda_max 1 e 08 iter 100 nu 5 fmin 0 00001 gmin 0 00001 Compare t_file_file plast3 test 1 3 data_plast3 1 3 weight 1 return 16 32 Z set Non linear material E amp structure analysis suite xoptimize evolution optimize evolution Description This section describes indeed the options available for the evolution type optimizer engine is used In that case an evolutionary or genetic algorithm is used for the optimization Evolution methods search the space of variables using random jumps Even though such j
36. 600 compare g_file_file g_file_file g_file_file g_file_file g_file_file g_file_file return tenx2 test tenx3 test min min min min min min 1 1 tx6x2x6 test 1 tx6x3x4 test 1 cr410 test frlx3 test 1 1 600 1 2 200 3 3 0 5 NNNNN NN max max max max max max 5000 20 5000 75 800 5000 EXP tenx2 exp EXP tenx3 exp EXP tx6x2x6 exp EXP tx6x3x4 exp EXP cr410 exp EXP fr1x3 exp 1 1 1 1 1 1 x xoptimize First is the template file for Bod AS 16 9 xoptimize COMpare compare Description The option compare constructs the function to be minimized Four comparisons are possible It is always possible to indicate a relative weight adding weight vweight where vweight is the relative weight The function to the minimized by the optimizer is given by PEZ A i where F is the function constructed by a compare instruction Example In this example x and y are function arguments and a b c are optimization variables optimize levenberg_marquardt function f1 a x 2 b x forty compare i_func_file f1 1 2 3 teri dat k values a 1 min 10 max 10 b 1 min 10 max 10 c 1 min 10 max 10 convergence return Note It is recommanded to normalize the functions involved in the optimization F and the con straints Note If one exclusively wishes to minimize a function f sub
37. 800 D1 600 min 5 max 5000 An example of the levenberg best file is best objective function 6 050340e 01 best values n 6 101396e 00 K 1 314714e 03 n2 5 967421e 01 K2 5 244540e 02 C1 3 100267e 02 D1 6 302586e 02 16 23 xoptimize value x xinit_from file init from file Description The option init_from_file filename enables initiating the optimization from the point written in filename This can be handy in some cases where one does not wish to change the inp file The initial values of the design variables are given as real numbers The order is the order of the variables cf note above this is the order of the msg and tra files When this option is used the syntax for the rest of the value is unchanged The value that follows the variable name is no longer the starting value since the starting value is read in filename but it is used as scaling variable Therefore the option init_from file filename permits separated initial and reference values 16 24 Z set Non linear material amp structure analysis suite x xoptimize x value format format Description The option format controls the output format of the variables declared as x in the tmpl files It can be important to output lots of decimals to reduce numerical noise for example in order to have accurate gradient calculation Example x value A 10 min 1 format 30 15e init_from_file init b 2
38. 9 fel Der Eel Yia mex Y Vas i nea Gee 0 Ymar lt Yo Z set Non linear material amp structure analysis suite 13 35 lt DAMAGE gt plastic This model integrates the damage as a function of the inelastic strain equivalent in the following manner d p Y so For the i th component of inelastic deformation Note that is calculated as 1 2 Pi ES deps xcreep Classical viscoplastic damage using the Hayhurst stress function The damage is calculated as x a ado BJ 1 a B J The rate of damage production will be calculated as x a k A EAS ee i o a a with Jo the maximum principle stress J the trace of the stress tensor and Jz the second invariant of the deviator 3s s 2 Coupling with plasticity Applying simply the damage mechanisms to a gen_evp plasticity model will only couple the stress calculation in the potentials and modify the elastic modulus For the hardening mechanisms to be coupled to the damage rate several additional changes must be made to the syntax Addition of one or more plasticity potentials to a behavior with damage causes the fol lowing equations to be used for the inelastic strain rate o D d o l djo to 84 1 d An h Am w The default situation interfacing damage to the potential only involves use of the effective stress in the place of the actual weakened stress This leads to the following set of evolution equat
39. L i i i i i i 600 500 400 300 200 100 0 100 201 0 005 0 004 0 003 0 002 0 001 0 001 0 002 0 003 0 004 0 0C sig11 eto22 13 42 20N lt ELASTICITY gt lt ELASTICITY gt Description An ELASTICITY behavior object is actually just an alias for COEFFICIENT_MATRIX see page 13 9 The class is frequently defined in the behavior descriptions however to further accen tuate its task in the scheme of the constitutive relation Virtually every location where this keyword is used a hypoelastic relation is employed o Da e Noting however that the total internal strain e may be calculated in some manner which extends it from the normal limitations of hypoelasticity e g the finite strain material trans formations The matrix Da is the elasticity matrix defined by the ELASTICITY class and can take many forms and vary according to any external parameter Z set Non linear material amp structure analysis suite 13 43 lt FLOW gt 13 44 lt FLOW gt Description This object class defines the model for inelastic flow in plastic and viscoplastic models and potentials Syntax The syntax to specify a flow object will consist of giving the keyword for a particular flow desired followed by a list of appropriate coefficients which are dependent on the model chosen The flow type may be chosen among the following laws CODE DESCRIPTION norton Norton power law hyperbolic hy
40. No T P no The spectrum is defined by the following form Z set Non linear material amp structure analysis suite 10 9 x behavior viscoelastic_s t spectrum limit double n1 double n2 double nt interger nc COEFFICIENT n0 COEFFICIENT See the figure for the meaning of nt nc and n0 nl and n2 can be read in the material file n1 and n2 or calculated such as u n1 gt limit and pu n2 lt limit Note By default limit is equal to 1 e 4 and nt to 30 The option viscous_effects defined the viscous effects tensor Cp x viscous_effects x1rt COEFFICIENT xlrc COEFFICIENT Cr is defined such as for i equal 1 to 3 Cr i i lrt Salt i for i equal 4 to 6 Cprli i lree So i i and if i j for i and j equal 1 to 3 isotropic condition Cr i j lrn So i j with Irn Irt x So 1 1 lre So 2 2 So 1 2 Finally the option reversible_asymptote is used to define the non linear funtion g c 10 10 Z set Non linear material amp structure analysis suite behavior viscoelastic_s reversible_asymptote beta COEFFICIENT p COEFFICIENT glo 1 beta y o Cp 0 P Remark beta 0 is equivalent to a classical linear assymptote Note Another definition of the asymptote plastic_asymptote is also implemented but not documented here because still under development Stored Variables The internal variables stored for
41. Non linear material j amp structure analysis suite simulate test yield surface vield_surface Description This option is used to create an ASCII file with the yield surface data at a load segment start or end time Any number of yield surfaces may be given for a single test The output files contain a list of the entire flux variable values for the surface taken in order followed by the angle Syntax The yield surfaces to output are defined in the following manner kyield_surface output_file name time time0 timel time2 criterion num potential num component compl comp2 degrees degrees angles angleO anglel angle2 factor factor eps eps rate rate0 ratel rate2 find_offset xoffset offset values time A list of one or more real values time0 timel time2 to define the time at which the yield surface is evaluated The times can be any time from 0 0 onward In the event that multiple times are given the surface scans will be given in the same file seperated by two blank lines criterion This gives the criterion name which will be used for the surface They are arbitrary values to match with zero or the rate if given potential A gen_evp behavior potential which will be used for the criterion By default all potentials input will be used to establish the material criteria for flow component Two strain names for the two flux components which are scanned An exam
42. Repeated experiments which merely provide a slight variation in response should be avoided while complex experiments with many interacting effects should be emphasized 16 6 x xoptimize Recommendations Some comments follow which are purely the personal preferences of the author but can probably help ahead of time with the management of typical real life optimization projects The fact of life is that optimization involves many trials of different models simulations and overall rapid iteration towards the solution both by the code and by the user Also it is relatively easy to find oneself in a situation where when lightly tweaking some parameters the last best solution gets lost It is really important to maintain control of the changes in input files models coefficients etc in order to safeguard against loosing valuable time Some hints are therefore e Use a hierarchical structure for different stages in the analysis and keep the number of files in each directory very specific to one task That is if you want to modify the initial values dramatically or continue from a previous solution make a new directory and copy the files before running A typical directory structure could be BasicIdentification exp_files trial1 Makefile simulation inp levenberg inp simplex inp trial2 Makefile simulation inp levenberg inp simplex inp continue2 Makefile simulation inp levenberg inp and so on
43. The number of times the loading segment will be run in the event of the cycle keyword loading table a tabular form which describes the loading for the simulation The table should have time as the first column followed by an appropriate list of imposed variables For tensor loading with fem behaviors the size of the behavior dimension will be determined from the number of components given Thus giving 4 variables in small deformation will give 2D behavior while 6 gives 3D Note that some models like the crystal potentials require 3D and thus 6 componnets to be given External parameters are imposed at this level as well using the prefixed nameing param var_name Note initial values are required rate this option is used for rate loading in the generalized simulator only i e not for fem behaviors The command allows simple rate loading to be defined for a given duration with the for keyword or with breakpoints which are to be determined with stop_at segment a segment of loading The optional keyword rate indicates that values are in rate form file indicates that the loading table will be given in the external ASCII file with name given by filename The syntax is exactly that desribed by loading table above Note if you use FEM output from a curve option the leading pound sign must be removed from the variable list 15 10 Z set Non linear material A amp structure analysis suite x x simulate xtest x xload
44. Z set modules This is because behaviors are a set of constitutive equations which get built from fundamental building bricks of sub models There is widespread re use of all these bricks between different behavior models It is therefore necessary to adjust our input syntax or at least documentation of it to allow for more flexibility Classes The most important concept for this chapter is the notion of a class of permissible options of which the user will choose one or more objects from that class in the material definition A class is an abstract notion of basic functionality and will henceforth be denoted by the following convention EXAMPLE_CLASS indicating that an object of type EXAMPLE_CLASS is permitted In the handbook one will find another section with heading EXAMPLE_CLASS which describes the different types allowable for the class An example is an ELASTICITY class which handles the calculation of stress from a strain usually employing a 4th order tensor of various modulus coefficients Because of this very general function many behavior models allow for an ELASTICITY instance In turn the elasticity class has many possible types which one can select to fill in an elasticity object isotropic orthotropic etc kelasticity lt ELASTICITY gt The keyword elasticity used here is in fact specific to the behavior model While we frequently see the same keyword indicating classes between behaviors this is not nec
45. a n n K K df_0 value d d1_0 value continued this behavior is Z set specific and therefore does not apply for Z mat for other codes Caliez M Approche locale pour la simulation de l caillage des barri res thermiques EBPVD Ph D thesis Ecole Nationale Sup rieure des Mines de Paris 2001 Z set Non linear material amp structure analysis suite u um Amax 16 0 7 T 14 0 12 0 10 0 8 0 F 6 0 4 0 F 2 0 F 0 0 2 0 i i i i 0 0 1 0 2 0 3 0 4 0 5 0 time s 0 0 1 0 2 0 3 0 4 0 5 0 time s T MPa T MPa 125 100 75 50 25 25 50 75 100 125 0 0 125 100 75 t 50 F 25 j 0 25 50 75 100 125 i i i i i i i 2 0 00 20 4 0 60 8 0 10 0 12 0 14 0 16 0 behavior chaboche debonding 3 0 4 0 5 0 time s u um Figure 3 Example in two dimensions of the evolution of the cohesive traction as a function of the opening displacement for two different loading cases uy t with ur t 0 thick red curves and ur t with uy t 0 thin green curves Top left applied load u t Note for 2 lt t lt 4gs the applied loading becomes negative but the response uyy remains 0 because of an implicit non penetration condition Top right response T t Bottom right u t vs T t Example behavior chaboche_debonding sigmax 100 deltan 1 e 5 deltat 1 e 5 a
46. a diagonal matrix of independent coefficients These coefficients are named hil11 hillN with N being 4 for two dimensional problems and 6 for three dimensional There is no problem giving the complete 6 coefficients in a 2D problem however Example potential gen_evp ev flow norton n 4 0 K 500 criterion hill hilli 1 hill2 hil13 hil14 hil15 hil16 OPRON N N 13 18 Z set No amp structure lt CRITERION gt lt CRITERION gt karafillis boyce Description Also known as the K B criterion the karafillis boyce criterion was developed in 1993 at MIT This criterion is constructed by mixing two yield functions f1 and 2 As shown in the equations below 1 represents a yield locus located between the Von Mises yield locus and the Tresca yield locus and 2 varies from von Mises to a theoretical upper bound as m changes from 2 to oo 1 c p1 c2 2Y where 1 181 Sal S2 Sal S3 S1 gm 511 So 93 be lil Sal 1851 and S are the principal values of the isotropic plasticity equivalent IPE stress tensor as defined below Y is the average yield stress in uniaxial tension and L is a fourth order tensorial operator which introduces material anisotropy S L B Syntax The basic input sytax here is criterion karafillis_boyce coefficients c1 c2 c3 c4 c5 c6 Example criterion karafillis_boyce m 2 0 c 0 0 c1 1
47. always be compiled and linked before running ABAQUS and the end user will therefore not need any additional development tools in the same manner as running Z mat without the plugins Z set Non linear material amp structure analysis suite Current status Since the initial releases many improvements have been made for the ABAQUS interface of Z mat Some issues still remain however Some of the additions with this version include e Continuing streamlining and performance improvements The distributed domain solvers in ABAQUS at versions 6 5 and above are well supported and are proven to give decent scalability with Z mat e Support for ABAQUS Explicit is complete e Improved automatic time stepping e Improvements in the simulation optimization tools including support for finite strain problems e Compatibility with the rest of Z set making one installation for sites with Z set and Z mat e External disk storage for state variables This allows models with thousands of state variables e Finite strain has been improved including now the addition of hyperelastic and Hyper viscoelastic models e Direct reading of the fi1 format is greatly improved Abaqus ODB files can also be read and written by Zpost Zmaster and Zebulon This data file interface is without question the most robust of all the Z mat interfaces e All the Z mat test cases use Z post e Support for all Abaqus 6 x versions e Zebulon elements can be us
48. amp structure analysis suite 14 9 lt MODIFIER gt lt MODIFIER gt runge_jacobian Description This modifier activates a mixed explicit implicit integration scheme performed in 2 steps i integration of the set of material integrated variables V using an explicit runge kutta method pas runge kutta t At Ae V with t the time at the beginning of the step At the time increment and Ae the strain increment loading ii once known yo calculated during step i perform a single implicit iteration to obtain an evaluation of the consistent tangent matrix gne Ao calc_grad_f t At Ae yates AV OAe where calc_grad_f is the Jacobian calculation function called at each iteration of the implicit theta_method_a integration method This scheme then combines the benefits of the 2 base local integration methods e automatic sub stepping with error control runge_kutta efficient for stiff set of differ ential equations e good quality consistent tangent matrix as provided usually by one step implicit methods and can be used when theta_method_a fails to converge or in replacement of the previously described auto_step modifier Syntax material integration runge_kutta kkbehavior behavior name runge_jacobian controls theta theta return where the optional command theta theta allows to specify the 0 value used for the tangent matrix calculation of step ii 0 1 correspon
49. by N 1 F oN 2 vc yai i where N is the number of lines The optimization variables x should affect one of the two files fnamel or fname 2 Syntax ifile_file fnamel cl fname2 c2 weight vweight 16 14 Z set Non linear material i amp structure analysis suite x xoptimize compare i_func_file compare i_func file Description This comparison is similar to i_file_file except that a function will be evaluated for all the x values of the reference file and the values will be compared directly The function to be optimized is given by N 1 F In 2 a vitra u Syntax The following syntax is used here i_func file funame tj tin y name weight vweight funame is the name of a function defined under function flname is the name of a column file t 1 t n are the columns id s representing the n arguments of flname other than optimization variables that also can be arguments of the function y is the column of flname representing the function values associated with the n uplets t 1 t n Z set Non linear material 16 15 amp structure analysis suite x xkkoptimize xxxconstraint 16 16 constraint Description The constraint option allows to create constraints that relate the different variables Constraints are functions that need to be less than or equal to 0 When this option is used an OPTIMIZER need to be called that can handle c
50. common to the various Z mat interfaces and are described in the Z mat interface file section page 2 5 However some commands are not supported by the SAMCEF interface while others are specific to this port Hence the various commands allowed in the Zsamcef interface file are summarized hereafter Only options that are indeed specific to SAMCEF will be described in detail Syntax debug local_debug ip x automatic_time limit namel vmaxl limit namei vmaxi save_tensor tname save_scalar sname needs_temperature x material file fname integration rotation x initialize variable dim dim x xbehavior return debug This command indicates that debug output will be generated during MECANO execution Output will be stored in a file named fname msg where fname is the name of the Z mat interface file local_debug ip This subcommand restricts debug output to the integration point number ip given as ar gument ip is an integration point counter managed internally by Zsamcef incremented during the loop on the elements and resetted to zero at the beginning of each newton global iteration Note that the OVMAXX SAMCEF user subroutine doesn t provide any information on the element integration point number that could allow a more meaning ful selection mechanism By default debug output will be generated for all integration 6
51. damage variables yes d T 2 tensor damage variable yes Y T 2 driving force for tensorial damage yes evi T 2 inelastic strain tensor yes evcum S inelastic strain equivalent yes alpha 1 T 2 kinematic hardening variable yes Example behavior visco_aniso_damage effective_stress C0 orthotropic c11 154844 0 c22 154844 0 c33 203236 0 c12 54844 0 xkkbehavior visco_aniso c23 49357 0 c31 49357 0 c44 50000 0 0 5 b11 b12 c55 50000 0 c66 50000 0 HO orthotropic c11 0 5 c22 0 5 c33 0 15 c12 0 3 c23 0 1 c31 0 1 c44 0 4 c55 0 35 c66 0 35 flow norton n 12 0 K 250 0 isotropic nonlinear RO 240 0 Q 70 0 b 180 0 kinematic nonlinear X1 C orthotropic c11 15000 00 c12 0 0 c23 0 0 c31 0 0 c22 15000 00 c33 50000 00 c44 7500 00 0 5 b11 b12 c55 7500 00 c66 7500 00 kinematic nonlinear X2 C orthotropic c11 30000 00 c12 0 0 c23 0 0 c31 0 0 c22 30000 00 c33 100000 00 c44 15000 00 0 5 b11 b12 c55 15000 00 c66 15000 00 D diagonal 180 0 return 11 23 x behavior visco_aniso Z set Non linear material 11 24 amp structure analysis suite Chapter 12 Other Models 12 1 Z set Non linear material 12 2 amp structure analysis suite behavior coefficient_diffusion Description behavior coefficient di Diffusion behavior which uses the COEFFICIENT to model variations in D with respect to the concentration J D C VC Syntax x behavior coefficient_di
52. entered here are local to the each damage object and must therefore be input for all applicable objects even if the coefficients have the same meaning Syntax damage type use_e_bar dont_use_e_bar xeta lt COEFFICIENT gt default 1 0 K_coeffs Vi Va V3 Va Vs Ve Vy Va J g lt G_FUNCTION gt where type may be from the following types CODE DESCRIPTION scalar scalar variables with fixed direction elastic_tensorial tensorial variable rate_tensorial tensorial variable use_e bar Makes the calculation of Y or Y use the tensor in place of e dont_use_e_bar use e to calculate Y or Y in place of This option is currently the default K_coeffs coefficients are entered to construct the tensor K use the compliance matrix S D3 and are as follows S11V1 S12Va S13V5 S22 Va S23V6 S33 V3 m Sas V7 sym 555 V3 eal note that the tensors are stored as Si S6 S11 S22 S33 Si2 S23 931 K Da Ho Dei The factors for V are entered in order after the K_coeffs keyword is entered See the behavior descriptions for examples Z set Non linear material amp structure analysis suite 13 3 lt ANISOTROPIC_DAMAGE gt K matrix form for the K This input is entered as an ELASTICITY object Only one definition for the matrix K may be given with the K_coeffs or K The coefficients correspond directly to the associate terms marked with a subscript 1 13 4 Z
53. flow law is a Norton type viscoplastic rate with a hardening effect E etw The flow law accepts coefficients K n m and v_0 Because when v 0 there will be no flow rate in the absense of vy and therefore v will never become anything other than null the coefficient should have a non zero value but possibly very small Z set Non linear material amp structure analysis suite 13 45 lt FLOW gt lt FLOW gt function Description This flow law is defined by a function which can be in terms of overstress f and cumulated plastic strain p Syntax The flow law will accept coefficients depending on the function For example the above flow law will accept K n p as coefficients Example A function such as a norton law combined with cumulative plastic strain could be of interest s LY ae This would result in the following syntax flow function K 120 0 n 5 0 p 10 e 3 13 46 Z set Non linear material amp structure analysis suite lt FLOW gt lt FLOW gt gsell Description This is a viscoplastic model appropriate for some polymer materials It includes some hard ening behavior using the cumulated viscoplastic multiplier v oo f m Ame Garces Note that at v 0 the term 1 e in the denominator will become zero setting the denominator to zero infinite initial strain rate To alleviate this numerical difficulty the term is modified to be 1 e v eo Ex
54. following calculations based on the principal strain eigenvectors pn and the fourth order tensors D are constructed their tensorial variables as Dj a 8 1 2 dy 18d 1 d 13 6 Z set Non linear material amp structure analysis suite lt COEFFICIENT gt lt COEFFICIENT gt Description Coefficient objects are used to enter the values for material coefficients Each behavior object may have any number of coefficients to parameterize the models for different materials The coefficients are themselves behavior objects however and therefore have a standard format for entry Coefficients also provide the means to add external parameter or local material variable dependencies Creating user dependency on the internal variables may however significantly alter the material model and invalidate integration methods The only sure use for arbitrary depen dencies on the integrated variables is with Runge Kutta integration and a time dependent flow law The tangent matrix may also be altered by these dependencies Coefficients which are a function of the external parameters are however robustly implemented and are valid for all integration methods Syntax Supposing that a material model coefficient C is required a syntax similar to the following will be given C COEFFICIENT where the term COEFFICIENT is to be replaced with a coefficient definition The replace ment syntax using the coefficient objects is given bel
55. follows showing some tabular coefficient input behavior linear_elastic kelasticity isotropic young temperature humidity 200000 e0 100 O 100000 0 il L 100000 0 200 O 50000 0 1 poisson 0 3 thermal_strain alpha temperature 1 e 6 0 1 e 6 1000 ref_temperature 0 0 coefficient masvol 7 e 9 return 9 12 lt BEHAVIOR gt lt BEHAVIOR gt Description This class of objects provides the basic building block for material models Each object type tries to cover as broad a range of behavior as possible using the idea of sub model objects to increase the possible combinations Syntax behavior BEHAVIOR modifier level commands coefficient coefficient list lagrange_modifier type We have broken the behavior models up into three classifications reflecting the following three chapters of this book The first is for models which make up significant frameworks for treating broad ranges of characteristics the details of which are fixed by selecting from a broad range of options and sub components The second group of models are secondary models in that they are coded in a specific fashion usually as a prototype stage on their way to being incorporated into the general class materials The third Other classification is for material models fitting a particular application which in general is not suitable for Z mat interfaces with standard mechanical codes e g debonding or spring behavi
56. for the particular case where there are two flow mechanisms which act under a single criterion This model also allows interaction between the isotropic hardening variable and the kinematic back stresses The model is particularly useful for accurate modeling of ratcheting phenomenon Cail95 ll f F LE Syntax kpotential 2M1C name criterion mises_2mic A1 lt COEFFICIENT gt A2 lt COEFFICIENT gt flow lt FLOW gt kinematic lt KINEMATIC gt name isotropic lt ISOTROPIC gt coefficient C12 lt COEFFICIENT gt a lt COEFFICIENT gt beta lt COEFFICIENT gt e The model requires giving mises_2mic as a criterion type This criterion will accept coefficients A1 and A2 scalar to simulate a localization process in each of the two mechanisms In this case the stress equivalent terms in the criterion will be calculated as fi J A s Xj 1 2 with j kinematic hardenings in each mechanism e In the event that the isotropic hardening variable is coupled to the kinematic back stress type nonlinear_bsi the radius will be calculated with kinematic interaction as 1 R ar 02 Ro 3 holon Q2 ay 02 Qr A corresponding isotropic interaction is introduced into the kinematic hardening vari able 2 a Ay gla RO br ay i LN where are the mechanisms and j are the kinematic variables in each mechanism e The coefficients a and b indicate that we desir
57. gen_evp behavior which provides a much more efficient implicit integration The behavior reduces the integration variables to a single tensor and a scalar per deformation potential Because the integration must assume certain forms for the potentials and hardening variables this behavior uses a sub set of the gen_evp options In particular there is no possibility for state interactions and the number of potentials implemented is reduced Domain modifying options such as damage or localization is nor currently implemented in this framework either Thermal deformations variable coefficients all the elasticity models all the flow laws and the majority of kinematic hardening models are implemented There is no limitation on the number or mixing of kinematic models which are entered per potential as long as they support the reduced integration Note that certain laws break distinctly the reduced integration and are not implemented i e Ziegler There is currently a limitation that the isotropic hardening be a function of the cumulated multiplier This means that the internal variable versions of isotropic model are not supported Note that non macro potential models such as the mono crystals are not implemented Syntax kkbehavior reduced_plastic modifier elasticity lt ELASTICITY gt thermal_strain lt THERMAL_STRAIN gt potential lt POTENTIAL gt name Stored Variables The stored variables for this mode
58. gradfn here n is the number of optimization variables The first fundamental idea in Levenberg Marquardt is that the last terms of hessianF can be neglected hessianF J7 WJ This is true in particular when the terms f x yi are small in comparison to hessianf which stands when the simulation is near the experiments and the largest eigenvalue of hessian f is not too large if not true another optimization method sqp for example should be used Necessary conditions of optimality state that the gradient of the objective function should vanish at the optimum z gradF x 0 7 m Linearization of Equation 7 about the current point x yields gradF xz hessianF 81 81400 81 8 The second idea underlying Levenberg Marquardt is to regularize the approximation of the Hessian of the objective function by adding positive terms on the diagonal and use this in Equation 8 The regularized approximation to hessianF is then strictly positive definite and Equation 8 can always be solved The fundamental equation used to update optimization variables is JEW Je Dll Ze ILW f xe y 9 where Az is a scalar positive parameter The principle of Levenberg Marquardt algorithm can also be derived from the linearized original optimization problem with a bound on the design variables This yields an interpretation of A as Lagrange multiplier associated to the move limit on the design variables The v
59. gt name isotropic lt ISOTROPIC gt var_coefs store_all The option store_all is used to make all associated force variables to be stored as well as the internal hardening variables This allows one to observe directly the effective back stresses or isotropic radius even in the case of coupling Other statements may be made about this model e The final form of the hardening will be determined by the options kinematic and isotropic which are given by the user If there is incompatibility with one of the hardening mechanisms with this potential an error message will be output as the invalid calculation is attempted Static recovery is allowed in both the isotropic and kinematic variables e The type of flow law and criterion f will be determined by the options flow and criterion Default values for these options are plasticity time independent flow and mises respectively e The flow direction is determined by the criterion chosen which is not necessarily asso ciated e The names of the internal variables will be dependent on the choices given by the user If no name is given for the potential the potential name henceforth referred to as pn will be et with being the sequential number of the potential in question ie 1 Z set Non linear material 13 83 amp structure analysis suite lt POTENTIAL gt 13 84 for the first potential etc In the absence of names for the kinematic var
60. in the elastic matrix will be set equal with a tag input after the transverse keyword It is best to explain this syntax through an example Cll C12 C13 0 0 0 Cii C13 0 0 0 e C33 0 0 0 ar c 0 0 sym 655 0 C55 which is created by elasticity transverse and the coefficients c11 c12 c13 c33 and c55 or the corresponding y1111 etc For the moment it is only possible to work with c11 and c22 equal instead of for instance equal c22 and c33 The following relations are also given for reference in the case of c11 C22 1 nv2 Ex ca _ gt AB E ee Vry ng Le AB ag Vyq Eg B 13 10 Z set Non linear material d amp structure analysis suite lt COEFFICIENT MATRIX gt _ 1 My Ez B c4 5 Ci Ci c55 Ces Guy Grz x 2 1 vey n E E A 1 Vry B 1 vry 2nv2 cubic Y1111 Y1122 Y1122 0 0 0 Y1111 Y1122 0 0 0 Y1111 0 0 0 D Y1212 0 0 sym Y1212 0 Y1212 orthotropic Yi111 Y1122 Y3311 0 0 0 ya222 Y2233 0 0 0 y3333 0 0 0 D Y1212 0 0 sym y2323 0 Y3131 An alternative naming uses c11 c22 c33 c44 c55 c66 c12 c13 and c23 or their symmetric counterparts anisotropic Y a11 Yi1i22 Y1i133 Y1112 Y1123 Y1131 Y2222 Y2233 VY2212 Y2223 Y2231 D Y3333 Y3312 Y3323 Y3331 Yy1212 Y1223 Yl231 sym Y2323 Y2331 Y3131 Example kelasticity isotropic young 200000 poisson 0 3 kelasticity cubic y1111 162321 0 y1122 78075 0 Z set Non amp structur
61. limit of the last given variable name Example This is an example for the problem 4022301 of ABAQUS The input file is the following this is for a custom behavior integrating the same Ziegler model as in ABAQUS material integration theta_method_a 1 0 1 e 7 1500 initialize_variable epcum 0 43 X11 128 0 X22 181 0 X33 53 0 behavior ziegler_test return Interface files parameter Darameter Description This command controls the translation of ABAQUS field variables to Z mat external pa rameters which can be used in coefficient dependancies Remember that the temperature parameter is always active in Z mat Syntax parameter ambient_temperature val field_variable var name location initial_value val kambient_temperature sets the ambient temperature used as T This is important for thermal strain calculations see page 13 94 In the event that this command is not used an additional state variable is added with fixed value of the temperature at the beginning of the problem if there are dependancies on temperature in the behavior that is It is probably desirable to use this command therefore if the initial temperature field is constant field variable add a new field variable to the problem with index location in the list of fields defined within the ABAQUS problem This index starts with 1 initial_value optional command with a similar meaning as ambient_
62. local optimizer The method is numerically simple and robust but slow for large scale problems A flow chart of the method is given in the figure hereafter The simplex method starts with a regular geometric figure called the simplex consisting of n 1 vertices where n is the dimension of the design space Then vertices are moved according to their respective values f There are 3 main steps during a sequential simplex search the reflection from the worst point to the best the expansion continuation of the displacement towards the best vertex when reflection improved f and the contraction of all the vertices towards the simplex gravity center when reflection has failed In the figure xh x1 xs and xm are the highest lowest second lowest point and the gravity center respectively fh fl and fs are associated cost functions Typically a 1 b 2 et 0 lt cc lt l This implementation integrates an optional automatic restarting procedure in an attempt to render the algorithm less sensitive to local minima In this case the new starting point is automatically evaluated based upon previous results Optimization constraints are also supported by means of a basic penalty technique initialize the simplex determine xh xs and xm fh fs fl Reflection xr xm a xm xt n n o fh lt fl fr lt fs gt fr lt th 1 replace xh by xr gt z e Y o Expansion xe xm b xr xm Contraction xc
63. mat internal format of shear variables to a real measure Shear components output are multiplied by a factor 2 from the actual tensor component t12 in the output is v2t12 Z set Non amp structure an 2 5 Interface files 2 6 state var engineering shear Transform shear variables to be output with an addi tional factor of v2 e g y12 2e12 This is now the default kstate_var_real_shear Divide the v2 term out of the shear components so the output is the real component of the tensor suppress_temperature Eliminate the setup for temperature as a parameter This optimizes slightly the computations so constant coefficients may be assumed kksymmetrize tgmat Make an extra step to symmetrize the material tangent returned from the Z set behavior verbose verbose message outputs kkplane stress modifier This command may be used to de activate the automatic detection of the plane stress condition and allows the use of an explicitly defined plane_stress modifier of the behavior instead Note that automatic plane stress treat ment is not implemented for all behaviors and that in the case of anisothermal loadings convergence may be very slow In those two cases the plane_stress modifier method should be preferred x zero_dt for first dt use a zero At for the pre step test with zero strain increment This pre step is used by ABAQUS to get the initial tangent modulus Time dependent materials may be non
64. may oc cur during integration of the behavior equations by Zmat Without a proper procedure such local divergence will cause either premature convergence especially in the case of anisother mal analysis under purely thermal loadings or run away newton iterations until the specified maximum number of recycles is reached and increment cutback eventually occurs Unfortunately there is nothing available in uvscp1 as in other user material subroutines to signal a local divergence back to Marc and force an immediate increment cutback However the enhanced scheme of the auto step command that allows to specify user criteria to control the step size may be used to implement some kind of emergency procedure The input data necessary to implement this mechanism from the dat file is not trivial and is described hereafter e activate the enhanced scheme of the auto step procedure by setting to 1 the 9 pa rameter of the second data block e choose to use user criteria as limits versus targets by setting to 0 the third parameter of the third data block e add a criterion on a Zmat variable that will cause increment cutback in case of its violation during local integration To select a particular user state variable a code such as 131x100 state variable id should be used as first argument of the fourth data block auto step 0 02 0 4 0 0001 0 1 100 6 1 0 3105035512 25554 5425 1330 cmc 10 0 01 In the above example the user crit
65. n 32x Note the aging effects are in the recall term for X2 continued Z set Non linear material amp structure analysis suite behavior aging 11 4 Syntax The basic input syntax here is behavior aging theta elasticity thermal_strain lt THERMAL_STRAIN gt model_coef lt ELASTICITY gt The following coefficients are available K n viscoplastic Norton law coefficients for f Ky C1 D1 nonlinear Armstrong Frederick kinematic hardening C1 is the kinematic modulus and D1 is the saturation rate The saturation back stress is occurs at C1 D1 C2 D2 nonlinear kinematic coefficients which have the aging effects applied to them RO Q b nonlinear isotropic hardening or softening with Q lt 0 having the same meaning as the nonlinear isotropic model RO_star isotropic aging effect on the yield radius Tau a_inf the two aging variable coefficients alpha optional thermal strain expansion coefficient Stored Variables The following variables are stored with this model prefix size description default eto T 2 total strain yes sig T 2 Cauchy stress yes eel T 2 elastic strain tensor yes evi T 2 viscoplastic strain tensor yes eme T 2 mechanical strain tensor yes evcum S cumulated viscoplastic strain magni yes tude age S aging variable yes alpha i T 2 kinematic back strain i 1 2 yes Note Early releases of this model misspell the model name as ageing
66. no_feas_pts_res no_ifeas_pts_res evolution also collects points that might not be the best overall but might be the best of their kind Those points are to be found at the end of the run in the file case evo gid They are divided in 2 groups the feasible and the infeasible points no feas pts res sets the number of feasible points that are collected and no_ifeas_pts_res the number of infeasible points The algorithm that collects those points make sure that they are different based on a distance metric that can be set with the command neighborhood_dist If two points are separated bby a distance smaller than neighborhood_dist they are considered as being close and only one of them will be kept in case evo gid A default value of neighborhood_dist is 1 20 x o Dimas Th min lag mult v Um where m is the number of constraints It enables to set the lagrange multipliers at the beginning of the runs Lagrange multipliers apply to each constraint separately and they are used here as penalties If a constraint is difficult to satisfy the corresponding lagrange multiplier should be increased Lagrange multipliers are automatically changed by the optimizer and they will eventually represent the real lagrange multipliers after convergence Default values are 1 lag_mult_step sets the amount of change of the lagrange multipliers after each evaluation of the function The lagrange multipliers are updated at each function evaluation according to
67. of the internal variable is written in the form i Amgin o X p Wrin X where m is the hardening normal and Wine a static recovery function linear The linear kinematic hardening has its internal variable evolve with the inelastic strain Mein n The only coefficient for this model is the C modulus units of stress The slope in a uniaxial test will be equal to the C value nonlinear The nonlinear model evolves much as the isotropic nonlinear model does with a slight change in coefficient meaning The evolution is the following 3D Mkin N 50 X Jo X The coefficients are C and D for the strain evolution and M and m for the static recovery term In the absence of these latter two there will be no static recovery calculation The saturation of this model occurs at C D in a uniaxial test at a rate determined by D Increases in D yield faster saturating more nonlinear behavior Static recovery is seen to follow a Norton type formulation in the back stress tensorial space This kinematic model supports RK TM or Reduced TM integrations nonlinear phi This model installs a kinematic variable with the following evolution 3D X 2C where the function is PCA bm 1 bm exp w where the material coefficients m and w are named phim and omega Note that w defines the rapidity of saturation in the non linear coefficient and m is a factor between zero and one interpolating t
68. or special features available in the user interfaces These differences will be noted in the description section for each command Note that the interface file name itself is very dependent on the particular solver which is being interfaced to For example with ABAQUS materials are assigned character names and that name will be the same ASCII filename to be opened by Z mat On other solvers such as ANSYS only a material number is given as an identifier and in that case a convention of naming the file as 1004 material number txt for example 105 txt for material id 5 Please double check in the different chapters specific to each solver for further information Syntax The following commands are available in the Z mat interface file Reading of the commands will stop when a return command or the end of file is reached automatic_time behavior debug external_storage material parameter save_energies skip_cycle state_var_engineering_shear state_var_no_change state_var_real_shear suppress_temperature symmetrize_tgmat verbose plane_stress_modifier zero_dt_for_first_dt These commands and their options are the subject of the rest of this chapter Some of the commands are simply switches and thus do not have any sub commands These simple commands will be discussed in the following state_var_no_change This command indicates that the user does not require changing the Z
69. output_name component compl comp2 directioni1 dir direction2 dir make_contour number num scale factor time times component xdirection1 xdirection2 make_contour xnumber scale time Example error_map shear_error test time 20 after loading to the yield surface scale 0 1 ten percent strain make_contour look at with Zmaster shear_error 15 9 x simulate k xtest load load Description This command defines a segment of loading for the simulation The load commands are executed in the order they appear and there can be any number of loads for the problem Blocks of loading defined seperately are usefull to change control or apply cycles in between single segements of loading The command looses some coherence in an attempt to give additional options and due to the fundimental difference in the loading for fem behaviors and the generalized simulator models Syntax Simulation loading is given with the following syntax kload cycle ncycle rate var rate for dval rate var rate stop_at break var dval dtime segment rate num segment num loading table file filename num The cycle keyword indicates that the loading is to be repeated a given number of times This may also be useful in the rate loading case for switching between rates see example following num The number of output points between each given loading segment in the loading table ncycle
70. p depasses the last value specified in the table the isotropic hardening no longer changes as if the isotropic hardening saturates linear pp linear hardening with an initial radius RO and slope H up to Ru i e R RO Hp for R lt Ru followed by perfect plasticy at R Ru nonlinear This law gives a nonlinear saturating evolution bp R kRO Q l e where the saturation radius will be RO Q for large p The law will reach 95 of the saturation value at p 3 0 b so that higher values of b give a more rapid saturation linear_nonlinear linear hardening with an initial radius RO followed by a combined linear and nonlinear evolution with coefficients H Q and b according to R RO Hp Q 1 e nonlinear_sum or nonlinear_double This law allows fine tuning of the isotropic hardening by use of multiple term evolution For instance two terms might be combined analogous to short and long term mechanisms There is no upper limit for the number of terms N The radius is calculated as N R R Qi 1 e i with coefficients RO Q1 Q2 QN and b1 b2 bN continued Z set Non linear material amp structure analysis suite 13 55 lt ISOTROPIC gt nonlinear_1 R RO Miso 1 Example An example of a three term nonlinear hardening with a very rapid initial hardening a very slow hardening third term and an intermediate softening negative Q2 Note these are not necessarily reasonable values i
71. page 13 61 There are currently two methods for specifying a rotation These are by vectors of the rotated coordinate axes in the global coordinate system and by Euler angles used for crystal orientation for example The first case is displayed in the following figure Z For the material rotation of this section the material gradient will be rotated rotation is applied before being integrated by the material behavior For small deformation mechanics this would be a rotation of the strain tensor 1 T Etot R Eta R The material behavior then solves for the flux in terms of the new gradient which is gt 0 for the mechanical problem Afterwards the flux is rotated to the global coordinates again o Ro R Rotation by giving Euler angles is similar The significance of the three angles is given in the following figure continued Z set Non linear material amp structure analysis suite 2 15 Interface files material rotation Syntax For rotations specified using coordinate axes rotation x1 2 y 2 x2 2 y 2 x3 2 y 2 The arguments x1 x2 x3 indicate the components of direction vectors for the transformed coordinate frame Exactly one direction is required in 2D problems and two directions are required in 3D The order of definition is not important The local coordinate system may be assembled with any of the geometrical axes The input vectors w
72. set Non linear material 7 amp structure analysis suite lt ANISOTROPIC_DAMAGE gt lt ANISOTROPIC_DAMAGE gt scalar Description Each scalar damage variable is defined using a damage direction input by the user 7 and an effective fourth order damage effects tensor K The modulus modification induced by a scalar damage variable is the following CoH 8 K nih amp Ni K Ni where is the scalar internal damage variable The above uses the following terms to measure the degree of opening strain Gj ii Q Tii A Ec Ni 7 Q fi 9 Fi D Ti 1 The material coefficient 7 is used to describe the influence of closing on the damage softening damage scalar std options n lt VECTOR gt orientation n the directions of the axes of damage for the isotropic variables entered as a vector Example Please see the examples in the anisotropic behaviors aniso_damage and visco_aniso_damage Z set Non linear material amp structure analysis suite 13 5 lt ANISOTROPIC_DAMAGE gt lt ANISOTROPIC DAMAGE gt elastic_tensorial Description This model using a 2nd order tensorial damage variable is calculated as follows 3 ar D K S nh Pn D K Pn n 0 where the summation over n is over the three principal directions of the strain tensor and D is a fourth order tensor constructed based on the second order damage variable dj This will use the
73. shear 10 7 sido 15 14 sintering 13 91 skip first 14 7 slip 13 92 small 15 14 solver 15 15 6 6 5 Z set Non linear material amp structure analysis suite spectrum 10 9 storage 3 17 strain_hardening 13 45 symmetrize 14 12 theta 14 10 theta method_a 2 13 time 15 9 15 17 transverse 13 10 transverse elasticity 13 10 two_sided 14 12 use_e_bar 13 3 use_last_tangent 14 8 USER MATERIAL 3 9 variable_friction 12 17 variable environnement 17 5 verbose 2 6 viscous_effects 10 10 volumic 10 7 yield_surface 15 17 Z mat 3 5 Z7_LICENSE 17 5 Z7 MAX NB DOF 17 5 Z7_TMP_DIR 17 5 Z7PATH 17 5 zebaba_v6 env 3 13 ziegler 13 59 19 5
74. temperature coefs for HASTELLOY X as given by Rowley and Thornton J Eng Mat Tech 118 19 27 1996 behavior bodner_partom kelasticity isotropic young 196 6e3 poisson 0 33 model_coef n 1 0 ZO 1860 Z2 1860 DO 10000 0 Zi 2390 Z3 603 mi 0 139 m2 3 49 Ai 1 0e 9 A2 1 0e 9 ri 1 r2 1 return 11 12 Z set No amp structure behavior finite strain crystal behavior finite_ strain crystal Description This behavior is a simple implementation of a finite strain formulation of a single crystal This behavior is included as an example of ZebFront programming and the source can be found in the developers manual This model only allows one crystal orientation to be input and works for Runge Kutta integration only This model works with the assumption of multiplicative plasticity where the deformation gradient F is broken into an elastic part Fe and a plastic part Fp Fe FF The elastic deformation gradient is separated into a rotation component and a stress compo nent Fe R Ue and the stress is calculated using the logarithmic strain measure from the elastic stretch o Da log F There is a yield criterion for each slip system fi m o Cai R g which is used to calculate the evolution F E gt o fi miF i is the integration of v fi a ysign m o Cai Dx ai y 3Only Runge Kutta integration is implemented Z set Non amp
75. while not greatly complicating the solution may not be handled in the simulation solution for a particular model In that event a rate dependant flow law must be used for example using a norton law with very small viscosity to approximate rate independence The basic solution proceedure rearranges the mixed equations to first solve for the total strain rates and then resubstituting them into the basic rate equation to find dsig For example a 2D solution could take the form 01 it _ Etoto D l 3 D 2 7 Da ni D Ein E Esp Dei Ee 3 ots 04 3versions before 8 2 do not allow the explicit keyword it is activated by the absence of a solver entry t starting with 8 2 rate independent plasticity is handled by gen evp and some ZebFront demonstration models Z se 2 8 15 15 x simulate k xtest solver From which the following equation would be extracted 1 A En al ie 4 Deigi Deigs 012 Etot19 Syntax The solver syntax accepts a number of options which determine the convergence and automatic time stepping controls primarily applicable to the newton solver syntax solver type algorithm algo type automatic_time divergence factor iteration iter iter_optimal opt iter max_dtime max time min_dtime min time ratio ratio security sec algorithm automatic_time divergence iteration iter_optimal max_dtime min_dtime ratio security 15 16 Z set
76. 0 y1212 180000 y2323 180000 y3131 180000 return 10 3 behavior damage elastic behavior damage elasticity Description This is a simple behavior for elastic energy based damage It is duplicated by the gen_evp damage option with type elastic This behavior is given as an example of a simple user model programmed without ZebFront The source is available in the developer handbook o 1 D Da to zeth 1 Y geel Da Eel D a max V y Yo Syntax behavior damage_elasticity kelasticity lt ELASTICITY gt YO COEFFICIENT alpha COEFFICIENT Stored Variables The grad variable is the gradient of temperature and the flux is the heat flux prefix size description default eto T 2 total small deformation strain yes sig T 2 Cauchy stress yes y_max S Y no damage S damage D yes Example behavior damage_elasticity kelasticity isotropic young 200000 poisson 0 0 YO 20 0 alpha 0 001 return 10 4 behavior hyper_elastic behavior hyper_elastic Description This behavior handles all simply hyperelastic material laws For cases of hyper viscoelastic or hyper viscoplastic models please see those corresponding behaviors Note that the syntax for hyperelasticity in Z mat has changed significantly with the 8 3 release and the un mixed hyperelastic laws are now available for use with the different Z mat interfaces All the prev
77. 0 0 ee ee 1 9 Material Frameworks 2 0 a a dll Z mat General Commands 2 1 Z imat interfaces ui a ge A hcg A A A 23 Interface Ples soros Tanek atana aeaa aa ias ah ote at Tees o 25 outomatictime ooa a a 2 8 ehavior ooa a a 2 9 EME sa s sicak eia ae e RR AAA Ge eH 2 10 io a E A 2d AA 2 6 a 2 13 ge AAA 2 18 TE Save energies 44455448 ea ERED 2 19 esla edad ce OSS GO ee oe a eS 2 20 Zmaster interfaces 0 ee 2 21 Z mat ABAQUS 3 1 Z mat ABAQUS interface ee 3 3 Current Status 264 06 c8 ade bse does ee da BD Berd 30 Site definition sposa a ee a Sal Interface ales Nebbia e A a eee e Hs a SE a 3 9 Output variables e 3 11 Extra files 3 13 User additions ooa e a a a SAIRE Examples pri We eee ele o Ae ae ee a a A a 3 17 Post calculations 2 ss e ce gon A e a eee 3 19 Z mat ANSYS 4 1 Zansys ANSYS interface aoaaa ee 4 3 Z mat MSC Marc 5 1 Z mat MSC Marc interface a a 5 3 Z mat SAMCEF 6 1 Z mat SAMCEF interface 0000000 ee eee 6 3 Z mat Cosmos 7a Z mat Cosmos M interface ooa e 7 3 Z mat LS Dyna 8 1 Zlsdyna LS Dyna interface e 8 3 Behavior functionality 9 1 Introduction to Behaviors 02 000 eee eee ee 9 3 Grad Fis dock e og de ew Ee cae Bee amp Ge ae hed we HAN ae Bie Le ee aw a 9 5 Material variables ee 9 7 Material levis hal ita a q AO A ws Qe a ere a de 9 11 BEHAVIOR 00 4 ra o e a e e eS 9 13 Material Model
78. 0 c2 1 0 c3 1 0 c4 1 0 c5 1 0 c6 1 0 Z set Non linear material amp structure analysis suite 13 19 lt CRITERION gt lt CRITERION gt linear drucker prager Description This criterion is a non associated criterion flow direction is not the same as the normal to the yield surface SL It is commonly used for soils and plastics B friction angle general coef Y dilatation angle general coef K ratio of triaxial yield in tension to triaxial yield in compression 0 778 lt K lt 1 S U 0 0 pl p 31 o 1 2 q 7s s r 3S S S 3 q 1 1 r t 1 1 Dz C k a f t ptanf d d 1 itang Oc O is the compressive yield d 1 itang Ot oz is the tensile yield d d a K7 T shear yield cohesion 4 g t ptany cda c 1 3tany defined in compression yield 1 c k 1 Hany defined in tension yield E E ape c E 927 l defined in pure shear cohesion 13 20 Z set Non linear material i amp structure analysis suite lt CRITERION gt 5 Note Since this criterion is not associated it should only be used with behaviors and criterion which accept a different criterion function from normal definition Syntax The criterion takes a few options and parameters The following assumes that the criterion is selected with a criterion command as in gen_evp behaviors criterion linear_drucker_prager friction_angle COEFFICIENT dilatation_angle COEFFI
79. 0 0 find_offset time 0 0 50 200 500 time 1000 rate 0 0 1 e 9 1 e 6 1 e 3 Z set Non linear material amp structure analysis suite Chapter 16 Optimization 16 1 Z set Non linear material 16 2 amp structure analysis suite Introduction Introduction Description The version 8 0 of Z set introduces a generalized optimization module which may be used to identify material coefficients optimize geometry etc The optimizer will modify tokenized parameters in a different user specified ASCII files in order to minimize the combined error of a variety of tests Each test will generally consist of one or more shell scripts or sub processes used for simulation of the test and a certain method of comparison with experimental reference data or optimal condition No explicit assumption is made to the nature of simu lation method so these simulations may be made using the Z set programs internally or by another means The real strength of this method is one can obtain the best comprehensive approximation to many data sets even if they are theoretically over constrained The optimizer problem and its solution are defined in an input text file similar to that for the other main program types The optimizer uses a template file for definition of the parameters to be modified Basic Concepts and Notations Optimization problems are formulated in Z set in the standard form 1 N minimize F z gt wil
80. 1 3 0 433 The mt data entry specifies the user routine to use and the nhv entry specifies the number of state variables required Zmaster interface The d3plot results files can be read via Zmaster directly as an alternate choice for post processing though the standard LS Dyna prepost is quite a nice environment and there may not be so much reason to do this Because there is no default suffix an added switch d3d is needed to indicate an LS Dyna file When a numbered series of d3plot files is to be read only the 1st file unnumbered should be specified on the command line Zmaster d3d d3plot Either the Zmaster Mesh Plot or Results buttons can be used Zpost interface Probably more interesting than running in Zmaster for commercial users is the ability to do post processing or results file translations The following is an example for extracting time displacement data at a node in a batch task execute with Zrun pp post_processing data_source d3plot open d3plot x global_post_processing file node output_number 1 999 nset ALL_NODE process curve control_energy bar impact test precision 3 node 1333 U3 return 8 4 Chapter 9 Behavior functionality 9 1 9 2 Z set Non linear material amp structure analysis suite Introduction to Behaviors Introduction to Behaviors Material behaviors in Z mat use by far the most dynamic and object oriented input of all the
81. 118441 volumic tau 0 1000000E 01 omega 0 29800651 volumic tau 0 3096638 omega 0 8500050E 01 volumic tau 0 2696395 omega 0 4522469E 01 volumic tau 6 517014 omega 0 5717688 return Z set No amp structure behavior viscoelastic_s behavior viscoelastic_spectral Description This behavior defines a spectral viscoelastic model The model defines the stress to the strain e by the following differential equations system a Co T a Eth Eth a T To i nt a 9 0 YX i 1 i ui D glo CMT Xi Co is the elastic matrix Note that So used latter is defined by Sy Co k g a is the viscous non linear function Ti and u define the spectrum Each mechanism X is associated with a relaxation time 7 weighted by ui The whole strain family X describes a gaussian continuous spectrum Note For the moment the thermal strains are not taken into account Syntax The material file structure for the viscoelastic_spectral model consists of an elasticity object the definition of spectrum of the viscous_effects tensor and of the assymptote The syntax for this behavior model is the following behavior viscoelastic_spectral modifier xelasticity lt ELASTICITY gt spectrum viscous_effects reversible_asymptote Options spectrum represent the spectrum which defined u and 7 see next figure 1 Ne y lt ex pa
82. 13 67 lt POROUS_CRITERION gt lt POROUS_CRITERION gt fkm Description This criterion is as developed by Fleck Kuhn and McMeeking Flec92 for metal powder compaction 6J2 27 Je 42 6a with coefficients fmax offset and fs named fmax offset and fs Syntax porous_criterion fkm coefficients Example A simple example from a test case is given below porous_criterion fkm fmax offset fs 13 68 Z set Non linear material amp structure analysis suite lt POROUS_CRITERION gt gurson Description lt POROUS_CRITERION gt This criterion was proposed by Gurson and is no doubt a widely accepted model The model was developed to capture the progressive microrupture through void nucleation and growth Since then it has been modified in various forms for implementation in a variety of fields ductile rupture of metals being the most applied one The model defines the criterion as 3J2 2 Ox I 2f qich 2 f where f qi q2 are coefficients of the model Names for these coefficients are fs q1 and q2 The coefficients q and q2 have units of stress Syntax porous_criterion gurson coefficients prefix size description default eto T 2 total strain yes sig T 2 Cauchy stress yes Example A simple example from a test case is given below porous_criterion gurson qi 1 5 q2 1 0 fs ft Z set Non amp structure an 13 69 lt POROUS_CRI
83. 14 16 17 0 0 19 20 0 1 0 301 461 311 391 30 d1 31 d2 32 d3 The above command adds user variables 30 31 and 32 to the t16 result file The corresponding values will then be accessed by the graphical post processor of Mentat Within Mentat the names given to those state variables will be respectively d1 d2 and d3 as defined by the post command Note that this output capability makes use of the user subroutine plotv to interpret correctly the user element codes An appropriate plotv code is provided in the Zmarc package However this means that the user cannot redefine this particular user subroutine for its own purpose e History definition section 5 4 Z set Non linear material amp structure analysis suite Zmarc interface The use of the auto step procedure for adaptative load step control is strongly advised Moreover starting with Marc2003 auto load doens t seem to handle anymore user ma terial implemented with the uvscp1 subroutine Also as described in the next section the enhanced scheme of this procedure can be used to provide Marc some feedback about local integration results obtained in the Zmat library This option should then be activated as well by setting the 9t parameter of the second data block to 1 auto step 0 02 0 4 0 0001 0 1 100 6 1 10 033 3 3771 2 Automatic time stepping and Zmat local integration For complex material behaviors and or large strain increments non convergence
84. 2 with a a constant representing the relative magnitude of T with respect to Ty and Cmar the maximum stress allowable by the element For the compressive case where uy lt 0 the normal component of the traction is modified to UN a HO 3 N with a a penalization factor In the literature a usually is at least 10a Figure 1 illustrates the typical response of the cohesive zone model under specific loads for the parameters as given in the example TN Qe Syntax behavior needleman_debonding sigmax Omar deltan n deltat 06 alpha a alphac Qe no_penetration continued this behavior is Z set specific and therefore does not apply for Z mat for other codes 2Needleman A A continuum model for void nucleation by inclusion debonding J of Applied Mechanics 54 1987 pp 525 531 Z set Non linear material amp structure analysis suite behavior needleman debonding 16 0 7 T 125 7 14 0 100 F 12 0 p 75 10 0 W 25 E 80 a 0 gt 6 0 iS 25 4 0 F 50 L 2 0 75 L 0 0 100 J 2 0 i i i i 125 i i i fi 0 0 1 0 2 0 3 0 4 0 5 0 0 0 1 0 2 0 3 0 4 0 5 0 time s time s 125 100 p 75 F 50 F 7 y 25 oO 2 0 FR 25 50 L 75 L 100 l l 125 AES EP NE REN S 0 0 1 0 2 0 3 0 4 0 5 0 2 0 0 0 20 40 60 8 0 10 0 12 0 14 0 16 0 time s u um Figure 1 Example in two dimensions o
85. 70 user manual Syntax Zlsdyna opts problem Compatibility The Zlsdyna interface is tested at the time of writing with LS Dyna 970 which requires building a custom executable from the development kit The interface has been tested with both single process and MPP versions of LS Dyna Unfortunately because of licensing restrictions NW Numerics is unable to re distribute modified binaries of LS Dyna so the compilation obligation falls on the end user In some cases NW Numerics has been able to assist in this compilation process so please inquire with the distributor This procedure imposes the following very strict requirements e Precisely the same compiler as defined by LSTC must be available and used for the build process e The development kit must be obtained from LSTC There are different development kits for the single and MPI based distributed domain solver e Check with NW Numerics on our testing level with the platform chosen Because of the many different computer distribution levels possible there is likely some configuration work to be done Note With LS Dyna 971 MPP versions there will be a more robust plug in style inter face will be implemented similar to ABAQUS and ANSYS In that case the Zlsdyna installation and version tracking will become a negligible effort All aspects of the user launch process will remain the same however Getting started Perform a standard installation of Z set including the
86. 9 Material variables Z set Non linear material 9 10 amp structure analysis suite Material file Material file The material and global scope coefficients to be used are defined in a separate file hence forth described as the material file The material file is a standard ASCII text file of form similar to the main input file Most instances where a material filename needs to be specified allows an optional integer value for the instance of behavior in that file the default instance being the first So when a material file is opened the program will search for the n th occur rence of the keyword behavior skipping all other data contained before Frequently for example and verification problems the material file is given in the same physical file as the referring input file for compactness and file management purposes Regardless of how or where the material file is located the material file is a separate entity from the other input commands with an independent command hierarchy starting at the x level The general structure of this file is the following behavior BEHAVIOR modifiers xfunctions list of function declarations behavior sub procedures kcoefficient coefficient name COEFFICIENT xsave_coefficients coef names plane_stress return behavior begins the definition of a material law The options which follow are of course specific to each material model coefficient indica
87. ACTION page 13 52 e If no flow command is given it is assumed to be plasticity see page 13 44 e All the ISOTROPIC objects listed later in this manual page 13 54 which do not have an integrated variable may be used for this model i e no static recovery If no isotropic command is given the code will assume isotropic constant and a value for RO should be given Only one isotropic hardening object is allowed but some of these objects contain multiple terms e Multiple kinematic objects may be given e Due to the anisotropy of deformation for the single crystals it is necessary to work in 3D geometries e In the absence of SLIP_INTERACTION see page 13 92 h1 1 and all other values are zero i e only self hardening e The axes with respect to which the slip systems are defined and thus the slip systems themselves can be rotated with a rotation command see page 2 15 for the correct syntax e The store_all command stores all local associated force variables such as the resolved shear stresses as well as the internal hardening variables Example behavior gen_evp elasticity cubic y1111 162321 0 y1122 78075 0 y1212 110615 0 kpotential octahedral ev flow norton K 100 0 n 10 0 kinematic nonlinear_phi C 20995 0 D 1105 0 phi 0 0 delta 0 0 Xbar 23 8 isotropic nonlinear RO 382 0 Q 7 93 b 2420 0 xinteraction slip hi 1 0 h2 1 1 h3 1 3 h4 1 5 h5 1 7 h6 1 9 potential cubic cu flow norton K 100
88. Ac al T t TE Tref a T t 0 T t 0 Tref In the previous equation the dilatation coefficient a T is supposed to be measured using Tref as the reference temperature Do not make any confusion between the initial time which is the time at the beginning of the computation usually t 0 and the reference temperature Tref is not related to any particular time it is just the temperature used as reference by the people who did the experiment to measure a To re define the reference temperature a coefficient ref_temperature must be input The method of calculation is schematically shown below Ae 0 T T r Tet temperature 3a standard coefficient 13 94 Z set Non li amp structure an lt THERMAL_STRAIN gt The coefficients required for the thermal deformation models are given below All coeffi cient types and dependencies may be entered for the thermal dilatation coefficients isotropic The isotropic model has only one coefficient for the dilatational secant which is named alpha anisotropic The anisotropic thermal strain object calculates different thermal strains along each axis in the material coordinate frame The dilatational coefficients names are alphai alpha2 and alpha3 to the three material axes Example thermal_strain isotropic alpha temperature 10 e 6 25 12 e 6 500 ref_temperature 100 Z set Non linear material amp structure analysis sui
89. Be ak ad a ES ES ES Reference A AI ee ee ee es Environment Variables 00000 eee ee a Bibliography Index Chapter 1 Introduction 1 1 1 2 Z set Non linear material amp structure analysis suite What s in this manual Description This Z mat user commands handbook covers the command syntax and some of the details for the different files related to use of Z mat This includes the material behaviors utilities and extra programs and interfaces to the different FEA codes which Z mat works with For users who are interested only in the Z mat interface to another FEA solver the primary source of information will be in the Examples Training and this Z mat User commands manual There is supplementary information in the other books however such as user devel opment and model theory The Zmaster program has increasingly expanded its capabilities and will continue to explore new interfaces with other software products The Post computa tions section in the Z set manual also has information on making batch post computations of imported results from various codes Handbook Summary The following list summarizes the documentation for all of Z set As part of our 8 2 8 3 developments greatly expanding the software documentation is one of our primary goals The list below is sorted in what we feel would be an appropriate sequence for the normal user starting with installation and reviewing capabilities to
90. CIENT K COEFFICIENT use_sigma_c use_sigma_t use_cohesion a ri Fe Example criterion linear_drucker_prager friction_angle 20 0 dilatation_angle 20 0 K 9 13 21 Z set Non amp structure a lt CRITERION gt lt CRITERION gt mises Description This criterion is the classical energy equivalent form due to von Mises Here the effective stress is calculated based on the J stress invariant 0 5 fo ana R 2 36 n af Example potential gen_evp ev flow plasticity criterion mises isotropic constant RO 300 13 22 Z set Non linear material amp structure analysis suite lt CRITERION gt lt CRITERION gt modified nouailhas Description This criterion modifies the nouailhas model above by basing the calculation of the I s on the actual tensors X in place of the deviator and includes an extra term E 3 1 12 fer Ea 20217 20414 ass asto R 2 l Te eee YN YN Tg S11827 S22833 S33811 la Sia 853 Si Ig S12 S93 S31 lg Sia 993 S31 U with S 0 X This criterion is fully implemented such that it will work with any normal gen_evp or reduced_plastic potential with any otherwise valid integration In 2D the 23 and 31 terms are taken as zero Z set Non linear material amp structure analysis suite 13 23 lt CRITERION gt lt CRITERION gt nouailhas Description This criterion is a ma
91. ERION gt isotropic lt ISOTROPIC gt T1 T2 g_function recovery_flow model_coef p pl p2 bt Yt_inf h_function Output Internal variables added by a delobelle potential instance are the following prefix size description default prvi T 2 inelastic strain tensor yes pncum S cumulated value of the yes pn alpha2 T 2 kinematic strain variable ag no pn_alphal T 2 kinematic strain variable a no pn_alpha T 2 kinematic strain variable a no yt S non radial hardening variable no Note that the program does not normalize the value of n such that n n 1 which could affect the meaning of the behavior and the influence of the anisotropic coefficients Compatibility limitations This potential is not valid for the reduced integration behavior It also does not implement the copy mechanism required for use in the polycrystal It may not be reasonable to make kinematic state variable coupling but it should work in the p coefficients This model should be valid with the damage mechanics damage or other similar gen_evp modifiers Coefficients should not be allowed to vary with VINT or VAUX variables The use of Yo is not exceptionally tested Example x behavior gen_evp elasticity isotropic young 80000 0 poisson 0 32 potential delobelle ev flow hyperbolic 13 78 Z set Non li amp structure an K 22 3 m eps0 202e 8 isotropic constant RO 99 5 44 lt POTENTIAL gt
92. IENT GO COEFFICIENT G_inf COEFFICIENT x shear xx volumic Options shear represent the shear mechanisms and are defined by the following form shear tau COEFFICIENT omega COEFFICIENT where the coefficient tau corresponds to the material constant 7 and omega to w as in equation Similarly the option volumic represents the volumetric mechanisms using the same coefficient material constant naming kvolumic tau COEFFICIENT omega COEFFICIENT Stored Variables The internal variables stored for this model are the total strain code etoxx the tensorial variables a code alpha xx and the 3 variables code beta prefix size description default eto T 2 total small deformation strain yes sig T 2 Cauchy stress yes alpha T 2 a variable no beta S 6 variable no The code names will replace the symbol with the sequential number of that variable type as given by the order of declaration and the xx symbols will be replaced with the tensorial components The default saving of variables in the output files are only eto and sig Specify other saved variables in the inp file Example x behavior linear_viscoelastic KO 42261 904761 K_inf 13500 0 GO 29098 360655 G_inf 0 xshear tau 0 4321660 omega 0 2324006 xshear tau 9 070154 10 7 x behavior linear viscoel 10 8 omega 0 1891879 shear tau 27 61690 omega 0 2665674 shear tau 102 8596 omega 0 3
93. Interface files automatic_time 2 8 automatic time Description This command is used to give parameters controlling the time stepping based on the conver gence and gross change in material variables Variables which control the time step may be taken from the FLUX or VINT data members Note This automatic time stepping controls the global convergence stepping which means that if there is a local divergence or violation of a limit variable the current increment will be thrown away and the global solution time step reduced One can use the auto_step beahvior modifier to control local only automatic time stepping see page 14 8 This command depends on the capabilities of the FEA solver used ABAQUS allows the material to control the next time step to be used while Cosmos and Ansys only allow the material to sub cut the time step by 2 Syntax The syntax for the automatic time stepping control is the following xxxautomatic_time security factor divergence div limit varl vall varN valN where the following parameters are used factor real value giving the maximum time increase factor for a well converged time step The value must be greater than one div dividing factor for a diverging increment The global solution step will be re run with a time step smaller than the rejected one by this factor varl a character name of a variable of the problem This can be from the FLUX or VINT variables
94. Material amp Structure Analysis Suite Materials manual Version 8 6 Z set 8 6 is distributed by Transvalor S A Centre des Mat riaux B P 87 91003 EVRY Cedex France http www zset software com support zset software com Neither Transvalor ARMINES nor ONERA assume responsibility for any errors appearing in this document Information provided in this document is furnished for informational use only is subject to change without notice and should not be construed as a commitment by the distributors Z set ZebFront Z mat Z cracks and Zebulon are trademarks of ARMINES ONERA and Northwest Numerics and Modeling Inc ARMINES and ONERA 2015 Proprietary data Unauthorized use distribution or duplication is prohibited All rights reserved Abaqus the 3DS logo SIMULIA CATIA and Unified FEA are trademarks or registered trademarks of Dassault Syst mes or its subsidiaries in the United States and or other countries ANSYS is a registered trademark of Ansys Inc Solaris is a registered trademark of Sun Microsystems Silicon Graphics is a registered trademark of Silicon Graphics Inc Hewlett Packard is a registered trademark of Hewlett Packard Co Windows Windows XP Windows 2000 and Windows NT are registered trademarks of Microsoft Corp Contents Introduction Ll What s in this manual 1 3 Conventions sa ea uce a a a a ene as Bee I5 Introduction to Z mat ooa a La System Requirements 2 2
95. Maximum number of restarts Default value is 0 ie no restart reflection Value of the reflection parameter a default value is 1 0 expansion Value of the expansion parameter b default value is 2 0 contraction Value of the contraction parameter c default value is 0 5 lag mult_step Step size used to update the penalty parameters associated to the opti mization constraint if gi gt 0 then A step gi Default value is 0 01 constraint tol Constraint violation tolerance value ie constraints are verified when gi x lt constraint_tol and the corresponding design point x retained as feasible De fault value is 0 001 Z set Non linear material 16 29 amp structure analysis suite optimize levenberg mar 16 30 Optimize levenberg_marquardt Description This optimizer Leve44 Mor 77 is a robust first order method uses gradients of the objective function specially meant for least square minimization It does not explicitly handle constraints The least square norm of the distance between simulation and experience can be written 1 F Ho y W F a 9 5 3 where f x is the N x 1 vector of simulations y is the N x 1 vector of experiments and W is the positive diagonal N x N weight matrix The first and second derivatives of F x are gradF x J W f x y 4 N hessianF JTWJ gt Wii fi x y hessian f 5 i 1 where J is the n x N matrix composed of gradf
96. P INTERACTION o 13 92 STRAIN NUCLEATION 13 93 THERMAL STRAIN aoaaa e 13 94 Modifiers 14 1 MODIFIER cuidas Eke ES a hae AEE RE EEG 14 3 MODIFIER lagrange polar 2 2 e 14 5 MODIFIER lagrange_rotate 2 ee 14 6 MODIFIER plane stress ooo ee 14 7 MODIFIER auto_step oaa ee 14 8 MODIFIER runge jacobian 2 0 0 02 02 ee ee ee 14 10 MODIFIER runge_rollover oaa ee 14 11 MODIFIER perturbation 0 0 0 000000 eee eee 14 12 MODIFIER explicit o 00200202 eee ee ee 14 13 MODIFIER bifurcation sp sdnso ese mu 04 0 408 ee ed 14 14 Model Simulation 15 1 Model Simulation 15 3 dig Ti AAA III 15 4 EKE A A ee A OS Eee Ge 15 6 Optimization 16 1 Introduction dado REMADE eR oe eke wow bes 16 3 da o feros ie 2k Re ek A HO AG a eR a a 16 5 coi e m ok amp 0 8 Ave ook amp A Ee A ee 16 10 compare t file file ace a so ae OR aa a 16 12 x compare 1A ble ane ea ee res Rw 16 14 kcompare ifuncfile a 16 15 RCS GRU sa Ab re ade hak se RK We es eS Ae ted 16 16 kcomparison_constraint ooo e a a 16 17 FEOS aa i E HA a E a E e lk SW et wa Be Y 16 18 A O amp ove ce Mo a ok WP ce ok ck ads oe bots 16 20 ale x tng a aim E a Be Seok He a ee MeSH tpt hi dad oR A Be A TU a oe he a id ontimize neldermead o oo aa a optimize levenberg marquardt aooo a optimize evolution e a e optimize augmented_lagrangian a Optimize single s o b a a
97. ROPIC_DAMAGE scalar 0 0 0 002 00000084 13 5 ANISOTROPIC_DAMAGE elastic_tensorial 0 13 6 COEFFICIENT e 2622444 04 48464 24 kk GSR SER OR E 13 7 COEFFICIENT MATRIX 0 0 0 0 00000 000002 eee eee 13 9 CONDUCTIVITY s eop i ioa nace h a a aa e a a a aa ie e 13 13 CRITERION 00 6 2 2 4 ee aa a ae Be a 13 14 CRITERION amnisotropic ee 13 15 CRITERION bron gt gt ss 1 nesre rrira s sy Eba 13 16 CRITERION castro Sl CRITERION bill ce eee eo ee eH e Gok Ee o a a 13 18 CRITERION karafillis_boyce 0 02 0 00020002000 13 19 CRITERION linear_drucker_prager o e o 13 20 CRITERION mises e s cu aooi k ea i a a a o A 13 22 CRITERION modified nouailhas 000 13 23 CRITERION nouailhas 2 2 o 13 24 CRITERION ratio 13 25 CRITERION tensile Mises 13 26 CRITERION tresca gt lt sororis repr isser disaksian 13 27 CRITERION unsym 2 a p a ee 13 28 CRITERION 2M1C 2 aaa 13 29 CRYSTAL KINEMATIC 2 aaa 0 eee eee 13 30 CRYSTAL_ORIENTATION 0 0 0 0 0 00 00 000022 eee 13 31 DAMAGE c 2 amp 44 4 3 a natia ape A Oe ee Bw mh ee eS 13 35 DIRECT_KINEMATIC 2 0 0 0 0 0000002 ee ee ee 13 38 DIRECT_KINEMATIC asaro aoaaa a ee 13 39 DIRECT_KINEMATIC non symmetric aaoo a 13 41 ELASTICITY ciao te ha Bie de e ee OE e a a iaa 13 43 FLOW oes rmac io e rs a eee o es ed 13 44 FLOW TURCO ee ete et A a Sk Oe ee a a 13 46 FLOW esell coc
98. T 2 plastic deformation gradient yes gamma V resolved shear strains yes alpha V back strains on slip system yes crss V current resolved shear stress yes Example behavior drucker_prager kelasticity isotropic young 2 25 poisson 0 125 isotropic constant RO 0 0011547 x xflow norton K 1 e 6 n 2 criterion linear_drucker_prager friction_angle 20 0 dilatation_angle 20 0 K 29 xmodel_coef Cdi 1 e 1 Ddi 0 0 Csi 1 e 1 Dsi 0 0 return 11 21 x behavior visco_aniso 11 22 behavior visco_aniso damage Description This model implements a model of viscoplasticity with fully anisotropic coefficients and dam age The model accepts a number of mixed damage components based on scalar or tensorial variables and any number of kinematic variables The later must be chosen from a sub set of the KINEMATIC objects described later in this chapter The compatible models are indicated in the later section Syntax behavior visco_aniso_damage modifier thermal_strain THERMAL STRAIN CO ELASTICITY HO COEFFICIENT MATRIX f low FLOW isotropic ISOTROPIC kinematic KINEMATIC keffective_stress keffective_operator damage ANISOTROPIC DAMAGE m moar closure m ti too t33 tie tog ta scalar_interaction full identity Stored Variables prefix size description default eto T 2 strain tensor yes sig T 2 Cauchy stress yes delta i S scalar
99. TERION gt 13 70 lt POROUS_CRITERION gt rousselier Description The Rousselier model is a thermodynamics model formed by coupling the plasticity and damage through free energy The criterion is defined as below V3J2 h q 01fDexp rx Ox with the coefficients c and D named sigmai and D Although the Rousselier model is very similar to the Gurson model a major point of difference between the two is that in Rousselier model the damage grows under pure shear and the non zero shear deformation occurs under pure hydrostatic pressure due to the shape of the yield function Syntax porous_criterion rousselier coefficients Example A simple example from a test case is given below porous_criterion rousselier Sigmal 200 D 0 85 Z set Non linear material amp structure analysis suite lt POROUS_CRITERION gt lt POROUS_CRITERION gt modified_rousselier Description V3J2 ah pe sa ha a where q2 D and sigma are coefficients named q2 D and sigmal Syntax porous_criterion modified_rousselier coefficients Example A simple example from a test case is given below porous_criterion modified_rousselier Sigmal 200 D 0 85 q2 Z set Non amp structure an 13 71 lt POROUS_CRITERION gt lt POROUS_CRITERION gt zhang niemi Description 242 4 1 5 1 x2 Cy The coefficients for the criterion are Ao Xe and fs named lambda0 chi_c fs Syntax
100. _damage kclosure 1 e 3 1 e 3 1 e 3 c0 orthotropic c11 c22 c33 c12 c13 c23 c44 c55 c66 N 5662e11 2 5662e11 2 6887e11 6 0439e10 8 2435e10 8 8 8 8 2435e10 5e9 5e9 5e9 damage scalar eta 1 0 5e 3 5e 3 5e 3 11 22 33 12 23 31 the model is coded in Aniso_damage z in the source dir zZfrontBehavior Z set Non amp structure a behavior aniso_ damage an 1 0 0 K_coeffs 1 0 0 0 0 0 0 7 0 0 0 7 g gl YO 1 69e4 Yc 1 6e5 delta_c 0 6 damage scalar an 0 1 0 K_coef s 0 1 0 0 0 0 0 7 0 7 0 0 g gl delta_c 0 6 YO 1 69e4 Yc 1 6e5 damage scalar an 0 0 1 K_coef s 0 0 1 0 0 0 0 0 0 7 0 7 g gl delta_c 0 6 YO 69e4 Yc 1 6e5 BR damage elastic_tensorial Q diagonal Qi 1 0 Qd diagonal Qdi 1 0 K_coeffs 1 1 1 0 7 0 7 0 7 0 5 0 5 0 5 g gl delta_c 0 6 YO 0 0 Yc 1 6e5 xxxreturn 11 6 Z set Non linear material amp structure analysis suite x x xbehavior becker_needleman behavior becker_needleman Description This model is a direct implementation of the viscoplastic porous damage model given by R Becker and A Needleman Effect of Yield Surface Curvature on Necking and Failure in Porous Plastic Solids J Appl Mech v53 491 498 1986 B 0 X B U B 3B B B 1 O 2 oF 20p 0a Where f is a modification of the porosity f so that if f lt fe f f and otherwise a fet 1 q1 fe f
101. a3 The strain is then defines as 11 01 s E22 A265 33 A3Es we must then have a a2 a3 3 13 91 lt SLIP_INTERACTION gt 13 92 Description The SLIP_INTERACTION object is used to model the inter system hardening of the isotropic In the absence of this option only self hardening is taken into account hi 1 and all other interaction parameters equal 0 tal potential the maximum number of interaction parameters is given in the section on lt CRYSTAL_ORIENTATION gt page 13 31 As an example the hardening matrix describing the variable for single crystal models lt SLIP_INTERACTION gt inter system hardening for octahedral slip systems is shown at the end of this section Note hardening between different crystal potentials for instance between cubic and octa hedral systems can be taken into account through the INTERACTION object see page 13 52 Syntax The following models are implemented for slip interaction in single crystals CODE DESCRIPTION slip standard Zebulon form slip This is the standard Zebulon format for full slip interactions described by Meri91 The coupled radius R for system i is Ri Ro X his Re Ro k 1 where Ri is the radius of slip system k as option e g Ro Q 1 e Bd Ba Bc Db Dc Da Ab Ad Ac Cb Ca Cd calculated from the isotropic variable h1 h2 h2 h4 h5 h5 h5 h6 h3 h5 h3 h6 h2
102. ables which can have deviatoric and spherical components The source for this model can be found in the developer manual The model uses elasticity criterion flow and isotropic classes An interesting use of this model is with a non associated criterion such as linear_drucker_prager There is however no such requirement so the model could be used with von Mises as well Any number of kinematic hardening variables are possible For kinematic 7 the back stress X is calculated as follows Xs Cs Os Xa Ca Qa Xi Xaq 0X 5 Noting that different back stress moduli are available for the two components The evolution of back stress is also separated in two components De a aX i s i mo Da A ln Xu ma E Ca a Note here that n is the criterions normal and not SL Syntax The syntax is in standard ZebFront format with a number of standard sub classes x xbehavior non_associated elasticity lt ELASTICITY gt flow lt FLOW gt isotropic lt ISOTROPIC_HARDENING gt kCriterion lt CRITERION gt x model_coef Cd1 COEFFICIENT Csi COEFFICIENT Ddi COEFFICIENT Dsi COEFFICIENT there is only a Runge Kutta implementation in Z8 0 this model will be implemented in gen_evp in Z8 1 11 20 Stored Variables behavior non associated prefix size description default F UT 2 deformation gradient yes sig T 2 total Cauchy stress yes Fp U
103. al culation of a full consistent tangent operator runge kutta only ZebFront models for example In this case global convergence of FE equilibrium iterations may be greatly improved How ever the increase of global time step allowed by this option is somewhat counter balanced by an increase of local integration cost for small strain 3D formulations one additional inte gration is needed for each perturbation of the 6 individual components of the symmetric Ae tensor Syntax kkbehavior behavior name perturbation perturbation_controls perturb pert symmetrize one_sided two_sided where the previous optional command are described hereafter perturb can be used to set the value of the perturbation parameter default value is pert 1 e 9 symmetrize this command activates symmetrization of the tangent operator default is no one_sided two_sided those commands control the way the input strain tensor is perturbated to calculate each column of the tangent operator In the two_sided mode default two integrations are needed to compute each column of the tangent perturbation of each e component by a value of pert while the one_sided option only needs one pertur bation by a value of pert in this case Example x behavior norton perturbation return 14 12 Z set No amp structure lt MODIFTER gt lt MODIFIER gt explicit Description This behavior modifie
104. allowed default 10 security factor set the maximum amount the step can enlarge e g 1 2 min_dtime takes a real value to set the minimum dtime before giving up and calling for a global divergence use_last_tangent use the last computed tangent matrix instead of averaging the sub step tangents re_ solve re solve the step initializing with the sub step result increment possibly leading to better global convergence forceit force sub stepping primarily for testing the process limit takes a list of integrated variable names VINT and maximum change values to ensure that any sub step will not have any greater increment than this one full_step_jacobian use the resulting computed full step variable increment to compute a new tangent matrix in place of the averaged sub step tangents Example The following is a typical example behavior gen_evp auto_step kelasticity isotropic young 170000 0 poisson 0 30 plane_stress potential gen_evp ev flow norton n 6 0 K 800 kinematic nonlinear Xi C 3000 0 D 50 0 kinematic nonlinear X2 C 3000 0 D 50 0 isotropic constant RO 10000 Z set No amp structure lt MODIFTER gt stepping_controls divergence 2 50 min_dtime 1 e 8 limit evcum 0 01 return Note For finite strain applications this will only work in the order as in the following example behavior gen_evp lagrange_rotate auto_step Z set Non linear material
105. alue of can therefore be iteratively adjusted to guarantee that the linearization performed is still valid and that progress in terms of the objective function is made The Levenberg Marquardt algorithm proceeds as follows Z set Non linear material amp structure analysis suite xoptimize levenberg mar 1 k 0 A Tk T0 2 Solve 9 for x41 3 If gradF xK41 lt gmin or F x41 lt fmin or number of F evaluations iter or k 1 zg stepmini stop 4 If F k41 lt F xx Ak 1 Ax nu k k 1 goto 2 5 f F k41 gt Flee Ak Ag nu goto 2 Gradients are calculated by finite differences Min and max bounds on the optimization variables are taken into account by projection into the feasible domain Syntax The following adjustable parameters are allowed in the convergence section perturb Magnitude of the perturbation in percent of the normalized design variables used to calculate gradient through finite differences Default value is 0 5 percent lambda0 Initial value of the A parameter which controls the algorithm Smaller values when closer to the solution lambda_max Maximal value of lambda Default is 1 e 07 iter Maximum number of function F evaluations before terminating Default is 100 nu cutting amplification factor of the lambda parameter on reduced or increased function value It was originally suggested to have 10 for this parameter default value A factor of
106. ample A simple example of purely viscoplastic material follows Because the yield radius RO is zero the material is always flowing The use of elasticity in this case is also a pseudo elasticity attempting to model a purely viscous material in a displacement based FEA model The higher the modulus the more approaches Eth behavior gen_evp elasticity isotropic young 100000 poisson 0 48 potential gen_evp ev isotropic constant RO 0 0 flow gsell e0 1 e 5 K 40 0 w 65 h 0 75 n 1 75 m 0 08 return Z set Non linear material amp structure analysis suite 13 47 lt FLOW gt 13 48 lt FLOW gt hyperbolic Description For this law the hyperbolic sin function is applied to the power law of overstress and in turn taken to a second power The flow is written A eps0 sinh lt f K gt with f positive The coefficient K must be non zero and the coefficients n and m default to one The flow law is fully implemented for Runge Kutta or the standard theta method It cannot presently be applied to the reduced integration Because the sinh can blow up with large values of f K a cutoff limit on that ratio is applied This can be user adjusted by entering a real value for cutoff in the law s coefficient section The default value is 10 0 which would result in an unrealistically high strain rate for this type of model Syntax The flow law accepts coefficients eps0 K n and m as out
107. ariable which is the summation of a brittle mode based on maximum principal stress values and a fatigue damage model like that described by Lema85b The scalar damage value is however applied to an anisotropic closure treatment utilizing 2 separate closure opening criteria The use of a scalar variable is an approximation assuming close to cyclically proportional strain paths The closure point is based on a strain criterion which shifts into compression as damage accumulates and the opening criterion is a sole function of the principle stress being positive Both terms are smoothed using an interpolation function with adjustable width Note that the opening and closing combined with the general difficulties of damage based models can lead to convergence difficulties The damage effects here are not really meant for predicting true failure but rather are needed to predict the LCF hysteresis loops Other methods of cast iron modeling are available using the cast_iron yield criterion and non symmetric kinematic hardening model Syntax The basic input syntax here is k kbehavior cast_iron thermal_strain lt THERMAL_STRAIN gt elasticity lt ELASTICITY gt isotropic lt ISOTROPIC_HARDENING gt x model_coef With the following coefficients available K n viscoplastic Norton law coefficients for f K Q1 D1 nonlinear Armstrong Frederick kinematic hardening Q1 is the saturation stress level and D1 is the satur
108. ation method This command is equivilent to that for a FEM material Currently only the explicit integration i e Runge Kutta methods are supported by the simulator rotation defines a material rotation which will be affected on the gradient flux combina tion for tensorial variables before and after the loading steps Note that the rotation defines the transition from global to material as in the finite element method continuedNote In the event of rotation and tensorial integrated variables the integrated variable values which get output are in the material coordiante system This will change in the future sometime so tests and examples which depend on that will change Z set Non linear material 15 13 amp structure analysis suite x simulate xtest output 15 14 output Description This option is used to create an ASCII file with the output values from the simulation Output is in column format with a heading of the variable names requested commented with the character Several output files may be specified while the default file name is the problem name without suffix appeded with test Syntax The yield surfaces to output are defined in the following manner output filename variable_list file filename variable_list sido precision digits small epsilon frequency options limit_output_var function mm nr mn Ma 1 variable_list a list of variables t
109. ation rate Any number of these terms may be added but both coefficients must be entered always and the numbering is sequential from 1 to N dmax dmax_b dmax_f damage limits preventing total failure e 0 e E Brittle mode damage a b A r Simple cumulated plastic strain fatigue mode damage delta e delta s Controls for the width of closure in strain dimensions e of 0 004 recom mended as a start and damage opening in stress dimensions s of 25 recommended deltad Shift parameter for progressively compressive closure as damage increases The closure point is dg x d coupled Set to 1 0 in order to have damage coupling to the kinematic hardening Z set Non l erial amp structure an x behavior cast_iron Stored Variables prefix size description default eto T 2 strain tensor yes sig T 2 Cauchy stress yes eel T 2 elastic strain yes eps_me T 2 mechanical strain yes eps_th T 2 thermal strain yes evi T 2 viscoplastic strain yes evcum S inelastic strain equivalent yes df S fatigue damage yes d_b S brittle damage yes Dsum S total effective damage yes alpha i T 2 kinematic hardening variable yes Example The following is a short example material file for gray iron behavior cast_iron kelasticity isotropic young 130000 poisson 0 26 yield isotropic constant RO 150 model_coef coupled 1 0 viscoplastic K 400 n 4 kinematic Q1 300 0 Di 80 brittle damage e 1 0 expon
110. avior instance a possible rotation defintion use mat defined in Alu mat for phase_id 1 behavior umat behavior umat Description This behavior is used to run a UMAT function within Z set It can be used to run Z mat using the ABAQUS interface within Zebulon or can be used to run a real Fortran UMAT within Z set which is perhaps very useful to be able to run the UMAT within the simulation module Syntax behavior umat constants num coef finite_strain skip_param cmname mat name umat_file fname depvar num sdv model_coef C value Example The following example shows a umat material definition which is linked in fact to the Z mat file on the right By default in the absence of a umat_file definition the umat behavior uses a Z mat one behavior umat suppress_temperature cmname visc3_zmat mat material depvar 2 file visc3_zmat mat coefficient integration theta_method_a 0 5 1 e 9 120 masvol 8 1e 9 external_storage return file oo store vars evi22 evcum buffer_size 3 behavior gen_evp kelasticity isotropic young 260000 poisson 0 3 potential gen_evp ev criterion mises flow norton n 7 0 K 400 kinematic nonlinear xi cC 30000 0 D 500 0 xisotropic constant 10 25 Z set Non amp structure a x behavior umat RO 130 0 return 10 26 Z set Non linear material amp structure analysis suite Chapter 11
111. ax understood by this potential is summarized below kpotential associated name flow lt FLOW gt flow lt RATE_VAR_FLOW gt criterion lt CRITERION gt kinematic lt KINEMATIC gt name kinematic lt DIRECT_KINEMATIC gt name isotropic lt ISOTROPIC gt var_coefs store_all Example The example given for the gen_evp potential may be run with this potential by only changing the potential name to associated behavior gen_evp elasticity isotropic young 260000 poisson 0 3 potential associated criterion mises flow norton_k_variable n 7 0 kinematic nonlinear A1 15000 0 Bp 30 0 isotropic constant RO 130 0 K non_linear_recovery Z set No amp structure lt POTENTIAL gt RO 200 A 0 0 Rp 1 0 parameters A N vdot0 sig0 m Bo1 B02 return 8125e 3 0e 11 PRRERPPRPRPA Y o ooo Z set Non linear material amp structure analysis suite 13 75 lt POTENTIAL gt lt POTENTIAL gt coupled recovery This potential provides a slight modification on the gen_evp potential in that it couples the back stress effect in recovery The kinematic variables are the only ones affected in this coupling The evolution for each kinematic variable j will use the following form Xj Amy 0 A Xj wj X X X 13 76 Z set Non linear material e amp structure analysis suite lt POTENTIAL gt lt POTENTIAL gt delobelle Description De
112. ber of other kinematic hardenings with the separate terms plotted below behavior gen_evp elasticity isotropic young 69000 00 poisson 0 3 potential gen_evp2 ev store_all criterion mises isotropic nonlinear RO 340 0 b 900 0 Q 210 0 kinematic nonlinear 1_ C 187500 D 1250 0 kinematic armstrong_frederick 2_ C 11250 0 D 150 0 kinematic linear 3_ C 1000 0 kinematic asaro 4 C 56250 0 D 750 0 return asaro1_tm asaro1_tm 500 T T T T T 200 T 7 T T T T T T T asaro1_tm test using 2 3 4 5 6 7 8 asaro1_tm test using 1 2 gt 400 i La J asaro1_im test usi es 150 f asaro1_tm test using 4 6 300 100 200 100 50 F ob 100 50 L 200 F 100 F 300 F 150 F 400 500 1 L L L i 200 1 i 1 L L L j 1 1 0 015 0 01 0 005 0 0 005 0 01 0 015 0 005 000 008 00B 001 0 0 000 002 008 0090 005 13 40 lt DIRECT_KINEMATIC gt lt DIRECT_KINEMATIC gt non_symmetric Description This kinematic hardening model provides asymmetric behavior between tension and compres sion as recommended for cast iron materials Hjel94 Jose95 This model takes the tensile coefficients for computing X if the trace of the actual stress 1 o is greater than the I1_trans value The evolution is therefore 3 D a A In a if use_alpha is set 3 D X C A In esa if use_x is set where the coefficients C and D are either C D or Ce De dep
113. binaries and shared files The install location will henceforth be referred to as the Z7PATH In the user compiled case the LS Dyna executable will be located in a common library directory With the shared library method used with 971 it will be necessary to specify the location of the LS Dyna executable via the Z7_DYNA_ROOT environment variable There are some test cases in the Zlsdyna directories in the validation test database For LS Dyna the Z mat interface file name is standardized to be umat41 or umat42 Note that because of the need to have an automated testing environment with all the LS Dyna validation cases in the same directory the testing program copies a Z mat interface file prob zmat to Z set Non linear material amp structure analysis suite 8 3 Zl1sdyna interface umat41 where prob is the basename of the prob k input before running Zlsdyna In fact this behavior is a convenienace option of the Zlsdyna command with the auto switch One can equivalently set the environment variable Z7_DYNA_AUTOCOPY to be equal to yes Input file change Like all the other Z mat interfaces there are some lines in the user s input deck the k file which must be changed to indicate that a user material is being used and to specify the amount of state variable storage The following is an example MAT_USER_DEFINED_MATERIAL_MODELS mid ro mt Imc nhv iorth ibulk ig 1 8 930 41 2 40 0 1 2 ivect ifail ithermal 0 0 0 pi p2
114. blems such as powder compaction and foam plasticity 3C Jo FR 0 where C and F are the coefficients named C and F Because the ratio between the deviatoric and pressure sensitivity is determined by the C and F coefficients we can get great flexibility by making these coefficients depend on the porosity state variable f A typical limiting case is that the material should behave in a fully deviatoric way at the fully dense condition when f 0 then C 1 and D 0 and similarly when the material is fully void there should only be pressure dependence when f 1 then C and D 1 Syntax porous_criterion elliptic coefficients Example A simple example from a test case is given below porous_criterion elliptic F f 0 0 5 La Cf 1 0 dd Z set Non linear material 13 65 amp structure analysis suite lt POROUS_CRITERION gt 13 66 lt POROUS_CRITERION gt elliptic_aniso Description This porous potential allows for a very general anisotropic anisotropic porous plastic material Anisotropic influence on the direct stress components for the ordinarily trace operator for the pressure term are replaced with a coefficient factored trace Anisotropic effects in the shear term can be implemented with the generally available shear_anisotropy option in the porous plastic material behavior which replaces the Jz term with an effective anisotropic measure of the shear criterion The potential is therefore
115. cifies a fully qualifies filename for the external storage Note that ABAQUS copies your input problem to a temporary directory so do not use relative path names for this one vars Specifies the variables which will be made available for output Zpreload can be used to determine the variable naming which is required here the Zebulon type names not sdv In the screen or log output the sdv type naming will be printed for example done with material file reading xx real state variables sdv 1 epcum sdv 2 epi22 Example The following lines are an excerpt from a Z mat material input file doghri_st which demon strates the usage of the external_storage keyword The material file can be found in the test database in Z mat umat_v61 external_storage file oo store vars epi22 epcum buffer_size 5000 Z set Non amp structure an Interface files material 2 12 material Description This command marks the definition of the materials in a structure to be studied The behavior of each material is defined in a file with special syntax see the chapter Material Behavior The purpose of this command is therefore to define the material file names associate these files to different element sets and specify other global applications on top of a material model such as rotation of material coordinates or give local integration methods Syntax x material file file standard std file
116. computation of the consistent tangent matrix replacement of the previous one that switches to to mixed integration only when the initial theta_method_a integration fails external wrapper enforcing the plane stress condition for material behaviors that don t handle this case internally activates calculation of a tangent matrix obtained by perturbation of the loading strain increment tensor Global convergence may be inhibited by the addition of the finite strain options especially corotational frame ones In this case it is advised to use small increment steps or automatic time stepping options in the global calculation sequences Large deformation methods Large deformation formulations in Z mat are available for the majority of material behaviors based on corotational transformation of the stress strain problem into an equivalent mate rial referential Corotational formulations are implemented because they are applicable to excepting behaviors with explicitly different treatment of finite strain Z set Non linear material amp structure analysis suite 14 3 lt MODIFIER gt 14 4 material models with tensorial internal variables and anisotropic response without modify ing the local evolution rules Lade80 Description of the models uses the following standard expressions L FF D i L L n L LT 1 2 1 where F is the deformation gradient and L the rate of deformation Bo
117. creating input files and eventually scripting and developing add ons to the software Release Notes Zmaster The basic overview of the software installation instructions and documentation for the graphical user interface Zmaster on all platforms The Zmaster manual also now covers all the base reference chapters such as environment variables user parameters function reference command line programs etc Examples Training This book is essentially the getting started documentation for the software The book describes Z mat simulation optimization material models and the FEA code use The examples cover setup of complete models and are meant to demonstrate the capabilities with relatively simple examples Z mat User commands This summarizes the command file formats and capabilities of the Z mat interface simulation optimization and material files for all of Z mat and Z set Z set User commands This summarizes the command file formats for the FEA related capabilities including meshing FEA solution post processing etc Developer A guide to the user extensible features of the software including scripting ZebFront material model development making plugins and the C programming API Plugins A guide to add on features available Theory Theory manual covering formulations under development Z set Non amp structure an 1 3 1 4 Z set Non linear material amp structure analysis suite Convention
118. croscopic model developed by ONERA for simulating anisotropic de formation of single crystals The model does not accurately represent the individual slip system deformations or their interactions but could be useful for efficiently modeling the basic anisotropic behavior of a single crystal The criterion is written e a a Ty St Shy S33 I gt S118522 S22833 S33511 la Sty S33 53 lg Sty 33 31 with S o X The criterion is associated _ of a Of Ak OF Als n 1 12 R Of Olg o OL da OL da Ola Oo Olg da This criterion is fully implemented such that it will work with any normal gen_evp or reduced_plastic potential with any otherwise valid integration In 2D the 23 and 31 terms are taken as zero 13 24 Z set Non linear material amp structure analysis suite lt CRITERION gt lt CRITERION gt ratio Description This is a classical type criterion which may be useful for some users seeking compatibility with other programs Its usefulness is as a viscoplastic overstress function i e when f gt 0 J E o R Note that R is a radius measure passed in by the controlling behavior or potential object and would normally be an isotropic hardening function The effective stress is likewise determined by the behavior and can include back stress influences etc Syntax The model accepts a single optional coefficient for L named L in order to allow the user
119. d below CODE DESCRIPTION gurson model to capture progressive microrupture elliptic_aniso generalization of the elliptic criterion for general anisotropy elliptic criterion for densification of material elliptic_fiber elliptic criterion for compaction of fibers in a powder matrix fkm NIOT modified_rousselier NIOT rousselier thermodynamic criterion through free energy cam_clay criterion to study the porosity of clay zhang _niemi NIOT The following pages discuss these models in details 13 63 lt POROUS_CRITERION gt 13 64 lt POROUS_CRITERION gt cam_clay Description This criterion is developed to study the porous behavior of clay In literature many modified versions of cam clay models have been developed recently to study the behavior of partially saturated soils Zmat currently inlcudes the basic Cam Clay model 3J5 a 11 3 pe 0 with pe and m coefficients named pc and m Syntax porous_criterion cam_clay coefficients Example A simple example from a test case is given below porous_criterion cam_clay pc ft 100 0 20 1 m 5 Z set Non linear material amp structure analysis suite lt POROUS_CRITERION gt lt POROUS_CRITERION gt elliptic Description The elliptic criterion is a simple ellipse in P q plane and allows a great deal of flexibility in adjusting the pressure sensitivity of plasticity This model can be used for general densification of pro
120. d that the last key ev was used as a pre fix for that poten tials variables Thus one has evcum for the plasticity viscoplasticity in this case multiplier and evi as components of the inelastic strain tensor The variable construction in this model can be represented as shown below lt BEHAVIOR gt lt POTENTIAL gt __ lt FLOW gt gen_evp eget VI evcum VI eel VA evi VA FL gt lt ISOTROPIC gt FL sig GR GR eto lt KINEMATIC gt Vi al1 Potential was lt KINEMATIC gt named ev Vi al2 9 8 Naming conventions Material variables The dynamic nature of the material assembly notwithstanding some conventions are given in the documentation and reflected in the default naming of variables A small summary table of some common names follows CODE DESCRIPTION eto total strain ETO material strain for finite strain This is the integration of the corotational strain measure not the logarithmic strain etc sig Cauchy stress eel elastic strain eth thermal strain evcum cumulated monotonically increasing scalar measure of vis coplastic strain Actually the integration of the viscoplastic multiplier epcum cumulated plasticity equivalent of evcum The naming dif ference is usually only symbolic porosity for porous materials Z set Non linear material amp structure analysis suite 9
121. d the gen evp behavior itself Z set No amp structure lt POTENTIAL gt C 30000 0 m 1 0 D 500 0 M 20000 0 isotropic constant RO 130 0 x x return Z set Non linear material 13 85 amp structure analysis suite lt POTENTIAL gt lt POTENTIAL gt gen evp2 Description The gen_evp2 potential is a modified version of gen_evp with different assumptions of harden ing and variables The potential allows use of DIRECT_KINEMATIC objects and RATE_VAR_FLOW laws which can both have arbitrary numbers of integrated variables and the kinematic law does not limit the calculation of X as a linear modulus function of a Syntax The syntax understood by this potential is summarized below kpotential gen_evp name flow lt FLOW gt flow lt RATE_VAR_FLOW gt criterion lt CRITERION gt kinematic lt KINEMATIC gt name kinematic lt DIRECT_KINEMATIC gt name isotropic lt ISOTROPIC gt var_coefs store_all Example This potential is nominally the same as the original gen_evp potential except for allowing the rate flow type and the direct kinematic types behavior gen_evp kelasticity isotropic young 260000 0 poisson 0 3 potential gen_evp2 ev flow norton n 7 0 K 400 criterion hill hilla 1 hilld 1 hillb 2 hille 1 hillc 3 hillf 1 kinematic armstrong_frederick C 30000 0 m 1 0 D 500 0 M 20000 0 isotropic constant RO 130 0 return
122. d to the fully implicit case default while 9 0 5 may be used to trigger semi implicit integration Example behavior gen_evp runge_jacobian behavior gen_evp runge_jacobian lagrange_rotate 14 10 Z set No amp structure lt MODIFTER gt lt MODIFIER gt runge_rollover Description This definition is an alternative to runge_jacobian see page 11 10 where the mixed scheme described previously is only attempted when a single step theta_method_a implicit integra tion fails to converge Syntax material integration theta_method_a kkbehavior behavior name runge_rollover runge_rollover runge eps norm iter nit min_dtime dtmin return where the optional command runge can be used to enter non default values for the runge_kutta integration method parameters see page 2 13 Default values are eps norm 1 e 3 and no control on the maximum number of runge kutta steps nit 00 or the minimum step size during sub stepping dtmin 1 e 19 Example behavior gen_evp runge_rollover behavior gen_evp runge_rollover lagrange_rotate 14 11 lt MODIFIER gt lt MODIFIER gt perturbation Description OA This modifier triggers the calculation of a tangent matrix EA obtained by perturbation of each component of the input strain increment tensor Ae or AF for finite strain models This particular scheme may be used for material behaviors that don t implement a proper c
123. d with use of the implicit integration However use of an implicit solution allows the possibility of divergence Which approach to use varies greatly with the problem at hand and some experimentation and experience may be required to find the best choice Many of the convergence control options below follow the same syntax as in the Zebulon FEA solver In fact the solution parallels very closely the RVE element but gives improved efficiency and convenience with the other simulation options The current solvers available are as follows CODE DESCRIPTION explicit default explicit solution newton iterative solution Explicit method The solution of mixed loading in the explicit solver requires some additional equations for the model derivative function the function returning rates for all state variables as a function of the current state This discussion applies primarily to the mechanical solution procedure while other simulation models would have a similar formulation requirement Fundamentally because the solver needs to support a mixed combination of stress and strain rates we need to write the complete equation for the rate of change in stress Da to Der 4 1 For rate dependant behaviors in and e are known while for rate independent behaviors the inelastic strain rate is a function of the total strain rate normally of the form n De Eto in i n Da n H 2 This term
124. data about the convergence of the run case evo gnut is an executable file that will automatically plot with gnuplot the main results found in case evo log case evo best contains the best solution found at the end of the run case evo gid contains good ideas that is to say good solutions different from each other classified in two groups feasible solutions that satisfy the constraints and infeasible solutions Parameters Parameters of evolution are given in the convergence section They may be taken from the following population_size Sets the population size of the algorithm i e the number of points that are processed by the algorithm Default value is 50 prob_Xover Sets the probability of crossover a number between 0 and 1 Default value is 0 8 prob_muta Sets the probability of mutation a number between 0 and 1 Default value is 0 2 max nb_analyse Sets max nb_analyse The search is stopped after max_nb_analyse calcu lations of the function Default value is 700 Z set Non amp structure an 16 33 optimize evolution max no progress Sets max _no progress The search is stopped after max_no progress cal culations of the function without improvement Default value is very large making it inactive no_records Sets the number of outputs recorded in the file case evo log This is the number of points that will be ploted then with the command case evo gnut Default value is 30
125. del and what is available for output Principally all material objects behaviors and their sub component classes have the pos sibility of the following variables grad is the gradient or primal observable input variable flux is the flux or dual output variable Normally thermodynamically conjugate with the grad var int integrated state variables These define the current state of the material and are the subject of the integration method Normally the more var int variables the higher the cost of local integration var aux auxiliary variables normally used for output or maintaining state information on a total basis secondary to var int ext param External parameters These are imposed using parameter statements in Zebulon or with field variables in other codes coefs material coefficients Can depend on any of the above Note however that the integration method or implementation restrictions can limit such dependence Each variable is assigned a name but unlike other codes where the relationship between model options is hard coded the naming scheme is not known a priori Much of the final naming is up to the user The example on the next page demonstrates how the names are constructed Variable attributes When asking for specific output of the material variables some additional attributes are available These are summarized as follows CODE DESCRIPTION scal fabs absolute value of scalar tens mises v
126. ding to a user defined function of p continued 13 54 Z set Non linear material amp structure analysis suite lt ISOTROPIC gt Only the laws with an internal variable may have static recovery and be used in state interac tions Isotropic hardening is available with positive values of the Q or H parameters depending on the model while softening occurs with negative values of these coefficients The saturation rate coefficients b are necessarily positive All parameters may have the normal dependencies through the COEFFICIENT mechanism see page 13 7 constant This gives the radius as a single coefficient RO linear or iso_linear Law with initial radius and a linear evolution depending on the cumulated inelastic strain p i e R RO Hp and using the coefficients RO and H power_law Gives a power law evolution according to R Ro K eo p with the coefficients RO K e0 n and p the cumulated inelastic strain Negative values for e0 are set to zero The case n lt 1 with ey 0 gives an infinite derivative at the onset of inelastic deformation and is therefore not allowed Use a very small value for e0 instead by_point Gives the isotropic curve as input by a list of points see the example The first column should be sigeq and the second the cumulated plastic strain equivalent iso table Gives the isotropic curve as input by a list of points directly in a table see example When the current value of
127. djustable parameters are allowed in the convergence section iter Maximum number of function f evaluations before terminating Default is 100 Note that this doesn t include function evaluations associated with the line search procedure perturb Magnitude of the perturbation in percent of the normalized design variables used to calculate gradient through finite differences Default value is 0 5 percent r0 Value of the penalty parameter r Default is 1 0 aug_conv Convergence parameter for dual problem based upon the relative variation of design variables Default value is 1 e 7 bfgs_conv Convergence parameter for the inner unconstrained optimization problem based upon the relative variation of design variables Default value is 1 e 7 oned conv Convergence parameter for the line search procedure Default value is 1 e 7 gradient tol Additional convergence parameter for the inner unconstrained problem based upon the gradient of the lagrangian function Default value is 1 e 7 Z set Non linear material 16 35 amp structure analysis suite optimize augmented lagrangian constraint tol Constraint violation tolerance value ie constraints are verified when gi x lt constraint_tol and the corresponding design point x retained as feasible De fault value is 0 001 16 36 Z set Non linear material amp structure analysis suite Description optimize single xoptimize single single is not an optimi
128. e A Makefile can ease the work of cleaning out a lot of secondary files but more impor tantly it is a very good way to clean those files without the risk of deleting important files by mistake I RF always set up a makefile more or less as follows all clean Zclean a rm f best Remember to use tabs for the target lines to clean the directory one then issues make clean Z set Non linear material 16 7 amp structure analysis suite xoptimize e It s helpful to have the experiment reference files is a centralized location as shown above but instead of using absolute path names use relative ones In trial2 for example an experiment file can be accessed as exp_files exp1 dat In this way the project can be moved without everything breaking To start a whole new iteration then one just copies the BasicIdentification directory elsewhere and the work starts this works in Win32 platforms the same 16 8 Z set Non linear material amp structure analysis suite Example This example is from EXAMPLES MAT Identify in738 STEP1 the material definition in738 tmpl coefficients young 14965 n n K K n2 n2 K2 K2 C1 C1 Di D1 RO 80 0 return 0 0000 optimize levenberg_marquardt convergence perturb 0 lambda0 5 iter 6 06 0 0 zrun Zrun Q S simulate x files in738 x values kauto_init_from_file levenberg best K 700 n 4 47 K2 500 n2 35 Ci 290 Di
129. e Chaboche model is described through a scalar variable A which characterizes the relative crack opening a Se Ey i where x x if x gt 0 and x 0 if x lt 0 With respect to the interface normal 7 un U n unt and dy y denote respectively the normal and shear opening displacements and y and r the corresponding maximum allowable values of their norms The damage variable Amar which is the maximum value of reached up until the current instant increases from 0 no damage to 1 for a broken element The normal and shear components of the cohesive traction T i e Ty 7 it n Tyr and Tr T Tw are defined by UN gt it 27 es TN Sy E Omas Tr ant Amaz F A g Ema nol 1 _ A 8 with a a constant representing the relative magnitude of Zr with respect to Ty Cmax the maximum stress allowable by the element and K and n model parameters When A lt 1 e 8 the finite values of the cohesive traction and the consistent matrix are guaranteed by the parameters df_0 and dfd1_0 For the compressive case where uy lt 0 the normal component is modified to UN Ty ac r 0 9 N with a a penalization factor In the literature a usually is at least 10a Figures 3 illustrates the typical response of the cohesive zone model under specific loads with the parameters as given in the example Syntax behavior chaboche_debonding sigmax Omar deltan n deltat 0 alpha a alphac
130. e an 13 11 lt COEFFICIENT_MATRIX gt y1212 110615 0 xelasticity young T 200000 0 200000 1000 poisson 0 3 elasticity transverse El 115000 Et 8500 Glt 4500 nult 0 32 nutt 0 40 13 12 Z set Non linear material amp structure analysis suite lt CONDUCTIVITY gt lt CONDUCTIVITY gt Description Thermal conductivity is available in istropic and anisotropic forms Conductivity acts much like the elasticity matrix does in mechanical problems except the thermal behavior accounts for direct coefficient variations with respect to the temperature g kVT Syntax conductivity type The following forms are available isotropic k 0 0 k 0 k 0 0 0 k where k is the only coefficient anisotropic ki 0 0 k 0 k2 0 0 0 K3 where the coefficients k1 k2 and K3 are to be entered Z set Non linear material 13 13 amp structure analysis suite lt CRITERION gt lt CRITERION gt Description The criterion object is used for specifying the calculation of an equivalent stress to be used in plasticity and viscoplasticity behavior models for each potential in a gen_evp material The criterion may also be used for determining the flow direction and in hardening evolution models depending on the application Syntax The syntax to specify a criterion object will consist of giving the keyword for a particular criterion desired followed by a list of appropriate coefficients
131. e command PLESOL SVAR5 1 Note With user materials in ANSYS the solver is by default set to not extrapolate integration point stresses to the nodal points In fact ANSYS only does this extrapolation by default for linear materials while most other codes assume that a least squares fit extrapolation method should be done in all cases In order to activate extrapolation the following lines can be used before the SOLVE command is issued ERESX YES With the Z set RST file reader direct integration point visualization is supported so unfortu nately there is no refined solution for this issue Z set Non linear material amp structure analysis suite Chapter 5 Z mat MSC Marc 5 1 5 2 Z set Non linear material amp structure analysis suite Zmarc interface Z mat MSC Marc interface Description The command described in this chapter allows to use a Z mat behavior within a MSC Marc analysis The interface with the Z mat library is implemented by means of the uvscp1 Marc user subroutine The choice of uvscp1 to build the interface against other candidate subrou tines available to implement user materials has been motivated by its flexibility Note however that Zmarc capabilities are by no means restricted to time dependent creep behaviors Syntax Zmarc j problem run_marc options gt where problem dat is the name of an MSC Marc input data file The Zmarc script is a simple copy of the standa
132. e the rrate command is given with one or more strain rates then the default value is 1 e 6 times the average of the specified strain rates On the other hand if the eps command is given but the rate command is not then the actual value is eps If the eps command is given while the rate command is given without specifying any strain rate then the actual value is 1 e 12 times eps Finally if the eps command is given and if the rate command specifies one or more strain rates then the actual value is eps times the average of the strain rates Optional rate values for an equipotential surface If more than one value is given surfaces will be placed in the same file with two blank lines between them The default is zero find offset This command is used to find the surface when the current position is outside of it A large rate value will be used to hopefully expand the surface such that the current position is inside and an average of that surface will be used to estimate the center An optional real value following the command sets this large rate factor while the xoffset default is quite arbitrarily 1 0 Allows setting the actual offset flux variable the estimated difference between current position and yield center in place of the automated method find_offset not recommended Each component of the flux tensor should be specified Example yield_surface yield_find_offset test degrees 5 0 factor 100
133. e the calculation of the coefficients C for the kinematic hardening and C12 kinematic interaction for special forms of the interaction matrix e g zero determinant Z set Non amp structure an 13 89 lt POTENTIAL gt lt POTENTIAL gt z6 gen evp This potential gives hardening variable evolution in terms of the un coupled internal state variables and not as a function of the associated forces The criterion still includes the coupled terms of course This type of interaction was given in versions 6 and below In the case of no interaction this potential is identical to the gen_evp potential Example 2 2 Xx gCX1EX1 zO imax 2 2 Xx2 gj CX22X2 3 Cint OXI but the evolution of the internal variables has no coupling The evolution equation for a nonlinear kinematic hardening variable is changed to Min n Da 13 90 Z set Non linear material amp structure analysis suite lt SINTERING_STRAIN gt lt SINTERING_STRAIN gt Description The mechanisms of sintering may be represented by a sintering strain s Syntax type anisotropic al COEFFICIENT a2 COEFFICIENT a3 COEFFICIENT model coefficient COEFFICIENT The replacements available for type are the following CODE DESCRIPTION non_linear f A f J coefficients A n foo noms A n f_inf The option anisotropic permits to enter a non isotropic strain with the use of the three coefficients a1 a2 and
134. e user routines in mpc f The user can override the default UMAT interface as well by modifying the file Z7PATHlib Zmat mech sd c and using the UF command switch Z set Non amp structure an User additions Z set Non linear material 3 16 amp structure analysis suite Example Example This is an example material file which can be used with Z mat Note that all input is case sensitive This example has the material definition in the file e3danis The following lines are the material related entries for the ABAQUS inp input file MATERIAL NAME e3danis DEPVAR 20 USER MATERIAL CONSTANTS 1 0 0 SOLID SECTION MATERIAL e3danis ELSET A1 Note that this syntax is very sensitive to positions and connectivity Commands are not case sensitive but filenames may be The command DEPVAR allocates in ABAQUS storage for the material variables at each Gauss point There is no way to dimension this quantity from the UMAT routine so the user is obliged to enter the correct number corresponding to the material model used Information concerning this quantity will be printed to the log file generated by the ABAQUS output material integration runge_kutta 1 e 3 1 e 3 behavior gen_evp thermal_strain isotropic alpha temperature 2 0e 06 0 1 1 0e 06 1000 1 xelasticity isotropic young 200000 poisson 0 25 potential gen_evp ev criterion mises flow norton n 4 0 K 500 kinematic nonlinear x1 C 10000
135. e yield radius is noted here to be the onset of plasticity and not the engineering yield stress It may thus be found to be significantly lower than expected Syntax The syntax to specify a isotropic hardening object will consist of giving the keyword for a particular law desired followed by a list of appropriate coefficients which are dependent on the model chosen The possible isotropic laws are the following CODE DESCRIPTION constant initial value only perfect plasticity linear or iso linear linear function of p power_law power law of p by_point hardening defined by a list of experimental points in an external datafile iso_table hardening defined by a table of points linear_pp linear hardening followed by perfect plasticity nonlinear nonlinear exponentially saturating function of p nonlinear_v1 nonlinear with an internal variable and coefs 1 nonlinear_v2 nonlinear with an internal variable and coefs 2 equivalent to nonlinear nonlinear_bsi nonlinear with kinematic interaction for use with the mises_2mic potential only linear_nonlinear combined linear and nonlinear saturating hardening nonlinear_sum multiple term nonlinear hardening nonlinear_double multiple term nonlinear hardening This law is rigorously equal to nonlinear_sunm but is retained for backwards com patibility Although the name suggests that only two terms are allowed more can be added nonlinear_recovery function hardening accor
136. eation chosen The table below summarizes the possible types of nucleation function CODE DESCRIPTION constant fa Ad a 2 gaussian fn fe exp y e Ji exponential fn 7 exp 2 The corresponding syntaxes are constant A COEFFICIENT A gaussian en COEFFICIENT En fn COEFFICIEN fn sn COEFFICIENT Tn exponential B COEFFICIENT B e0 COEFFICIENT 0 H Z set Non amp structure an 13 93 lt THERMAL_STRAIN gt lt THERMAL_STRAIN gt Description This object is used to define the calculation of a volumetric thermal strain Syntax The syntax for this object requires only input of the model coefficients standard form The types of thermal strain available are the following CODE DESCRIPTION isotropic Isotropic thermal dilatation anisotropic Anisotropic thermal dilatation The default type is isotropic The coefficients for the thermal strains are secants That is to say that the thermal deformation p is given by the relation Ethi ai T T Tref where a T is the secant dilatation coefficient T is the temperature and Tef is a reference temperature zero by default NOTE unexperienced users usually get confused about the exact signification of T ef Let us consider to clarify everything the calculation of the incremental thermal strain at a given time t it is assumed that the computation starts at t 0 without thermal strain
137. ed as a UEL with output to an ODB file or other Zebulon supported output This includes full state variable name and typing information e Optional post processing step to translate all the Z mat SDV variable names to be the proper named and typed variable in a new ODB file Z set Non linear material amp structure analysis suite 3 6 Z set Non linear material amp structure analysis suite Site definition Site definition There are a number of site definition files which must be configured to make the Z mat program additions work with ABAQUS These will most likely be configured by NW Numerics during the installation The location of the abaqus executable to use is adjustable There are two possibilities for defining the path The first is to edit the file Z7PATH 1ib Zmat ABAQUS_ROOT and make an entry for the machine name the name given via hostname and the path to the ABAQUS installation directory The second method is to define the environment variable ABAQUS_ROOT to point to the abaqus directory When launching the script will automatically link the Z mat library and all plugins with the libZmat unix or zmat win32 DLL prefixes found in the standard search path see the Zmaster release manual reference section on search paths Unix configuration The most important issue for the Z mat programs to work is the definition of an environment variable Z7PATH to point to the root directory of the Z mat distribution see re
138. ehavior can alternatively be launched by the following standard SAMCEF command that chains the bacon mesher with the mecano_zmat user module samcef ba zm problemn 1 MECANO Input The main Z mat modification needed in a standard MECANO input file concerns the MAT command used to define material properties Syntax is the following where the BEHA parameter that usually allows to specify the name of a standard MECANO material behavior is replaced by a ROUTIN parameter followed by the name of the Zmat material file MAT NOM MATERIAU ROUTIN zmat_fname Elastic parameters definition is needed but values are not meaningful YT 10 NT 0 3 For anisothermal problems thermal expansion coef A should be set to 0 and defined in the Z mat file by means of a thermal_strain object A 0 where zmat_fname is the name of a Z mat material file Note that 6 3 Zsamcef interface e definition of some elastic properties coefficients YT and NT is required in the SAMCEF input file However values given for those coefficients have no incidence on the results since the actual definition of the elasticity coefficients is given in the Z mat material file e for anisothermal problems the value of the thermal expansion coefficient needed to calculate thermal strains should be given in the Z mat file and it is safer to set the A coefficient to zero in the SAMCEF input file Z mat interface file Most of the commands are
139. ending on the above check on the stress Note that in the use_x case the evolution is not the complete derivative where the terms involving the change in C with temperature are not taken into account Syntax The basic input syntax here is kinematic non_symmetric I1i_trans coef value Ct coef value Cc coef value Dc coef value Dc coef value M coef value m coef value use_x use_alpha Only one choice of use_x or use_alpha can be used default is use_x The default value of I1_trans is 0 The coefficients M and m are the standard Norton like static recovery coefficients continued Z set Non linear material amp structure analysis suite 13 41 lt DIRECT_KINEMATIC gt Example The following example shows the use of this kinematic model in combination with the cast_iron yield criterion behavior gen_evp kelasticity isotropic young 126000 poisson 0 265 potential gen_evp2 ev criterion cast_iron ratio 3 associated 1 kinematic non_symmetric x1 Ii_trans 50 Ct 300000 0 Dt 5000 0 Cc 30000 0 De 500 0 isotropic constant RO 100 0 return 200 T 200 T T cast_iron1_yield test using 1 2 cast_iron1 test using 2 3 LAS MA 100 H i pe 100 4 200 L bef blond v 200 i i i i R E uy el 300 H J sig22 sig22 300 400 500 lt i pt E Hl J 400 oo eet a B i 4 600 i i i L 500 L hi
140. ent e_0 2 0 criterion E 1000 approx critical stress progressive closure delta_d 0 006 shift in strain closure according to d delta_e 0 008 width of strain transition return 11 10 Z set Non amp structure a behavior bodner_partom Description This behavior is an implementation of the classical model due to Bodner and Partom The model is viscoplastic and incorporates scalar and tensorial hardening variables There is no initial yield radius thereby allowing inelastic deformation at very low stress levels over long periods of time The state and evolution equations are the following Z 2Z Z0 8B u Dp D exp Evi VAS u 0 y0 0 Z2 35 S U 0 A Dpa Ja J 38 8 W 0 vi VAS 0 Ec Eto Evi Zi m Z Zi Zo Wp B ma Z3u B W 1 Syntax behavior bodner_partom behavior bodner_partom thermal_strain lt THERMAL_STRAIN gt elasticity kmodel_coef lt ELASTICITY gt Coefficient names aren ZO Z2 DO Z1 Z3 m1 m2 Al A2 ri r2 Stored Variables prefix size description default eto T 2 total strain yes sig T 2 Cauchy stress yes evi T 2 inelastic strain tensor yes Zi S isotropic drag stress yes beta T 2 kinematic variable yes p S inelastic strain equivalent yes Ztot S Sum of Z parts yes 11 11 behavior bodner_partom Example The following is a simple example of the Bodner partom material using room
141. er handbook including discussion of all the command line switches used to control the specifics of the Z mat launch The script will initially launch ABAQUS and then be called again by the ABAQUS pre processor in compile and link mode By default the launch submits the job to the ABAQUS queue and therefore the script exits rapidly even though the job continues in the background To see the status of the calculation look at the problem log file e g tail f myprob log or run with the fg switch ABAQUS Input The definition of a material for the Z mat behaviors always uses an external file to establish the model components and coefficients Z mat never uses the material parameters defined in the ABAQUS inp file This is because the Z set coefficient definitions are much more flexible in their definitions and are integral to the actual structuring of the material model to be used Global dependencies are established using the temperature parameter or other global field variables Other commands are available in addition to the behavior definition which control the local integration method implicit mid point Runge Kutta explicit etc variable initializa tions automatic time stepping parameters depending on the maximum allowable variable increments and the local rotations Linking summary The Z mat library is delivered as a dynamic shared object which can be linked to other programs The library is entirely programmed in C b
142. erature 300 0 700 0 poisson 0 3 F 0 5 G 0 25 H 0 75 A 500 0 A1 3240 0 A2 1 78e8 A4 8 89e 13 B 5 0e12 Ci 0 143 C2 1 0e 10 Fsa 1 815e 7 11 17 x behavior matmod_z 11 18 Fsb 4 99e 8 Fsm2 2 32e 7 Fsm3 3 25e 6 H1 0 0070 dR H2 6 64e 4 Y dFdef H3 2 0e 26 dFdef irr k 1 9859 kp 91 0 kq 3 0 n 4 5 p 0 5 Qs 60000 0 Q4 8400 0 Tt 930 0 Z2 1 0e23 Z3 1 0e12 beta2 6 0 beta3 3 0 phi flux phi 0 o Z set No amp structure behavior memory behavior memory Description This behavior is a ZebFront implementation of a strain range memory isotropic hardening model described by Lemaitre and Chaboche Lema91 The model has 2 non linear kinematic hardening components coefficients C1 D1 C2 and D2 and a Norton type flow law coeffi cients K and n Q Qo Qsat Qo exp 21q R Ro bQr 3 Syntax behavior memory xxelasticity lt ELASTICITY gt model_coef coefs Example behavior memory xelasticity isotropic young 260000 poisson 0 3 model_coef n 7 0 K 100 C1 30000 0 D1 80 C2 100000 D2 1200 RO 150 0 b 150 QO 400 Qsat 350 mu 100 return Z set Non amp structure an 11 19 behavior non associated behavior non associated Description The non_associated behavior is a ZebFront behavior used as an example for non associated deformation with kinematic hardening vari
143. erion used to monitor convergence is defined on user state variable number 30 element code 1330 The criterion defines that this variable at any integration point of the element set named cmc should not increase of a value of more than 10 0 defined in the fifth data block over an increment If the increase of the variable exceeds the limit value specified the auto step procedure will discard the load increment and the step size will be cut back accordingly Z set Non linear material amp structure analysis suite 5 5 Zmarc interface 5 6 More precisely denoting by At the current step size Av the maximum variation of variable v found by local integration during the current increment cycle and Umar the limit value specified if Av gt Umax a new icrement will be attempted with a lower step size calculated as Umax At Av Additional commands may then be used in the Zmat problem zebulon file to control increment cut back in case of local divergence Those commands are the following ones divergence_variable 30 20 The above command select variable 30 to monitor local convergence and specify that in the event of divergence a Av value of 20 should be sent back to Marc ie two times the Umax limit value defined in the auto step command Hence the effect will be to force a division by 2 of the global step size in the event of local divergence When using this scheme care must be taken to carefully select the vmar lim
144. es in a time dependent viscoplastic potential and a time independent plasticity potential 2 2 3Cx10x1 SCintaxa 30x20 x2 3Cint x1 Xx1 Xx2 7 The example material definition for this type of interaction is as follows 13 52 Z set No amp structure an lt INTERACTION gt behavior gen_evp kelasticity isotropic young 170000 0 poisson 0 30 potential gen_evp ev flow norton n 1 0 K 20300 kinematic nonlinear X1 C 2000 0 D 50 0 isotropic constant RO 20 0 potential gen_evp ep kinematic nonlinear X2 C 25000 0 D 10 0 isotropic constant RO 850 0 interaction ev X1 ep X2 25000 0 return The names X1 and X2 were given in order to have readable names for the kinematic variables In this syntax it is important to notice that a specification ev X1 is different than ev X1 because the kinematic names are localized within each potential 13 53 lt ISOTROPIC gt lt ISOTROPIC gt Description This object class defines models of isotropic hardening for use in a variety of material behaviors and potentials Isotropic hardening causes an isotropic expansion or contraction of the yield surface in tensorial stress space The isotropic hardening may be a function of the simulated multiplier which is normally equal to the cumulated plastic strain equivalent p or in terms of its own internal variable The latter must be used for cases of static recovery The initial value Ry for th
145. espectively the opening displacements corresponding to the maximum cohesive traction of the normal and shear components The damage variable Amaz Which is the maximum value of A reached up until the current instant increases from 0 no damage to 1 for a broken element In this model the ratios PY and 2 have to be the same The normal and shear components of the cohesive traction T ie Ty T it n Tyr and Tr T Ty are defined by u F Ty iy F Amar Tr a F Amaz F A Omax 1 A 5 with a a constant representing the relative magnitude of with respect to Ty and Omazr the maximum stress allowable by the element For the compressive case where uy lt 0 the normal component of the traction is modified to Te we Fw 6 UON with a a penalization factor In the literature a usually is at least 10a Figure 5 illustrates the typical response of the cohesive zone model under specific loads for the parameters as given in the example Syntax behavior crisfield_debonding sigmax Omar u0n UoN u0t Uor deltan n deltat 06 alpha a alphac a continued 3this behavior is Z set specific and therefore does not apply for Z mat for other codes Alfano G and Crisfield M A Finite element interface models for the delamination analysis of laminated composites mechanical and computational issues Int J Numer Meth Engng 50 2001 1701 1736 Z set Non linear materia
146. essarily so The function of each sub command will be described in the discussion of the behavior model itself What defines the syntax which follows this line is the ELASTICITY notation indicating an elasticity matrix should be input Again the use should then go to the ELASTICITY section of the handbook and investigate the possible models for this option Many behavior models also include the possibility of multiple instances of certain key words These possibilities will be described in the section of the containing class behavior is a material piece class but there are many others which can contain sub pieces themselves The standard notation for multiple instances of a class is to include three dots following the data entry line kinematic lt KINEMATIC gt This means that the material at this location can take any number of kinematic entries in any order and with no restriction on type Example An example file follows which is of a simple elasto viscoplastic model with non linear isotropic hardening and two kinematic hardening components Note that the behavior has taken two objects an elasticity matrix and a potential dissipation potential with an inelastic deformation associated to it The material behavior is gen_evp which stands for generalized Z set Non amp structure an 9 3 Introduction to Behaviors elasto viscoplastic see page 10 13 The potential has in turn taken on a number of sub
147. esults files is restricted to one tensor and or scalar only Corresponding FAC codes are 1399 and 1499 that should be requested by an appropriate SAI command in the SAMCEF input file SAI ARCHIVE ALL_ELEMENTS STYPE 1399 user scalar 1499 user tensor The save_tensor and save_scalar commands then allow to specify which Z mat variable will be saved in the results files kkneeds temperature Z mat automatically detects that the temperature should be stored in the state variables when a material coefficient dependence on this parameter is de fined in the behavior However if all material coefficients are constant temperature is Z set Non amp structure an 6 5 Zsamcef interface 6 6 removed from the state vars management to cut down storage requirements In this case the thermal strains calculated by the thermal_strain object will always be zero The needs_temperature command may then be used to force storage of the tem perature and allow thermal strain calculation even if no coefficients are temperature dependent material As decribed in the Interface file section page 2 12 this bloc of commands is used to set integration methods parameter command integration define local axis for the calculation of material quantities command rotation initialize material variables etc A different file may also be specified that will contain the actual behavior definition behavior commands by u
148. ex interaction and criterion 2M1C memory gen _evp with strain range memory suvic SUVIC complex hardening evolutions If the option name is given the names of the inelastic deformation tensors will be con structed from the names given By default the names will be generated automatically based on the type and number by order of definition of each potential It is generally advised to use the names ev for the first viscoplastic potential and ep for the first plastic potential Z set Non linear material amp structure analysis suite 13 73 lt POTENTIAL gt 13 74 lt POTENTIAL gt associated Description This potential takes the same form as the gen_evp potential described above but alters the criterion to be associated with the hardening mechanisms input The criterion form can be written f fer p 7 YX R LO X where fer is the criterion as calculated by the lt CRITERION gt object entered after criterion There are some additional restrictions with this potential type due to numerical or physical restrictions The resulting behavior includes a nonlinear yield zone radius dependence on the R isotropic variable A dependence also is introduced with the kinematic hardening variables on the isotropic radius As the kinematic back stress is increased through monotonic straining the yield radius is decreased thereby increasing the Bauschinger type effect reduced yield on reversal Syntax The synt
149. f a ti y t Y i 1 Y gt 5 wil file yi 1 t 1 by changing zres such that g x lt 0 j 1 ny 2 F is the cost function scalar g is a vector of constraints x are the parameters to be opti mized t tags the experiment experiment number time and w is the weight associated to experiment i A variable x set of parameters such that g x lt 0 j 1 ny represents a feasible point vice versa infeasible Z set s optimizers are primarily meant for parameter identification of material behaviors Therefore the default cost function F is the least square distance between experiments and simulations and constraints g are used to bound and or to relate parameters with each other Of course other general type of optimization problems can be addressed There are two main categories of optimization methods local and global optimizers Global optimizers seek x such that F x lt F x Vres Local optimizers look for x such that F a lt F x Ve such that x x lt e Typically local methods iterate from a set of variables x in the search space S to another based on information gathered in a neighborhood of x Zeroth order optimizers use exclusively Z set Non linear material amp structure analysis suite 16 3 Introduction 16 4 the value of F and g First order methods additionally use gradF and gradg second order methods hessianFF and hessiang or an approximation of grad and hessian Gl
150. f the evolution of the cohesive traction as a function of the opening displacement for two different loading cases uy t with ur t 0 thick red curves and ur t with uy t 0 thin green curves Top left applied load u t Note for 2 lt t lt 4gs the applied loading becomes negative but the response uyy remains 0 because of an implicit non penetration condition Top right response T t Bottom left Amaz t Bottom right u t vs T t If no_penetration is specified a broken element continues to prevent penetration Example behavior needleman_debonding sigmax 100 deltan deltat alpha alphac return e 5 e 5 PRP O w 12 5 behavior crisfield debonding 12 6 behavior crisfield debonding Description This behavior is used for the special problem of interface debonding See the command create_interface_elements and similar in the Z set user manual on how to insert cohesive elements in the mesh The Crisfield model is described through a scalar variable A which characterizes the relative crack opening 1 x af 2 1 E ON _ 4 uot 4 1 nr won vor N m where x x if x gt 0 and x 0 if x lt 0 With respect to the interface normal 7 un U 1 unt and dy un denote respectively the normal and shear opening displacements and dy and r the corresponding maximum allowable values of their norms The parameters uoy and uor denote r
151. ffusion D COEFFICIENT Stored Variables prefix size description default dc V gradient of concentration yes J V flux of concentration yes C S the concentration yes Example xkxkbehavior coefficient_diffusion D 5 50339E 22 50339E 22 02370E 20 39143E 20 02221E 18 56706E 18 56706E 18 56706E 18 NN NRP OR 01 return C 1000 oO OOO Ome 29 40 55 59 66 1000 12 3 behavior needleman debonding 12 4 behavior needleman debonding Description This behavior is used for the special problem of interface debonding See the command create_interface_elements and similar in the Z set user manual on how to insert cohesive elements in the mesh The Needleman model is described through a scalar variable A which characterizes the relative crack opening MORO o where 1 x if x gt 0 and 1 0 if x lt 0 With respect to the interface normal un 4 1 unt and dy U y denote respectively the normal and shear opening displacements and y and r the corresponding maximum allowable values of their norms The damage variable Amaz which is the maximum value of A reached up until the current instant increases from 0 no damage to 1 for a broken element The normal and shear components of the cohesive traction T ie Ty T it m Ty and Tr T Ty are defined by UN de 27 2 TN Sy E Omas Tr ag E Amaz F A Cmax 1 A gt
152. forms All Win32 platforms use Microsoft Visual C On SGI systems the development foundation package may be required on older systems This package is supplied with all the MIPSpro compilers or can be purchased separately The package is required for the system libraries and linker which are not supplied with the standard system The C compiler is required only for user additions to the package Also the software is currently compiled on IRIX 6 5 which will generate an undefined symbol error for earlier systems A workaround is now available so if you need that please contact your distributor 2The development of Z mat interfaces requires of course operating copies of the mating code at our site for development and maintenance It is frequently possible for additional platforms to be added per request possibly with a supplemental charge Please inquire to your vendor regarding any additional such desired ports Z set Non linear material amp structure analysis suite 1 9 System Requirements 1 10 Z set Non linear material amp structure analysis suite Material Frameworks Material Frameworks One thing which needs mentioning right away with regards to the Z mat documentation is that the material models are in general not documented with respect to the type of material but rather the model framework Each framework can be considered an assembly of different user created building blocks which then finalize the fu
153. h a given ratio relating them or use isotropic hardening in only the tensile or only the compressive with extra coefficients given for the non hardening one Probably the calling application requires that an R be given so defining both Rt and Rc is not allowed Re ratioR R R if ratio is entered Re Rc R R if Re is entered Re R Ri Rt if Rt is entered The different tension and compression yield values Re and R are applied to two distinct different yield functions as follows 1 2 Fi s s Tr o Re Ri Rei 1 2 Fo 3s s Re The transition from the tension yield F to the compression yield F is determined if the trace of the effective stress 7 X is less than R See the section for the non_symmetric direct kinematic model on page 13 41 for a demonstration of the model s effect Syntax The basic input syntax here is criterion cast_iron ratio value Re value Rt value associated O 1 Only one choice of ratio Rc or Rt may be given as discribed above If the associated is set to 1 the F yield function will be used all the time The default is associated behavior Example xcriterion cast_iron ratio 3 associated 1 Z set Non amp structure an 13 17 lt CRITERION gt lt CRITERION gt hill Description The Hill criterion allows modeling of anisotropic behavior in the criterion and flow directions 3 1 2 fer 39 Mnu g R where Mp is
154. h are too large usually lead to poor global convergence Too small values will not converge due to numerical roundoff 1071 is about the limit Convergence will rarely take more than 25 iterations and should not take more than 50 If this is the case there may be some t Non erial Interface files material integration error in the integration make a bug report or the material parameters are excessive damage laws may provoke this If the local iterations are greater than 50 it is probably better to reduce the global iterations or use automatic time stepping global or local The default integration is dependent on the material law used Most behaviors modeling plastic or viscoplastic materials use a default of the 0 method with theta 1 0 eta 1 e 9 and max_iteration 200 Example plasticity or large deformation integration theta_method_a 1 0 1 e 9 50 difficult viscoplastic case integration theta_method_a 0 5 1 e 6 100 complex law integration runge_kutta 1 e 3 1 e 3 2 14 Z set Non linear material amp structure analysis suite Interface files x material rotation rotation Description This material option is used to change a coordinate systems by rotation It is used here to simplify specification of some materials anisotropy etc but the syntax is general Other ap plications using the rotation object include specification of grain orientations for polycrystals see
155. h in turn is grouped according to the orientations and volume fractions of material The syntax for the model is localization poly model_coefficients coefs grains grain list file filename 13 61 lt LOCALIZATION gt Example behavior gen_evp xelasticity isotropic young 200000 poisson 0 30 localization poly grains 149 676 15 61819 154 676 1 149 676 15 61819 154 676 1 150 646 33 86400 155 646 0 2 model_coefficients C 50000 D 100 potential octahedral flow norton n 25 K 50 isotropic nonlinear RO 100 Q 50 0 b 50 0 kinematic linear C 2500 interaction slip hi 1 0 h2 h3 h4 h5 h6 return PPP Pe oOo OOO Oo 13 62 Z set No amp structure an lt POROUS_CRITERION gt lt POROUS_CRITERION gt Description This behavior object is used to enter the citerion for a porous plastic material The description of these models will use the following notation CODE DESCRIPTION od stress tensor s deviatoric stress tensor J2 the second invariant of deviatoric stress 38 S Il first invariant of stress Trace g Oy current flow stress Syntax The syntax for a porous criterion requires that a type be given followed by whatever coeffi cients are allowed for the particular model As in all of Z mat these coefficients are entirely context sensitive porous_criterion type coefs The available list of porous plastic models are summarize
156. h1 h2 h5 h3 h6 h4 h5 h5 h5 h6 h3 h2 h2 h1 h5 h6 h3 h5 h3 h6 h4 h5 h5 h4 h5 h5 h1 h2 h2 h6 h5 h3 h6 h3 h5 h5 h3 h6 h2 h1 h2 h3 h5 h6 h5 h5 h4 h5 h6 h3 h2 h2 h1 h5 h4 h5 h3 h6 h5 h5 h4 h5 h6 h3 h5 h1 h2 h2 h6 h5 h3 h6 h5 h3 h5 h5 h4 h2 h1 h2 h3 h5 h6 h3 h5 h6 h3 h6 h5 h2 h2 h1 h5 h4 h5 h5 h5 h4 h6 h5 h3 h6 h3 h5 h1 h2 h2 h3 h6 h5 h3 h5 h6 h5 h5 h4 h2 h1 h2 h6 h3 h5 h5 h4 h5 h3 h6 h5 h2 h2 h1 Bd Ba Bc Db Dc Da Ab Ad Ac Cb Ca Cd Bd Ba Bc Db Dc Da Ab Ad Ac Cb Ca Cd For each crys lt STRAIN_NUCLEATION gt lt STRAIN _NUCLEATION gt Description This option allows application of different methods from which the nucleation of porosity may occur Syntax The nucleation mechanisms are defined as follows crack_like type yield COEFFICIENT porosity_yield COEFFICIENT model _coefficient COEFFICIENT crack like keyword indicating that the mechanisms of porosity creation takes the form of cracking or loss of material yield allows to define a value of plastic strain below which there is no nucleation porosity yield Defines a value for the trace of the stress tensor below which there is no nucleation The law of nucleation is given by fn ACA where is the plastic multiplier The form of the function A is variable according to the type of nucl
157. he D coefficient between initial and saturated values This kinematic model works in RK TM or Reduced TM Mkin N P A nonlinear_evrad This model limits the ratcheting effect in biaxial conditions by comparing the flow direction with the back stress Evolution is calculated as follows 3D myn n 1 31 n 22x 20 The coefficients are defined such that uniaxial response is equivalent to the nonlinear model given equivalent coefficients The coefficient names are C D and eta This model works in RK TM or Reduced TM but has no static recovery 13 58 Z set Non linear material amp structure analysis suite lt KINEMATIC gt ziegler This model describes a back stress with hydrostatic and deviatoric components o xX _ DX 9 Mkin 70 X C spa 7a M a which takes be no static the coefficients C D M and m In the absence of the latter two there will recovery The Ziegler model may not be used with the reduced_plastic integration nonlinear with_crit Mkin n og DJ X w 1 DJ X soy E Example xkinematic nonlinear_evrad C D eta Z se 2 amp structure an 40000 500 0 4 t Non 13 59 lt KINEMATIC gt lt KINEMATIC gt aniso nonlinear Description This kinematic model implements anisotropic coefficients into a KINEMATIC behavior object Note that this model does not include the 1 5 term in the modulus coefficients so there are no
158. he sub commands will be described in the next pages of the manual x value rm xinit_from_file fname auto_init_from_file fname format fmt vnamel fixed vinil min vmin1 max vmaxl1 log log a mm vnameN fixed viniN min vminN max vmaxN 10g 1o0g where vname the variable name vini its initial value also used for scaling double vmin its min value and vmax its max value Scaling is important particularly when the variables that are handled are of widely differing magnitudes Without scaling matrices used by the optimization algorithms are typically ill conditionned Scaling is automatically performed in Z set using vname vini instead of vname It is possible to have different initial and scaling values using the init_from_file command fixed fix the value to the initial and remove the variable from the optimization problem min set the minimum allowable value for the variable max set the maximum allowable value for the variable log log treat variables as being log s of the values to be substituted in the files the tmpl substitutions if log is selected the variables entries in the tmp1 file will be substituted not with the variable but instead e If the option log is chosen the program will use e Note that the order in which the values are given is not the order in which they are handled thus printed by the optimizers For instance when reading the results of
159. hys Solids 40 1139 1162 1992 A E Green and P M Naghdi A General Theory of Elastic Plastic Con tinuum Arch Rat Mech Anal 18 251 281 1965 Z G rdal R T Haftka Elements of Structural Optimization Kluwer Academic Publishers 1992 H E Hjelm Yield Surface for Grey Cast Iron Under Biaxial Stress J Eng Mater Tech 116 148 154 1994 B L Josetson U Stigh and H E Hjelm A Nonlinear Kinematic Hard ening Model for Elastoplastic Deformations in Grey Cast Iron J Eng Mater Tech 117 145 149 1995 P Ladev ze Sur la Th orie de la Plasticit en Grandes D formations ENS Cachan LMT Internal Report No 9 1980 J Lemaitre and J L Chaboche Mechanics of Solid Materials Cam bridge University press 1985 K Levenberg A method for the solution of certain non linear problems in least squares Quaterly of Applied Mathematics 2 164 168 1944 Z set Non linear material amp structure analysis suite 18 3 18 4 Mill76 Mor 77 Nagt82 Neld65 Pilv94 Pilv96 Simo98 Schit91 Zhou97 A Miller An Inelastic Constutive Model for Monotonic Cyclic and Creep Deformation Part I and II J Eng Mater Tech 97 113 1976 J J Mor The levenberg marquardt algorithm Implementation and theory In G A Watson editor Numerical Analysis Proceedings Lec ture Notes in Mathematics pages 105 116 Springer Verlag Berlin Ger many 1977
160. iables kn default names will be of the form pna_ v with being the sequential number of the kinematic variable in the potential s kinematic list With these comments the internal variables added by a gen_evp potential instance are the following prefix size description default pnvi T 2 inelastic strain tensor yes pncum S cumulated value of the multiplier yes kn T 2 kinematic strain variable no Note that the cumulated value of the multiplier is only sometimes equal to the equivalent cumulated inelastic strain for Von Mises criterion for example but not for Hill The current version of the potential does not allow for calculation of the true equivalent for cases where J p Example An example viscoplastic model with Norton flow Hill type criterion and kinematic hardening is given here as an example using the gen_evp potential The dissipation potential flow term only and criterion may be written as Q 0 X M 0 X P R 2BXx X R Ro 2Q f X M X R 11 which leads to the evolution rules ol 2M o X aF A Teq En SAGE with 0 90 KX M o x behavior gen_evp kelasticity isotropic young 260000 0 poisson 0 3 potential gen_evp ev flow norton n 7 0 K 400 criterion hill hilla 1 hilld 1 hillb 2 hille 1 hillc 3 hil1f 1 kinematic nonlinear xi 2This of course means in addition to those created by other potentials an
161. ial shear component Engineering output is available by using the kkstate_var_engineering shear option This is true for variables in the integrated vector and the auxiliary variables VINT and VAUX variables The GRAD and FLUX vari ables always have the factor removed however e The integrated and auxiliary variables VINT and VAUX are stored sequentially in the vector prefixed sdv in ABAQUS e For mechanical problems the stress variable is named S and the strain E with all behavior as in ABAQUS standard e Some extra variables such as the energy output variables are not yet calculated Z set Non linear material amp structure analysis suite Dutput variables Z set Non linear material 3 12 amp structure analysis suite Extra files Extra files The compilation and linking of UMAT routines Z mat included are controlled by parameters in the abaqus_v6 env file located in the Site directory of the ABAQUS distribution Alterations must therefore exist in the active abaqus_v6 env file to link with the Z mat li brary An abaqus_v6 env to do this is supplied in the Z7PATH 1ib Zmat directories There is a default abaqus_v6 env file and the option to have specific files for different machines example files exist and it should be obvious how to manipulate these The abaqus_v6 env file which is needed will be copied into the calculation directory in order to be the first read configuration file and can thus be verified by
162. iated with the con straint Example comparison_constraint s_file_file 55 fat_al2 test 1 3 fat_al2 exp 1 3 0 0001 Z set Non linear material amp structure analysis suite 16 17 x xkkoptimize xxxfiles 16 18 files Description The files option is used to declare files where the optimization variables are to be replaced during the trial evaluations of the error function The following diagram shows the function of the template files in order that the the optimizer can alter the execution data for simulations in a general way file impl R R load Load Current Optimizer ai Variables R Load ra algorithm i file oes R 93 502 Shell load 324 0129 Compare NH Zrun The program detects variables to be optimized in the tmp1 suffixed versions of the files by searching for alphanumeric strings with the following format a z A Z 0 9 1 Thus the indicates that the parameter is to be optimized and the following token string is used to reference the variable in the solution References are needed to give initial values define constraints on the variables etc If the file exists with the name given with the files command the initial values will be taken from that file Otherwise the value command must be used see page 16 21 If a variable name is repeatedly found in several files functions they are treated to be the
163. ic and kinematic hardening Many other features are also available for modifying the behavior including models for nucleation of porosity fine tuning the numerical implementation and studying the onset of bifurcation instabilities Please note that the kinematic hardening for porous plasticity is fundamentally different from what is used for non porous unified viscoplastic models such as in gen_evp BessXX The purpose of kinematic hardening is also not so much to simulate cyclic behavior but rather to provide control of the yield surface curvature Many porous plastic analysis problems involve finite strain Please refer to the docu mentation for lt MODIFIER gt at page 14 5 for the specifics of different corotational finite strain methods Note that frequently we use the no_J option where the det F volumetric adjust ment of the Cauchy stress is ignored The reason to do this is because the volumetric change effects on the stress are essentially resolved by the porous potentials A common theme in porous plasticity is that a matrix stress a is solved for based on the macroscopic nominal stress current plastic strain p and current porosity f UUU Ife O_O O The means of localizing to the effective matrix stress is therefore given by a potential function o which must always be satisfied olg f ox 0 Since the matrix stress o is the real material porous plasticity uses the measure 0 R as the overstre
164. ighted sum of reference simulation comparisons specified using the compare commands The variables of the optimization are specified in the values sec tion and must correspond to one or more entries in the optimization files listed in files These optimization files are in fact templates for real files which alter the simulation result of commands listed in shell or zrun entries The optimizer thus constructs new input files for the simulations with the current optimization variables inserted in the appropriate locations 16 5 x xkkoptimize The figure below shows a basic diagram of the interaction between the optimizer and any number of sub simulations which generate the data to be compared with experimental results Comparisons 1 gt simi a exp1 L sim2 lt exp2 H e Zrun o0 opt variables __ i sim3 ZN exp3 ry Function value error sim4 CN exp4 run lo simsa S exp5a sim5b exp5b sim5c exp5c In general hopefully the number of simulation experiment comparisons will lead the problem to be over constrained Its the optimizers job then to find the best fit If certain experiments are important the user will employ weights on the comparisons functions to make them more dominant in the function evaluation Remember that the best must robust results will be found with many diverse experiment conditions
165. ile and the calculation terminates USER MATERIAL this defines that there is a user behavior As as parameter to this command one must give a CONSTANTS option with at least one coefficient This coefficient is not used in the Z mat behavior however Z set Non amp structure an 3 9 Interface files ABAQUS commands for initializing the state variables giving a material orientation and material coefficients are not used with Z mat There are instead alternatives which may be defined in the separate Z mat material file see the commands starting at page 2 12 3 10 Z set Non linear material g amp structure analysis suite Output variables Output variables All the material variables should be available for output in ABAQUS calculations if the external_storage option is not used This should include the GRAD FLUX VINT and VAUX variables as shown with the Zpreload utility The variables will all be stored as SDV variables Caution There are some tricky spots which remain in the Z mat output which may not be obvious to the new user These are summarized below e The shear components of symmetric tensional variables are natively stored with a factor of v2 which is removed by default at each exit of the z mat routine This operation takes up some CPU however so it can be suppressed by using the state_var_shear_alter command Also the default transformation for state variables is to change them to the real tensor
166. ility and robustness due to the new ability for ANSYS to load shared libraries dynamically e Z mat MSC Marc Marc fully supports Z mat material models and there is an interface for results files reading Z mat SAMCEF SAMCEF is supported by the Transvalor group in France only e Z mat LS DYNA The LS DYNA fully supports the user materials numbers 41 and 42 cur rently The remaining material numbers are left for the user to optionally select The Z mesh Z post and Zmaster codes allow for inputting of the k file as well as the d3plot results files There is currently no output to the LS DYNA formats Cosmos M Cosmos is no longer supported because of lacking customer demand This port could potentially be re activated upon request Later in the manual these interfaces are discussed in detail Z set Non linear material amp structure analysis suite 2 3 Z mat interface 2 4 Z set Non linear material 5 amp structure analysis suite Interface files Interface files The Z mat interface file exists as a medium to configure the interface translation and provide extra convergence parameters for the local integration This interface effectively duplicates the controls which exist in the Zebulon FEA input file All the different Z mat platforms target FEA systems use the same basic controls de scribed in this chapter Some certain commands may however have functionality specific to one or some of the codes due to limitations
167. ill also be normalized by the program to automatically make unit vectors Using the notation here that t1 is the first direction vector defined and t2 is the second for 3D problems direction vectors of the coordinate system are defined as follows The first vector is collinear to t1 The second vector is a vector in the plane defined by t1 t2 and is perpendicular to t1 The third direction will always be calculated using the vector product of the first two vectors The t vectors will replaced by those given by you using the x1 x2 x3 choices For rotations specified using Euler angles rotation Q1 Q da 2 16 Z set Non linear material amp structure analysis suite Interface files x material initialize_ variable initialize variable Description This command is used to give initial values to the variables of a material Currently only constant uniform values are allowed This command is used in the place of the initializing commands in ABAQUS Syntax The syntax for the automatic time stepping control is the following kkinitialize_variable varl vall varN valN The syntax is free format except for the fact that variable name and initial values must be given in pairs The definable parameters are var a character name of a variable of the problem This can be from the FLUX or VINT variables Each component of a tensorial or vector variable must be initialized separately var real value for the
168. ing model in the test definition continuedExample An example test definition for use with a finite element behavior was given in the previous section page 15 1 A simulation model 1D simulation only example follows simulate test relax12 time_ini 5 0 load file relax12 load 2 presently July 1997 all the gen evp models are implemented as are some ZebFront FEM models others are in development Z set Non linear material amp structure analysis suite x x simulate x test model ddi file relax12 mat integration runge_kutta 2 e 3 2 e 3 output time eto sig evcum epcum return Z set Non linear material 15 7 amp structure analysis suite x simulate k xtest constant parameter constant_parameter Description This option is used to set parameters that are used in the material behavior temperature for instance It replaces the parameter bloc in a standard computation and as its name suggests only allows constant parameter values Syntax constant_parameter paraml valuel param2 value Example constant_parameter temperature 200 depth 60 15 8 Z set Non amp structure a simulate xtest error_plot error_plot Description This option is used to get error maps for integration algorithms Under non proportional loading Syntax The error maps to output are defined in the following manner error_map
169. interface Description Currently we are not providing any implicit interface for Z mat with Cosmos Users are encouraged to contact the distributor if they require a separate interface for Cosmos Unfor tunately demand for this port has been extremely limited Like many of the older style interfaces the user interface for Cosmos M required compila tion of a custom executable and therefore requires specifically the compiler and development environment recommended by SRAC The build scripts are still supplied with Z mat distri butions and it is very likely a user could modify that for current versions of Cosmos The last supported Cosmos release was 2 8 Z set Non linear material amp structure analysis suite 7 3 Zcosmos interface 7 4 Z set Non linear material j amp structure analysis suite Chapter 8 Z mat LS Dyna 8 1 8 2 Z set Non linear material amp structure analysis suite Zlsdyna interface Zlsdyna LS Dyna interface Description The Zlsdyna port applies to the user material facility within the explicit dynamics code LS Dyna Implicit integration modes are not supported for this interface so the port is strictly explicit and therefore somewhat different from the other codes The user is referred to the LS Dyna documentation sections under the MAT chapter of the user commands manual for topic MAT_USER_DEFINED MATERIAL MODELS and also to in formation included in the Appendix A of the 9
170. internal variables a to which the backstresses are associated are thus scalar and distinct from the tensorial kinematic hardening laws in the macroscopic potentials They are related to the backstresses X through X x0 Ca with x0 and C parameters having the dimensions of a stress Trick a large negative offset xO might be used to model unidirectional slip provided that the same positive offset is added to the corresponding isotropic hardening These hardening laws will apply uniquely for the monocrystal potentials Permissible crystalline kinematic types are with their additional parameters are linear Qi Y nonlinear i Yy DX y C nonlinear phi uj D X Xbar C with vi 1 phi phi e delta vi Z set Non linear material amp structure analysis suite lt CRYSTAL_ORIENTATION gt lt CRYSTAL ORIENTATION gt Description This class is used to load in particular crystal slip systems into gen_evp crystal potentials see page 13 80 or in seperate crystal behaviors The crystal orientation will define the number of slip systems in the model as well as the number of independent interaction parameters between these slip systems The default orientations are as follows For cubic crystals the 1 O 0 axis is oriented horizontally to the right along the zebulon z axis 0 1 0 vertically upwards along the Zebulon y axis and 0 O 1 out of the paper towards the reader along the Zebulon z ax
171. ions f f 0 H p X fp E E E 00 0600 _ 00 5 H p OH from which it is noted that the hardening forces H are related to the internal strain analogue variables h by the same linear relationship H M h 13 36 Z set Non linear material amp structure analysis suite lt DAMAGE gt Example behavior gen_evp xelasticity isotropic young 260000 poisson 0 3 damage isotropic creep alpha 0 75 beta 0 0 A 3000 r 5 3 k 15 coupling damage_hardening potential gen_evp ev var_coefs flow alt_norton n 7 0 K 2070 K2 1600 0 K3 19 0 kinematic nonlinear C inv_one_minus dv 15000 0 D 300 0 kinematic nonlinear C inv_one_minus dv 6000 0 D 100 0 xisotropic constant RO 130 xxxreturn 13 37 Z set Non l amp structure a lt DIRECT_KINEMATIC gt 13 38 lt DIRECT _KINEMATIC gt Description This object defines a class of kinematic hardening tensorial back stresses which can have a more general state variable form and possibly nonlinear relationship between the integrated strains and the associated stresses In the gen_evp behavior framework these models must be used with the following potentials only CODE DESCRIPTION gen_evp2 Generalized viscoplastic potential 13 86 The kinematic models all support static recovery and possibly have more than a 1 1 relation between the integrated variable size and the kinematic back stress size forcibly the active tenso
172. ious individual behaviors for each potential form have been deprecated though a compatibility syntax is still provided The hyperelastic potential is defined by a material component for this task which is shared between the other laws employing such a potential There are several main classes of hyperelastic rules which can be inserted in this behavior depending on their assumptions and integrated rules The following type are allowed e default HYPERELASTIC_LAW objects e isotropic HYPERELASTIC_LAW objects which are somewhat more specific and where cer tain properties of the potential tangent can be made e mixed hyperelastic models which are necessary for use with the Zebulon hyperelastic element but cannot be used with Z mat interfaces These will be deprecated in the next version when the incompressible element is changed Syntax behavior hyper_elastic thermal_strain lt THERMAL_STRAIN gt hyperelasticity lt HYPERELASTIC_LAW gt mixed_hyperelasticity lt MIXED_HYPERELASTIC_LAW gt kisotropic_hyperelasticity lt ISOTROPIC_HYPERELASTIC_LAW gt model_coefficients eet FS eo eo Example behavior hyper_elastic khyperelasticity arruda_boyce model_coefficients mu 0 893 lambda 9 0 d 0 1 return Z set Non amp structure an 10 5 x behavior linear viscoel behavior linear _viscoelastic Description This behavior defines a generalized linear viscoelastic Ma
173. is For hexagonal crystals the directions in the basal plane are depicted in the following figure after Tome and Kocks 1985 and the c axis coincides with the Z set z axis B 1210 y 0110 o 2110 x 2110 y 1120 The crystal orientation will provide the localization tensors for the different slip systems 7 in a crystal Ti mMmM o with 7 the resolved shear stress on slip system and the macroscopic stress tensor For each slip system 7 in the particular crystal set the second order Schmid tensor m is defined as follows with 7 the normal of slip plane i and the corresponding slip direction Syntax lt creating command gt type interaction h coefs c_over_a c a value In absence of the interaction command only self hardening is taken into account i e hi 1 and the other coefficients are 0 For some hexagonal crystals the ratio of the length of the c axis to the length of the a axis is needed continued Z set Non linear material 13 31 amp structure analysis suite lt CRYSTAL_ORIENTATION gt 13 32 The following crystal systems are available cubic This orientation is for the 6 FCC cubic systems with up to 3 hardening coefficients TES IS LO LO AA ES OoOorRrRO O RRPOOOO o Na m m S Pree FO OO El E E Es a octahedral This type of crystal is used for the 12 FCC octahedral slip systems with up to 6 hardening coefficients basal
174. it value Typically the value should exceed likely variations for the variable selected and the divergence_variable increment value set accordingly to produce an increment cut back of the required size Example The following listing summarizes the options needed in a visco dat Marc input file when using the Zmarc interface title visco parameters section state var 19 19 creep 0 0 1 end model definition section isotropic 1 visco plas isotropic 0 0 0 0 materiall 20000 0 3 8 E 6 2 E 5 0 0 0 0 0 0 0 0 all_element post 14 16 17 0 0 19 20 0 1 0 301 311 7 evcum control 100 10 2 0 0 1 1 0 1 0 0 001 0 0 1E 8 0 0 1 0 0 1E 4 1 E 12 Z set Non linear material amp structure analysis suite Zmarc interface history definition section auto step 0 02 0 4 0 0001 0 1 100 6 1 10 033337 2 gt 1308 a11_element 10 0 01 The Zmat behavior is defined in a separate visco zebulon file included hereafter The cooresponding model is a typical Chaboche viscoplasticity model Note that the value of the young s modulus will indeed be 150000 as defined in the Zmat file and that the value of 20000 given after the isotropic command of the dat file has no impact whatsoever on the results material integration theta_method_a 1 1 e 9 100 divergence_variable 8 20 behavior gen_evp kelasticity young 150000 poisson 0 3 potential gen_evp ev criterion mises flow norton n 7 K 1200
175. iterion lt POROUS_CRITERION gt flow lt FLOW gt isotropic_hardening lt ISOTROPIC gt strain_nucleation lt STRAIN_NUCLEATION gt kinematic lt POROUS_KINEMATIC gt shear_anisotropy lt CRITERION gt porous_potential a Hf lt SMATRIX gt Hp lt SMATRIX gt broken_behavior lt ELASTICITY gt radiabatic_heating no_C_trick save_D save_L x bifurcation_D bifurcation_L perturbation additional_var_aux The following sub options control the global behavior operation while the rest of the specific model will be determined by the dynamic components chosen most important of which is the porous potential additional_var_aux allows requesting that additional auxiliary variables be added to the model output These can be chosen from triax p1 p2 p3 These variables are closely coupled to the behavior so can be used for additional coefficient dependencies adiabatic_heating includes adiabatic heating via plastic work and temperature is included as a state variable named T broken behavior is used to enter an elasticity matrix to be used as the behavior after failure has been reached The measure of breaking is determined by the models potentials there could be different criteria for several potentials together Hf Coupling term for porosity given above The matrix is read in as a series of real floating point values to fill the matrix Note these are not general coefficients but fixed
176. ized debonding u um T MPa 3 Time s Time s 100 50 max 0 1 2 3 4 5 2 0 2 4 6 8 10 12 14 16 Time s u um Figure 5 Example in two dimensions of the evolution of the cohesive traction as a function of the opening displacement for two different loading cases uy t with u t 0 thick red curves and ur t with uy t 0 thin green curves Top left applied load u t Note for 2 lt t lt 4gs the applied loading becomes negative but the response uy remains 0 because of an implicit non penetration condition Top right response T t Bottom left Amar t Bottom right u t vs T t 12 13 Z set Non amp structure a x behavior diffusion behavior diffusion Description Diffusion behavior is analogous to the stationary thermal behaviors J DVC Syntax behavior diffusion kinter_phase_diffusion val phase D COEFFICIENT comp_max val comp_min val Stored Variables prefix size description default dc V gradient of concentration yes J V flux of concentration yes C S the concentration yes phase S phase id in input order yes Deff S effective D at point yes Example behavior diffusion inter_phase_diffusion 8 e 10 phase oxide D 1 e 7 comp_min 1200 0 phase metal D 5 e 9 comp_max 400 return 12 14 behavior linear _ spring behavior linear_spring Descripti
177. jected to a constraint one could proceed as follows In the master file optimize inp optimize lt OPTIMIZER gt function f a exp 1 7b constraint cos a b compare i_func_file f 1 unreachable_goal dat values a 1 min 0 max 10 a 2 min 2 max 5 convergence return 16 10 Z set Non amp structure a x xoptimize compare where the file unreachable_goal dat contains a lower bound on f for example 0 here The optimizer will minimize the distance between the lower bound in the reference file and f Note that if the optimizer is Levenberg Marquardt the lower bound should be near the real minimum of the function otherwise the Levenberg Marquardt approximation might be poor and convergence impaired Z set Non linear material amp structure analysis suite 16 11 xoptimize compare t_file file 16 12 compare t file file Description This comparison is used to compare two files names fnamel et fname2 with a time weighted averaging Files are columns files containing doubles For each file one considers a relation yi t i 1 2 interpolated from columns y1 and t1 To compare two files one considers the instersection of columns t1 and t2 One defines t_ max min min t min max max tetl tet2 tetl tet2 The function to be optimized is given by 1 Ao f 0 wilt de The optimization variables x should affect o
178. k and forth is required Also there are additional inputs required to control Z mat outside of ABAQUS The following figure outlines The interaction of different programs and the use of input files Z sim Zebulon FEA Integration i FEA Code UMAT FEA Z mat method Z mat e g ABAQUS m translation and mH behavior control routine integration Z mat behavior file model definition coefficients FEA code input Z mat input e g ABAQUS inp file file The ABAQUS inp file The use of an externally defined material behavior in ABAQUS requires a number of special entries to be made in the ABAQUS inp file Some of these entries are superfluous given the structure of the Z mat library but are nevertheless required to satisfy ABAQUS s umat interface The entries are e MATERIAL command to define the different materials of the problem The name given to this command using NAME will be the name of an external file containing a Z mat behavior definition see previous section e DEPVAR command which establishes the storage per integration point for the material variables This value must be greater or equal best case of the size determined by Z mat for the behavior There is no way except for user intervention to size this value so the line must be included If the value is too small for the behavior an error message is printed in the 1log f
179. kinematic nonlinear C 126000 D 380 isotropic constant RO 10 return Using the Zpreload utility on the above material file would produce the following output Zpreload visco zebulon Reading behavior in file visco zebulon Flux Name Sigll sig22 sig33 sigl2 sig23 sig31 Grad Name eto11 eto22 eto33 eto1l2 eto23 eto31 Z set Non amp structure a 5 7 Zmarc interface 5 8 var_int Name eel11 sdv1 eel22 sdv2 eel33 sdv3 eel12 sdv4 eel23 sdv5 eel31 sdv6 evcum sdv7 al111 sdv8 al122 sdv9 al133 sdv10 al112 sdv11 al123 sdv12 al131 sdv13 var_aux Name evil1 sdv14 evi22 sdv15 evi33 sdv16 evil2 sdv17 evi23 sdv18 evi31 sdv19 done with material file reading Temperature not needed This allows to select the number of state variables needed by the behavior 19 variables in the example that should be given as argument of the state var command State variable number 7 is the cumulated plastic strain named evcum for this particular Zmat behavior This material variable will be stored in the Marc results file using the appropriate post elem var code 7 in this case This variable is also used to monitor local divergence 1308 code to define the user criterion used in the auto step procedure and a corresponding divergence_variable is included in the Zmat file to control the increment cut back in case of local divergence Note that Marc always use the first state variable to store the
180. l amp structure analysis suite behavior crisfield debonding 16 0 7 T 125 7 14 0 100 F 12 0 751 10 0 30 25 E 80 0 gt 6 0 25 l 4 0 Egl 2 0 p 75 0 0 100 J 2 0 i i i i 125 i i i 0 0 1 0 2 0 3 0 4 0 5 0 0 0 1 0 2 0 3 0 4 0 5 0 time s time s 125 100 p 75 50 F 7 y 25 F oO 0 FR 25 50 L 75 L 100 F i i i i 125 i i i i i i i 0 0 1 0 2 0 3 0 4 0 5 0 20 00 20 40 60 8 0 10 0 12 0 14 0 16 0 time s u um Figure 2 Example in two dimensions of the evolution of the cohesive traction as a function of the opening displacement for two different loading cases uy t with ur t 0 thick red curves and ur t with uy t 0 thin green curves Top left applied load u t Note for 2 lt t lt 4gs the applied loading becomes negative but the response uy remains 0 because of an implicit non penetration condition Top right response T t Bottom left Amaz t Bottom right u t vs T t Example behavior crisfield_debonding sigmax 100 u0n u0t deltan deltat alpha alphac return ererrr rere 12 7 behavior chaboche debonding 12 8 behavior chaboche debonding Description This behavior is used for the special problem of interface debonding See the command create_interface_elements and similar in the Z set user manual on how to insert cohesive elements in the mesh Th
181. l are the following prefix size description default eto T 2 total small deformation strain yes sig T 2 Cauchy stress yes eel T 2 elastic strain no ein T 2 total inelastic strain tensor yes The variable ein is only stored in the event of multiple potentials The separate inelastic strain tensors for each potential and their hardening variable names will be given for each separate potential type This behavior must be used with a 9 method of type A Example An example the input for which can be found in test Kinematic MAT is given below behavior reduced_plastic elasticity isotropic young 185000 poisson 0 3 potential gen_evp ev Z set Non li amp structure an behavior reduced plast store_all flow norton K 05 n 2 0 kinematic nonlinear_with_crit C 600000 D 1000 omega 0 50 mi 1 m2 1 eta 1 e 12 isotropic constant RO 400 return Z set Non linear material 10 17 amp structure analysis suite behavior porous plastic 10 18 behavior porous_ plastic Description This material model is used for damage and densification of porous materials for which the flow rule is associated The model will be fabricated based on an assemblage of various objects to model the elasticity criterion flow and various hardening isotropic and kinematic and nucleation options The model supports multiple potentials viscoplasticity anisotropy and combined isotrop
182. le interactions in the gen_evp behavior object Syntax The syntax of the interaction types depends on the type of interaction Generally there will be a specification of the type of interaction and two identifying tokens which define the variables which interact This structure is summarized below interaction type item1 item2 where type may be from the following types CODE DESCRIPTION iso Crystalline isotropic hardening interaction default In the absence of type the default state interaction will be implemented as described by Cont89 This interaction calculates associated forces including terms of other internal variables The coupling will be stated by using the user supplied name of a potential and the user supplied name of hardening mechanisms interaction PI H P2 H lt COEFFICIENT gt iso This interaction will link the isotropic variables of one class of slip systems with another latent strain coupling between two mono crystal potentials The coupling is written n Ri Ro Qi X 1 eg j l syntax for this type of coupling takes the names of the two potentials and a coefficient definition named h interaction iso namel name2 h lt COEFFICIENT gt Note for interactions between slip systems within one potential one should use the SLIP_INTERACTION class see page 13 92 Example This is an example of the state law default coupling to link two kinematic variabl
183. lease notes The next important thing is to source the Z7PATH 1ib Z7_cshrc file to set up additional environment variables These two definitions can be put in a users cshrc file for the C shell The second most important environment variable is the Z7MACHINE variable All the scripts which access binary executables use the Z7MACHINE variable to determine where and which bi nary to run By default if the variable is not set before sourcing the Z7PATH 1ib Z7_cshrc file the machine type will be set as setenv Z7MACHINE uname Sometimes this is not suffi cient to distinguish an architecture so the user may add additional machine types Additional architectures may be defined for different machines in the Z7PATH lib MACHINE_TYPES file This file is also used to define different compilers to be used The Release Notes Zmaster manual has more information in the Configuration chapter Windows configuration Aside from specifying the ABAQUS_ROOT position no special work is needed for running Zmat on windows platforms Only a command line interface is available however Z set Non amp structure an 3 7 Site definition 3 8 Z set Non linear material j amp structure analysis suite Interface files Interface files The fact that Z mat is developed for use in Z set Zebulon FEA natively and that the interface with codes like ABAQUS is based on a Fortran subroutine implies that a certain amount of translation bac
184. linear if the time step is gt 0 even with zero strain increment because of stress relaxation under fixed displacement The Z mat material file The Z mat material file is the input which determines which constitutive model from the available models in Z mat to use and then specifies the particular coefficients accordingly This file is the same as input for Zebulon and for the Z sim The input format is the subject of chapters 4 and 5 Note By default the input file name for the material file is the same as the Z mat interface file so the behavior definition can follow the Z mat interface commands continued Z set Non linear material amp structure analysis suite Interface files Example The following small material file is a simple example of Z mat use taken from the ABAQUS interface tests which puts together some of these concepts Many more examples will of course be given in the different code specific chapters and around the discussion of each sub command suppress_doing_first state_var_no_change suppress_temperature material integration theta_method_a 1 0 1 e 10 1500 initialize_variable epcum 0 43 X11 7 529e 03 X22 1 065e 02 X33 3 118e 03 behavior gen_evp xelasticity isotropic young 2 1e5 poisson 0 3 potential gen_evp ep flow plasticity criterion mises isotropic nonlinear RO 200 Q 2000 0 b 0 26 kinematic nonlinear X C 25500 0 D 81 return Zed
185. lined above Example A simple example follows flow hyperbolic K 22 3 m 1 44 eps0 202e 8 cutoff 8 Z set Non linear material amp structure analysis suite lt FLOW gt lt FLOW gt modified visco Description This flow law is a Norton type viscoplastic rate using a strain hardening or softening viscocity term Let the following terms be defined ae E K Ko Q 1 e With which the flow law is written A d exp ad Syntax The flow law accepts coefficients KO Q b n and alpha Note There is another version of this flow called norton_hardening which reduces to a Ka ai 3 Z set Non linear material amp structure analysis suite 13 49 lt FLOW gt 13 50 lt FLOW gt sellars_tegart Description This is a flow rule given by C M Sellars and W J Tegart in 1969 as a proposed rate equation for hot forming conditions The use of a hyperbolic sine function allows for increasing overstress at low strain rates which is followed by essentially a saturation level of overstress Another way of describing the model is viscous at low overstress levels followed by essentially rate independent behavior for high stresses Normally this behavior would be combined with hardening viscoplasticity and not taken as a pure viscous creep law The rule is given as tapad Note that the Z mat formulation utilizes a ratio of the overstress by a normalizing flow stress oo Once the overstress become
186. ll model definition The commands for configuring Z mat can be classified as follows e Controls and context are commands which adjust the specific numerical run Note for Zebulon runs these controls are defined in the Z set users manual so this section does not apply These are all x level commands in the Z mat control file filename depends on specific interface chosen e Framework This part is determined basically by a selection of a behavior model type pair All sub commands after the behavior declaration will be context sensitive e Components Z set Non linear material amp structure analysis suite Material Frameworks Z set Non linear material 1 12 amp structure analysis suite Chapter 2 Z mat General Commands 2 1 2 2 Z set Non linear material amp structure analysis suite Z mat interface Z mat interfaces The current version of Z mat Z mat 8 3 supports the following interfaces e Z mat ABAQUS Both ABAQUS Standard and ABAQUS Explicit are supported With ABAQUS there are perhaps the most comprehensive set of features due primarily to the very robust user capability within ABAQUS In this regard Z mat is constantly look ing for additional paths of interface and with the 8 3 version we have added significant ODB input and output functions and also UEL interfacing for all the Zebulon element formulations e Z mat ANSYS The Zansys interface has improved immensely in terms of stab
187. lobelle s potential implements a special form of kinematic hardening evolution using mul tiple tensorial variables The implementation is based on the work described in Delo96 The class allows any CRITERION FLOW object to be used and uses the ISOTROPIC object in a somewhat different manner than the gen_evp based potentials There is a limitation on the ISOTROPIC objects which can be used such that no additional integrated variables are added The inelastic flow is controlled using a scalar CRITERION value for the overstress _of Oa where the function f is selected with the criterion option below The tensor x is the current back stress not sum of back stresses as in other models The scalar flow magnitude is a function defined in terms of f using the flow option as in other potential models The inelastic strain rate tensor is also defined as in other models using the normality principle so j n The initial hardening slope for kinematic variables follows a flow normal which is modified from the inelastic strain by scalar hardening and a 4th order tensorial orientation matrix 1 0 x n m 3 R A Yo Ti n The isotropic function R A A is the cumulated equivalent inelastic strain is chosen using the isotropic option below Note that only ISOTROPIC objects which have no integrated variables may be used e g no recovery The T matrix is entered using the T1 command required The tensorial back s
188. looking at that file after an execution possibly add comments to make the env file creation clearer The user can add configuration options in their customized personal files also The stan dard abaqus_v6 env file will not be used in this case replacing that with the file named zebaba_v6 env replaced only for Zmat jobs The Zmat program will search first in a users home directory followed by the local execution directory The environment file shipped in the Z mat for HP UX is for example link_sl Zmat link_v6 usr ccs lbin 1d64 b ashared_archive k n FPD vnocompatwarnings pd L pi D s c E h U o U F ZA ZB AL lpthread lcps 1c1 compile_cpp Zmat compile_v6 compile_fortran Zmat compile_v6 In the standard Z mat validation tests in the directory test Z mat umat_v61 we have the custom file zebaba_v6 env with the following ask_delete 0FF split_dat 0N For personal files one may wish to remove the ask_delete parameter Z set Non amp structure an Extra files Z set Non linear material 3 14 amp structure analysis suite User additions User additions Extensions to Z mat User functions and classes may be added to the Z mat library without limit This is one of the advantages of working with Z mat as a site can create a library of user functionality in combination with Z mat and use it repeated without distributing the source files for each problem run Also the user classes will be automa
189. low Non linear finite element analysis consists of a loop over all elements in order to fabricate the global DOF residual vector and possibly fabricate the stiffness if needed In turn there is a loop within the element over the integration points in order to numerically integrate the elements volume integrals At each integration point the new increment in primal variable is calculated using the increment of degrees of freedom and their derivatives this is where grad comes from and this is passed to the material behavior with the current value of state variables MAT_DATA Gradient grad BEHAVIOR Delta gradient delta_grad integrate Internal variables IV Auxiliary variables AV External parameters EP Flux Tangent matrix SS Sst Z mat used for other codes such as ABAQUS establish a similar relationship where the UMAT interface adjusts itself according to the material primal dual couple Z set Non amp structure a 9 5 Grad Flux 9 6 Z set Non linear material amp structure analysis suite Material variables Material variables As introduced in the previous section material behaviors in Z mat are dynamically created by the user through the assemblage of material sub objects The example given of a gen_evp behavior on page 9 4 was certainly structured this way Of interest to the user is what variables are contained in the mo
190. lpha 1 alphac 1 e3 n 22 6 K 0 18 df_0 44260000 dfdl_0 O return Bottom left Amaz t 12 9 behavior generalized debonding 12 10 behavior generalized_debonding Description This behavior is used for the special problem of interface debonding See the command create_interface_elements and similar in the Z set user manual on how to insert cohesive elements in the mesh The Generalized model is based on the consideration of the characterization of interfacial properties and permits to use three different shapes for the cohesive law bi linear tri linear and trapezoidal This model is described through a scalar variable A which characterizes the relative crack opening 9 9 050 6 6 0000 Of 1 1 10 i un eea Gary aeaa where x x if x gt 0 and x 0 if x lt 0 The parameter is the relative displacement defined as y uy lie 11 With respect to the interface normal Uy uyn and r U UN denote respectively the normal and shear opening displacements The parameters o and d are respectively the relative displacement associated with the interfacial strength 7 and the one attained when the energy release rate is equal to the fracture toughness Go It should be noted that the evolution of To resp Gc as a function of the mixed mode ratio is defined by the stress criterion resp the propagation law Finally the parameter d i
191. ls For final use we then let the different implemented bricks define the specifics That is to say the user always chooses the final model form e g specific evolution or state equations in the input file after development is finished In that way each model is really a model class or framework within which a user has a high degree of flexibility One can also add to the types available for these building bricks This not only lets one work on a smaller specific aspect but allows extending the capabilities of every model using that particular abstract type In this book examples of the general behavior frameworks are the subject of the chapters Material Models page 10 3 Secondary Models page 11 3 and Other Models page 12 3 The material bricks are described in the Material Components chapter beginning on page 13 3 In addition to the material behaviors and the development kit the Z mat product also ships with a number of additional programs bundled One such program is the ZebFront pre processing language which greatly aids the development of user models Others which are optionally included are the Simulation module and the Optimization module These two combine to make a very powerful material coefficient identification tool One can efficiently simulate and identify using the exact same model code as is used in the finite element code This will virtually eliminate an extra testing verification step and ensu
192. lved in the analysis This is needed by Marc because the uvscpl user subroutine can only be used within the creep algorithm creep 0 0 1 e Model definition section Z set Non amp structure an 5 3 Zmarc interface The visco plas parameter of the isotropic or orthotropic command must be selected to activate the use of material integration by means of the uvscpl user subroutine Note that either isotropic or orthotropic materials can be selected indifferently since values of the material coefficients given as arguments of these commands are ignored by Zmat that reads the material definition in a separate problem zebulon file isotropic 1 visco plas isotropic 0 0 0 0 materiall 2 E 4 3 E 1 8 E 6 2 E 5 0 0 0 0 0 0 0 0 1 to 1000 To benefit from the consistent tangent matrix calculated by most Zmat behaviors and accelerate the convergence of the global equilibrium iterations the full newton raphson algorithm should be selected by setting the 6 command to 1 parameter of the control control 1000 10 2 0 0 1 1 0 1 0 0 001 0 0 1E 8 0 0 1 0 0 1E 4 1 E 12 Output of material variables to the Marc results file The post command allows to select which material variable should be stored in the results files In this case the element codes that should be given as argument of the post command is a negative integer value such as varid where varid is the number of the user variable required for output post
193. moment Name Z set No amp structure behavior gen_evp verifications are strongly advised with the v command line switch or using the verbose output option Example The first example is for a viscoplastic behavior with two kinematic hardening variables and a Von Mises criterion see the following sections for the sub model syntax behavior gen_evp elasticity isotropic young 200000 poisson 0 30 potential gen_evp ev criterion mises flow norton n 7 0 K 400 kinematic nonlinear C 15000 0 D 300 0 kinematic nonlinear C 6000 0 D 100 0 isotropic constant RO 130 0 x return Different cases using this behavior are described more fully in the example handbook This behavior is designed to work normally with all the integration methods and gives the best tangent matrix possible for a given model The use of specialized options may however limit the use to a certain integration or otherwise The user of this behavior is therefore advised to try the theta method method integration on a volume element and adjust solution parameters according to the messages output if any 3This process will be automated for the best combination in later versions of the code re amp set Non linear material structure analysis suite 10 15 behavior reduced plast 10 16 behavior reduced plastic Description The reduced plastic behavior is an alternate formulation of the
194. n The plane stress modifier allows any material behavior to be run in plane stress conditions without extra terms being added to the model This is at the cost of extra local iterations but with the benefit that extremely complex cases can be treated effectively e g multi mats runge kutta models multi potential deformations multiplicative finite strain etc Syntax The following options are available after the plane_stress_controls heading skip_first The code attempts to predict the plane strain effect ahead of time which in some cases can push the nonlinear computation in the wrong direction Using this flag prevents that step xeps default from theta method or 107 iter default from theta method or 200 Example The modifier order is important for this object to be used properly Some typical examples follow behavior gen_evp plane_stress behavior gen_evp plane_stress auto_step behavior gen_evp lagrange_rotate auto_step plane_stress Z set Non amp structure an 14 7 lt MODIFIER gt 14 8 lt MODIFIER gt auto_step Description The auto_step modifier applies a local method of substepping for any material behavior in an attempt to pass divergences and improve accuracy without cutting back the global time step divergence div num takes parameters div real for the division factor to make when a divergence occurs and num int for the maximum number of successive divergences
195. n The functions have been generalized in code versions greater than 7 1 to have a natural equation like form and apply more widely throughout the program In addition to coefficient definitions the functions may now be used to define load waveforms apply to the optimizer etc More applications will be added as well The functions follow a C like syntax and may be defined in terms of pre defined functions sin log etc and named parameters of the problem What parameters are allowed and available depends on application Syntax Objects which are functions may now be entered using a C like format This must include a semi colon at the end of the function definition to terminate the reading of the function Many operators exist which have the same meaning and order of selection as in C Coefficients which are functions still require the keyword function to follow the coefficient name but are otherwise generally given in terms of the relevant parameters The following operators are defined in functions gt lt 7 gt lt as are the following functions triangle floor asinh acosh atanh asin acos atan cosh sinh tanh ceil sqrt neg abs sqr sin cos tan exp 1n Hx H Pre defined functions may take complex arguments of other expressions or functions triangle function used to make a sawtooth waveform with period 1 of the parameter floor largest integral value not greater than x H Heaviside function Equal to 1 for x gt
196. nalysis suite lt DAMAGE gt lt DAMAGE gt Description This object class permits addition of damage mechanisms to a behavior assembly of type gen evp These models are of the type continuum damage mechanics CDM and thus provide interaction through alteration of the elasticity modulus with damage and calculation of plasticity with the use of an effective stress Damage models may be used in the gen_evp behavior with and without inelastic defor mation potentials The coupling with inelastic deformations and their hardening variables is discussed below Syntax The damage mechanisms are added through the use of a token damage input after the kelasticity declaration The general syntax is damage dama_type elastic plastic creep coupling type There is a restriction currently that the damage statement must come after the elasticity statement in the behavior The number of coefficients for each option depends of course on on the particular damage model selected The currently implemented types are summarized below CODE DESCRIPTION elastic elastic damage anisotropic_elastic anisotropic elastic damage with scalar and tenso rial variables plastic plasticity damage which depends on the rate of inelastic deformation creep time dependent damage fatigue cyclic damage elastic The coefficients here are BO et alpha The damage is calculated directly at a given time as 1 X
197. nd problem processing for all the different interfaces Generally the Z mat user could be interested in the following e Opening results files for visualization and rendering The following simple commands are examples Zmaster odb my_calculation odb Zmaster my_calculation fil Zmaster ansys_calc rst e The 8 3 6 version includes the Simulation GUI interface for setting up and working with material simulation and fitting work e Mesh files can be imported and saved to different formats with sets and other boundary condition data preserved e Many of the Z mat validation test cases use a post processing step to extract X Y data in an automated manner Zmaster can be used to plot general ASCII file data using the Plot button Zmaster doghri test More detail on the file format translators and use of Zmaster is given in the Release Notes Zmaster handbook Z set Non amp structure an Zmaster interfaces Z set Non linear material 2 22 amp structure analysis suite Chapter 3 Z mat ABAQUS 3 1 3 2 Z set Non linear material amp structure analysis suite Z mat interface Z mat ABAQUS interface Description The commands described in this chapter are used to enable a Z mat material model for use within ABAQUS Syntax Z mat jobs are launched via the Zmat command line script only Zmat opts problem The command syntax for Zmat is given in more detail in the Release Notes z Zmast
198. ne in the evolution The coefficients are to be entered into COEFFICIENT_MATRIX objects see page 13 9 Min n DCX _ Xllo y wrin CEQ X Ee 10 Any of the coefficients can of course be a function or table of the temperature or other parameter The equivalent term X g above is calculated as follows IXllo X Q x Syntax kinematic aniso_nonlinear name C lt COEFFICIENT_MATRIX gt D lt COEFFICIENT_MATRIX gt xi lt COEFFICIENT gt defines recovery exists Q lt COEFFICIENT_MATRIX gt overrides global m lt COEFFICIENT gt ditto M lt COEFFICIENT gt Example kinematic aniso_nonlinear xi C cubic C1111 20000 0 30000 0 1 5 C1122 0 0 C1212 20000 0 D cubic D1111 500 D1122 0 0 D1212 500 13 60 Z set Non li amp structure an lt LOCALIZATION gt lt LOCALIZATION gt Description This object selects a localization model to be applied to the different potentials of a gen_evp type behavior Syntax Localization is indicated within a gen_evp behavior with an entry of the following type localization type From which the following localization types may be chosen CODE DESCRIPTION poly polycrystal multi grain model poly The polycrystal mode here is a generalized form of that described by Cailletaud and Pilvin Cail92 Cail94 Pilv94 Several potentials of type crystal will be assembled to form a slt phase of the material whic
199. ne of the two files fnamel or fname2 Note Because of the time weighting of the error the density of comparison points is not important for the comparison function although more points will be more accurate Also if the time scale of a test changes this method can totally miss important features of the response For example if a hold time loading profile of 10s 300s 10s is applied the emphasis will be on the response during 300s Any details of the 10s segments will essentially be lost Syntax t_file file fnamel t1 yl fname2 t2 y2 weight vweight Z set Non linear material amp structure analysis suite x xoptimize compare t_file file compare g file file compare g file file Description This comparison is a generalized file file method based on point densities The user therefore has to think about the distribution of comparison points either in the simulation or reference files in order to best control the quality of error estimation Either file ref or simulation can have more points and the points of the smaller will be interpolated between points of the larger file This assumes that the larger file will have points who s linear segment will more closely approximate the real curve Files must contain continous column data of real floating point format values Lines can be commented with or The function to be optimized is given by E Ly e al ls efh with J being
200. ng an optional name on the same line and giving the appropriate coefficient definitions on the following lines This is summarized below where the keyword specifying a KINEMATIC object is assumed to be kinematic kinematic type nom coefficients where the possible substitutions for type are CODE DESCRIPTION linear linear hardening nonlinear nonlinear Armstrong Fredrick hardening with static recovery nonlinear ai same as the nonlinear model but using more ac curate asymptotic integration ziegler nonlinear hardening based on the Euclidean norm La nonlinear_phi nonlinear with cumulative influence nonlinear_evrad nonlinear with reduced ratcheting nonlinear_with_crit linear nonlinear with criterion aniso_nonlinear nonlinear model using coefficient matrices for the coefficients Kinematic models are all formulated in state variable form where the stored integrated variable is analogous to a strain translation in tensorial strain space The back stress component is then calculated using an appropriate modulus Most of the kinematic models use the convention for calculating the back stress 2 X Ca 3 with X the back stress and the internal variable Material softening through kinematic variables is not thought to be physically reasonable and so the modulus coefficients C should always be positive Z set Non linear material amp structure analysis suite 13 57 lt KINEMATIC gt Evolution
201. nt fo y 6 X M s X R where s is the deviatoric component of stress k lt cmd gt anisotropic matrix type coefficients The input matrix type indicates one of the COEFFICIENT_MATRIX type keywords and the coefficients will depend on the matrix chosen e g diagonal orthotropic etc Example brief example using the anisotropic criterion is criterion anisotropic orthotropic c11 44667 c22 58 c33 666 c44 0 c55 1 7 c66 0 c12 18 c23 4 c31 26667 The criterion command indicates the application of the created criterion object in the higher level so can generally be different depending on the application Z set Non linear material amp structure analysis suite 13 15 lt CRITERION gt lt CRITERION gt bron Description The Bron criterion allows modeling of anisotropic behavior in the criterion and flow directions The proposed yield function is defined by an equivalent stress 6 a1 1 a a yr ye s3 ls Si lst sal 3b 2 Y BES 152 58 15315 where SE _ _3 are the principal values of a modified stress deviator s defined as follows s L ck 3 3 73 3 4 3 0 0 0 5 3 E c 3 ck 3 0 0 0 Lie c 3 ck 3 ck cK 3 0 0 0 aa 0 0 0 4 0 0 0 0 0 0 sn 0 0 0 0 0 amp a bl b and a are four material parameters that influence the shape of the yield surface but not its anisotropy which is only controlled by che a Thereby
202. o be output The available variables consist of the var int and var aux variables listed when the program is run with the v command line switch and the imposed external parameters file used to specify an output filename sido output compatible with the sidolo program and graphical utilities precision gives the number of significant digits 3 by default with which the variables are written small_ specifies a small value epsilon 1 0e 9 by default below which the absolute output value is considered zero Note this command is not related to the global parameter Solver SmallForTest which plays a similar role for the test output of the finite element solver frequency similar to the output frequency command of the finite element solver see the Z set user manual limit_output_var defines a function of one or more output variables or of time which inhibits output if its function value is smaller than 0 5 Example output example test time sig11 sig22 evcum output evcum damage output file strain test time etol1 eto22 eto33 eto12 file stress test time sigl1 sig22 sig33 sig12 Z set No amp structure xkkkSimulate x xtest ksolver solver Description This command defines the solution method for the simulation The default solver is an explicit Runge Kutta method In some cases the Runge Kutta integration may not be available for a material model or greater efficiency can be achieve
203. oadings and outputs may be repeated in the input sequence to create complex cases The model definition must be compatible with the solver type chosen Many simple simulation models are only compatible with the Runge Kutta integration with other FEA specific material models with implicit integration only must be used with the iterative Newton solver If the model is not compatible a run time error message will be issued Syntax The definition of a test case within the simulation will follow the syntax below test test_name load model type output solver type time_ini time_end var_mat_ini yield_surface error_map constant_parameter simulation plugin Each of these commands takes at least some extra input The different sub commands are all described fully in the following sections Use of at least one load command is required although multiple entries are possible The model must be defined as well either through the use of a defined default behavior using the model keyword before the test instance see page 15 1 For the explicit solver more accurate this may be a simple ZebFront model of type SIMUL_MODEL or a finite element behavior properly modified for the simulation mode The syntax for a FEM behavior does not take a behavior type after the model command The model name will be found in the material file after the command behavior Specialty simulation models do require the type follow
204. obal optimizers typically rely on pseudo stochastic transitions in the search space in order to be able to escape local optima we do not consider optimizers based on enumeration of all possible local optima Practically an important difference between global and local optimizers is that global optimizers are slower to converge but offer greater guarantees on the quality of the solution produced In many cases convergence of global optimizers is so slow that a solution cannot be found in a reasonable time Optimization methods can also be divided into methods that explicitly handle constraints 2 SQP and the others Levenberg Marquardt Simplex evolutionary algorithm Penal izing f is a simple way of transforming a constrained optimization problem into an uncon strained optimization problem Ng minimize Fp F x S pimax 0 gi x i 1 where p is a vector of positive penalty parameters The exponent a is usually taken larger than 1 typically 2 for gradient based optimization methods in order to ensure differentia bility The tricky aspect of penalization is in choosing p If p is to small the solution to the optimization problem will not satisfy the constraints On the contrary if p is taken too large convergence to the optimum might be difficult Optimizers that explicitly handle constraints do not require that the user specifies p Further details on optimization in mechanics can be found in G r92 Four principal optimi
205. oefficient names K n and alpha double_norton This model is a two term variation of the Norton law in order to model changes in flow mechanisms over a wide stress range lt f K gt lt f Ko gt with the required coefficients K n1 K2 n2 plasticity This flow type indicates time independent plasticity f 0 The use of plasticity may limit integration to implicit only in the case of some complex models There are no coefficients inv_exp This law provides an exponential dependence on the inverse of the effective over stress Aexp 220 with the coefficients n A alpha and pO where pO is optional default 0 interface_control This flow rule is expressed 1 kyo a ETE dom with the coefficients k1 k2 m d d represents a grain size flow_sum_inv This model is similar to the flow_sum rule but sums the inverse of the different flow rules i 1 2 E Ba where the terms are given by the various sub laws different than sum_flow and flow_sum_inv exponential crystal This law is a physically based flow law for crystalline slip which can be used with the crystal POTENTIAL models actually it can be used anywhere viscoplasticity is allowed f ni 22 y gamma0 exp var i 2 Note that the terms for this equation may be composed of function coef ficient types in the event that a functional form is desired For example FO_RT function 6 8e4 1 9868 temperature strain_hardening This
206. on This behavior class is used to specify linear response for spring or truss elements element formulation linear_spring or spr F kU Where F is the spring tension and U is the axial displacement of the spring Note that k can vary with any external parameter but not in relation to U Syntax behavior linear_spring k coef By default there is no thermal dilatation in the model Example A simple spring definition behavior linear_spring k 1 e4 return 12 15 x behavior thermal 12 16 behavior thermal Description This is the basic thermal behavior The conductivity is determined using a CONDUCTIVITY object Transient thermal problems require that a coefficient capacity be defined as well global behavior coefficient see page 9 11 The behavior calculates the heat flux from the gradient in temperature g kVT The enthalpy term is T dH Cp T dT TO where the integration will be carried out numerically if the heat capacity depends on the temperature Syntax behavior thermal conductivity CONDUCTIVITY coefficient capacity val Note that capacity and the coefficients in the conductivity object can be a variable coef ficients e g tables functions etc of the temperature variable This gives the model the possibility of including considerable non linear effects Stored Variables The grad variable is the gradient of temperature and the flux is the heat flux
207. on as found on page 15 13 as is the command solver found on page 15 15 Note that this includes the level Example The following is an example of a complete simulation file with a single test definition See the following pages for descriptions of the individual commands x simulate test funny define a test name which defines the default output load start the loading section segment 100 100 outputs per load segment below time sig11 eto22 sig33 eto12 sig23 sig31 0 0 O O O O O O 1 0 O 1 e 3 0 O O O 2 0 O 1 e 3 0 5e 3 0 O 3 0 O 1 e 3 0 5e 3 0 O 4 0 O 1 e 3 0 5e 3 0 O 5 0 O 1 e 3 0 5e 3 0 O model standard model definition with file funny mat integration file name rotation integration runge_kutta 1 e 3 and other options lIntroduced in 8 2 yield_surface yield0 test degrees 5 eps 1 e 12 component sig22 sigl12 time 5 0 output time eto22 sig22 etol2 sigi2 return Z set Non linear material amp structure analysis suite make a yield surface output xkkkSimulate the default ascii file for output is funny test from above xtest def 15 5 x simulate xtest 15 6 test Description This command marks an individual test condition to simulate Loadings output and model specification will be contained within this option The output file name will be determined by the test name given after the command L
208. on Mises equivalent of tensor tens trace Trace of tensor tens p1 Principal eigen values of tensor also p2 and p3 vec eq Equivalent of vector Because of the dynamic nature of the object construction it is often difficult to strictly define the names of all the stored variables ahead of time Users are thus strongly advised to observe the stored variables by using the v command line switch or verbose output option Z set Non linear material amp structure analysis suite Material variables An example of accessing these secondary variables in a Zebulon output statement follows output component sig mises sig pl sig p2 sig p3 sig11 sig22 sig33 sig12 etoll eto22 eto33 eto12 Example Taking the gen_evp material file example given previously page 9 4 and running it with verbose set on by default in Z mat for ABAQUS or with a v switch running in Zebulon or Z sim gives the following output Flux Name sigll sig22 sig33 sigl2 Grad Name etol1l eto22 eto33 etol2 var_int Name eel11 eel22 eel33 eel12 evcum all11 al122 al133 al112 al211 al222 al233 al212 Var_aux Name evili evi22 evi33 evil2 Default Output etol1l eto22 eto33 etol2 sigl1l sig22 sig33 sigl2 evcum evili evi22 evi33 evil2 In fact what happens here is the behavior is put together by the different bricks with each brick naming its own variables Note that the potential line input was potential associated ev an
209. onstraints for example levenberg marquardt cannot do it Syntax The syntax is constraint FUNCTION lambda0 where lambda0 is an optional value for the initial lagrange multiplier associated with the constraint Example constraint A b 0 01 In this case the optimizer will change A and b such that A b lt 0 Z set Non linear material amp structure analysis suite x xoptimize comparison_constraint comparison constraint Description The comparison_constraint option can be used to add constraints that force the solu tion near some critical points of the reference curves Note that there may be no solution satisfying the constraint In this case an appropriate value of the convergence parameter constraint_tol should be used to allow some constraint violation see the convergence options of the corresponding optimization method Syntax The syntax is COMparison_constraint s_file file xref fnamel t1 yl fname2 t2 y2 lambda0 1 where xref is the value along the x coordinate for which a constraint is added to enforce v x y2 x fnamel fname2 are the names of the two files used in the comparison tl t2 are the column numbers in files fnamel and fname2 that are used to define the x coordinates yl y2 are the column numbers in files fhamel and fname2 that are used to define the y x values lambda0 is an optional value for the initial lagrange multiplier assoc
210. or the optimization algorithm Initial values and bounds are to be given for each function and file optimization variable using the value command page 16 21 Syntax The syntax is x function name FUNCTION where name is the name given to the function If a variable name is repeatedly found in several files functions they are treated to be the same and therefore only one optimization unknown is created Example The horrible function from Ackley xoptimize sqp xfunction f1 20 exp 0 2 sqrt 0 5 x1 2 x272 exp 0 5 cos 4 3 14159265358979 x1 cos 4 3 14159265358979 x2 20 2 71828182845905 compare i_func_file f1 1 goal_ackley values x 1 1 min 5 max 5 x2 0 5 min 5 max 5 16 20 Z set Non li amp structure an x xoptimize value value Description The value command is used to initialize the variables to be optimized The initial value of the variables is used to normalize them It is also possible to indicate min and max values for the variable Some algorithms need these values an error message will be given if they are missing Variables can conveniantly be taken out of the optimization by using the fixed keyword in the variable initialization All fixed variables will still be substituted in the tmp1 files but they remain at the given initial value throughout the optimization Syntax The syntax for variable initialization follows T
211. ormalization Standard RK error calculation for each integrated variable will be normalized by either the increment of the variable or this second parameter whichever is greater the resulting error is compared with the first parameter The Runge Kutta integration with the gen_evp material behavior provides a tangent matrix in models with a single inelastic deformation This matrix is however not consis tent with the integration scheme and thus yields less than optimal global convergence The explicit integration also performs poorly in heavily time dependent problems such as viscoplasticity However some complex models are only implemented with this method theta_method_a The 6 A method is the standard integration for the majority of material Z se R amp structure an laws requiring integration x t At a t t t 0At At This method requires 3 parameters to describe the convergence These are first the 0 value real followed by the residual required for convergence real and the maximum number of local iterations in the integration integer The value for 0 must be greater than zero and less than one It is strongly advised to use theta values of 1 for time independent plastic materials and 1 2 for time dependent viscoplastic problems Time independent plasticity will normally show strong oscillations about the solution for values of 0 less than 1 Reasonable values of convergence range from 1078 to 1071 Values whic
212. ors specific to Zebulon Finite Strain The behaviors are normally defined using small strain assumptions These models may be transformed to finite deformations rotations using one of the behavior modifiers described on page 14 3 The hyper_elastic behavior models are however formulated specially with total Lagrangian assumptions and must therefore be used with the appropriate total Lagrangian elements Z set Non linear material amp structure analysis suite lt BEHAVIOR gt Z set Non linear material 9 14 amp structure analysis suite Chapter 10 Material Models 10 1 Z set Non linear material 10 2 amp structure analysis suite behavior linear elastic behavior linear elastic Description This behavior class provides classical linear elastic behavior with optional thermal deforma tion The behavior understands two blocks from which it is defined Syntax behavior linear_elastic modifier kelasticity ELASTICTY thermal_strain THERMAL STRAIN By default there is no thermal dilatation in the model Example Two examples of linear elastic behavior follow behavior linear_elastic kelasticity isotropic young 200000 poisson 0 30 return behavior linear_elastic thermal_strain anisotropic codilail 1 0e 06 codila2 2 0e 06 codila3 3 0e 06 elasticity orthotropic y1111 350000 y2222 280000 y3333 280000 y1122 150000 y2233 120000 y3311 15000
213. os ac ga a RR ee ee a e a 13 47 FLOW hyperbolic aoaaa aa a 13 48 FLOW modified_visco 2 13 49 FLOW sellars_tegart 2 a 13 50 QW SUM fe sb aa de Hcg a NR Tis Aon Hem amp MG de ea 13 51 INTERACTION 0 ee 13 52 ISOTROPIC vostra bee be PRE aa Pe Eh ee ee ee 13 54 KINEMATIC das ptas a eee Re ee eR wa ee 13 57 KINEMATIC aniso_nonlinear o aoao a a a ee ee 13 60 LOCALIZATION 2 24 208 ra Rw wee ee 13 61 POROUS_CRITERION e as aapa 0 000 0 eee ee 13 63 POROUS CRITERION cam clay 0 2 00222020004 13 64 POROUS_CRITERION elliptic o e 13 65 POROUS CRITERION ellipticaniso 13 66 POROUS CRITERION fkM o 13 68 POROUS_CRITERION gurson e 13 69 POROUS CRITERION rousselier o o a 13 70 POROUS_CRITERION modified _rousselier 13 71 POROUS CRITERION zhang niemi 13 72 POTENTIAL sso setara manip p aaae e aie ee 13 13 POTENTIAL associated ecr ace e poe aoe aoe u e ua ee ee a 13 74 POTENTIAL coupled_recovery e 13 76 POTENTIAL delobelle o e 13 77 POTENTIAL crystal 2 ee ee 13 80 POTENTIAL gen evp 0 0 00002 eee ee 13 83 POTENTIAL gen evp2 20 02 0000 ee eee eee 13 86 POTENTIAL suvic c sa cau 2 ee ee 13 87 POTENTIAL 2M1C aaaea 13 89 POTENTIAL z6_genevp 0 02 020002 eee ee ee 13 90 SINTERING STRAIN 0 0 0 0 200200000 rrr eee 13 91 SLI
214. ow c type parameters CODE DESCRIPTION equivalence coefficient which is the value of a variable same as equivalence function coefficient which is a function of variables see chapter Functions equivalence coefficient which is the value of variables stepwise step wise tabular values default tabular description in terms of variables Example The first example is for a tabular coefficient This example has an equivalent stress sigeq as a function of the cumulated flow and the temperature Note any number of variables may be given If the parameter values are out of range from what is given in the table and error will result sigeq epcum temperature 400 0 0 0 20 0 350 0 120 0 290 0 200 0 Z set Non linear material amp structure analysis suite 13 7 lt COEFFICIENT gt 450 0 0 002 20 0 410 0 il 120 0 330 0 n 200 0 500 0 0 01 20 0 460 0 n 120 0 400 0 200 0 The second example uses functions to describe the coefficient value Function syntax is described more fully in the Functions chapter Note parameter names must be on the same line as the function declaration young function 230 1 e 2 temperature temperature 2 0 The last example assumes a parameter is calculated in the material law called Bpaiv This example will set the coefficient value to the value of that parameter at all times kinematic nonlinear A1 40 0 Bp Bpalv 13 8 Z set Non linear material i amp struc
215. perbolic sin function applied to power law of strain_hardening gsell modified_visco sellars_tegart function abq_strain_hardening norton_exp double_norton flow_sum flow_sum_inv inv_exp interface_control plasticity use_global_function exponential_crystal overstress Norton type viscoplastic rate with hardening viscoplastic model for some polymers viscoplastic rate using strain hardening or softnening Coupled with hardening to study variable strain rate A function in terms of overstress and cumulated plastic strain flow class available through ABAQUS exponential saturating Norton law two term norton law summation of norton terms summation of inverse norton rates viscoplastic according to Aexp p po ac interface reaction flow time independent plasticity uses a function defined elsewhere physically based exponential flow law esp useful for crystal deformation lt f K gt The default type of flow is plasticity norton This law corresponds to the classical Norton creep power law The coefficients are chosen to normalize the stress term and then apply the exponent with f positive The coefficients K and n must be non zero Z set Non linear material amp structure analysis suite lt FLOW gt norton exp This flow provides a limit stress approximating creep at low stress levels and plasticity at high stresses lt f K gt expla lt f K gt which uses the c
216. ple would be to give sig11 sig12 for the components degrees The sweep angle which will be used for each step in the surface Note that fineness of the surface depends on this but also that the sweep center be in the center of the surface Being close to the surface in one point increases the number of output points because it dominates the point of view angles Instead of using the sweep angle to define the steps a list of angles in degrees angleO anglel angle2 can be specified If both degrees and angles are specified the degrees command will be ignored unfortunately gradient values cannot yet be used to scan for strain space yields surfaces etc Z set Non linear material 15 17 amp structure analysis suite x simulate xtest yield_surface 15 18 xfactor A magnitude of the flux gradient which is considered large for the surface Look in the output file for bad value lines marked with a comment line If there are bad values increase the factor The default value is 400 eps A positive real value eps specifying the degree of convergence in the surface The actual value depends on the strain rates as specified by the rate command rate the If neither eps nor rate commands are given then the default value is 1 e 1 If no eps command is given and the rate command is given without specifying any strain rate then the default value is 1 e 1 If no eps command is given whil
217. puted at node 2345 of the structure Note that some mesher operations can be included in the post computation as well to generate nsets for example which were not included in the abaqus model during the pre processing stage x post_processing data_source fil open doghri fil x global_post_processing file node output_number 1 999 nset ALL_NODE process curve doghri test precision 4 node 2345 eto11 sigil return Note For Zansys the capability and input is quite the same thing except that the file format should be data_source rst and the problems rst file should be placed in the open input Z set Non amp structure an Post calculations Z set Non linear material 3 20 amp structure analysis suite Chapter 4 Z mat ANSYS 4 1 4 2 Z set Non linear material amp structure analysis suite Zansys interface Zansys ANSYS interface Description The Zansys functionality mirrors very much the same principals as in the Z mat for ABAQUS port and so we refer the user to that documentation as well This section provides a getting started guide to Zansys Syntax Zansys opts problem gt Getting started Perform a standard installation of Z set including the binaries and shared files The install location will henceforth be referred to as the Z7PATH The launch procedures for Zansys will also need to be able to locate the ansys Note In versions prior to 8 3 6 it
218. r is used with ABAQUS Explicit to provide the total integrated coro tational strain One may equally use the lagrange_polar and lagrange_rotate modifiers but these duplicate many calculations already done by ABAQUS before entry into VUMAT and therefore are costly Z set Non linear material amp structure analysis suite 14 13 lt MODIFTER gt 14 14 lt MODIFIER gt bifurcation Description This behavior is used to make bifurcation analysis At each iteration it find the solution of the following minimization problem min 7 C ii ERS C is usually the consistent tangent operator which means that the solution to the previous problem depends on the time discretization but may also be the tangent one The solution vanish to zero when localization occurs It works with any mechanical behavior and add the following auxiliary variables theta the first angle of phi the second angle of available only in 3D det_min the minimum of the determinant Note that the coefficient of the underlying real behavior may depend on these auxiliary vari ables It is possible to specify x bifurcation_controls non_linear_bif to take into account non linear geometry which induces new terms in the minimization coming from the Jaumann derivative Z set Non linear material amp structure analysis suite Chapter 15 Model Simulation 15 1 Z set Non linear material 15 2 amp structure analysis suite
219. r size for given problem dimension Syntax The syntax consists of specifying the type of kinematic object supplying an optional name on the same line and giving the appropriate coefficient definitions on the following lines This is summarized below where the keyword specifying a DIRECT_KINEMATIC object is assumed to be kinematic kinematic type name coefficients Example A duplication of the classical Armstrong Frederick kinematic class is implemented for verifi cation and testing purposes Normally using the nonlinear KINEMATIC type is the model to choose An example use of that class is kinematic armstrong frederick C 40000 D 500 Z set Non linear material amp structure analysis suite lt DIRECT_KINEMATIC gt lt DIRECT KINEMATIC gt asaro Description This kinematic hardening model provides nonlinear modulus behavior forming a hysteresis loop with slight S shape Normally this kinematic type would be combined with other linear and nonlinear hardenings to fine tune cyclic behavior 1 2 de a a C tanh D X gt D aeq f Oleg Qi n Syntax The basic input syntax here is kinematic asaro name c coef value D coef value M coef value m coef value continued Z set Non linear material amp structure analysis suite 13 39 lt DIRECT_KINEMATIC gt Example The following example shows the use of this kinematic model in combination with a num
220. rag stress yes R T 2 kinematic rest stress yes Example The following is a simple example of the MATMOD material corresponding to the material in Miller s original paper As given by Mill76 Tests matmod x behavior matmod 11 15 x behavior matmod kelasticity young temperature 1 93e5 23 0 1 55e5 538 0 poisson 0 3 model_coef Al 0 108 MPa 1 A2 2 27e 7 MPa 1 B 1 e15 sec 1 C2 0 69 MPa H1 1930 MPa H2 100 n 5 8 Q 91000 0 cal mol Tm 1800 0 Degree K return 11 16 behavior matmod_z behavior matmod z Description This model is an implementation of the MATMOD Z equations due to Miller Mill76 The model accounts for isotropic kinematic hardening and presents a particular form of temper ature dependence in the material coefficients Syntax x behavior matmod thermal_strain lt THERMAL_STRAIN gt kmodel_coef Stored Variables prefix size description default eto T 2 total strain yes sig T 2 Cauchy stress yes lam_vp S plastic multipliers yes lam_ir R S yes Fdef S yes Fsol S yes evp T 2 viscoplastic strain yes eir T 2 irradiation strain yes Example The following is a simple example of the MATMOD Z material corresponding to the material in Miller s original paper Zircaloy model from Oldsberg Miller and Lucas STP 681 1978 x behavior matmod_z model_coef E function 9 65e4 9 65e4 5 51e4 temp
221. raint 16 16 files 16 18 function 16 20 shell 16 26 value 16 21 auto_init from file 16 23 format 16 25 init from file 16 24 erin 16 27 simulate test 15 6 constant_parameter 15 8 error_plot 15 9 load 15 10 model 15 13 output 15 14 solver 15 15 vield_surface 15 17 behavior porous plastic porous_potential 10 23 behavior aging 11 3 behavior aniso_damage 11 5 behavior becker_needleman 11 7 behavior bodner_partom 11 11 behavior cast_iron 11 9 behavior chaboche_debonding 12 8 behavior coefficient diffusion 12 3 behavior crisfield_debonding 12 6 behavior damage elasticity 10 4 behavior diffusion 12 14 behavior finite_strain_crystal 11 13 behavior gen_evp 10 13 behavior generalized_debonding 12 10 behavior hyper elastic 10 5 behavior hyperviscoelastic 10 12 behavior linear_elastic 10 3 behavior linear_spring 12 15 behavior linear_viscoelastic 10 6 behavior matmod 11 15 behavior matmod_z 11 17 behavior mechanical_step_phase 10 24 behavior memory 11 19 behavior needleman_debonding 12 4 behavior non_associated 11 20 behavior porous_plastic 10 18 behavior reduced plastic 10 16 behavior thermal 12 16 behavior umat 10 25 behavior variable friction 12 17 behavior visco_aniso_damage 11 22 behavior viscoelastic_spectral 10 9 abaqus_v6 env 3 13 algo
222. rd run_marc script where commands needed to link automatically the Z mat package to build a custom marc executable have been added Therefore standard options of the run_marc procedure are also available with the Zmarc command MSC Marc Input The definition of a material for the Z mat behaviors always uses an external file to establish the model components and coefficients Z mat never uses the material parameters defined in the Marc dat file In the current implementation the definition of the Zmat behavior should be given in a file named problem zebulon Several additions to a standard Marc dat file are necessary to activate the use of Zmat Some of them cannot be accessed by means of the Mentat graphical interface and should be done directly in the dat file Those commands are listed hereafter e Parameters section The state vars command should be added to specify the number of material variables needed by the Zmat behavior The Zpreload utility can be used to compute the number of variables required In any case Zmat outputs to the log file the correspondence between the Marc user state variables and Zmat the behavior components If not enough state variables are available for the behavior the analysis is stopped Otherwise a warning is printed if more variables than necessary have been specified state vars 20 20 The creep procedure should be activated by means of the creep command even if no creep effects are invo
223. re the calculation is sensitive to input data or format Z set Non linear material amp structure analysis suite 1 5 1 6 Z set Non linear material amp structure analysis suite Introduction to Z mat Starting with version 7 2 of Zebulon approx 1997 the program has been modularized into components relating to finite element methods and components for material simulation and optimization These later programs are grouped into Z mat which while of course is natively implemented with all of Z set also includes interfaces to other codes One of the more interesting aspects of this is to be able to use Z set material behaviors as an extension set to codes which support user materials such as ABAQUS Standard ABAQUS Explicit ANSYS LS Dyna MARC and Cosmos M The Z mat product is thus mainly a library of material behavior routines constitutive equations which can be interfaced with FEA software and its supporting utilities In con trast with other FEA software products however Z set and Z mat are built on C with a strong object oriented design and many utility programming classes for advanced tensorial mathematics Such advanced program design techniques have enabled the software to be enormously extensible on many different levels of sophistication In developing extensions to Z mat a user can make new behaviors using the many abstract building bricks to create a modular flexible model based on fundamenta
224. res compatibility of behavior between the different stages of material modeling The optimization works efficient ly on multiple experimental simulation data sets and can even be used in conjunction with structural calculations Finally with versions 8 3 and greater Z mat has been expanded to include more method level capabilities such as pre and post processing of results along with other analysis add ons such as cycle skipping and user elements It is our hope that Z mat will grow to be a large scale CAE complimentary product for commercial and academic users although they are general purpose and can be used with subjects that have nothing to do with materials or finite elements Z set Non linear material amp structure analysis suite 1 1 1 8 Z set Non linear material amp structure analysis suite System Requirements System Requirements Z mat is an integral part of Z set and therefore is implemented on all the Z set platforms Floating licenses allow the user to employ model simulation and coefficient calibration on desktop systems while the Z mat interface can be used on different platform servers optimized for large FEA runs Also all file formats used by Z set and Z mat are platform independent including the reading of externally created binary files such as the abaqus fil or ansys rst files Specifics outlined below relate to the interfaces with the Z mat available solvers External interface
225. ress components X see page 13 30 which oppose 7 and scalar isotropic variables AN modeling the change in resolved shear stress length on plane i Multiple kinematic components may be specified but only one isotropic The other contributions to the isotropic hardening come from la tent hardening i e from interactions with other slip systems of the current potential see lt SLIP_INTERACTION gt on page 13 92 and or with slip systems of other crystal potentials see lt INTERACTION gt on page 13 52 The variables are shown schematically below for the specific case of only one kinematic back stress and all contributions to the isotropic radius contained in R Resolved Shear NY Stress T B Viscoplastic System elastic zone Viscoplastic Syntax The syntax of each crystalline potential takes the following form potential lt CRYSTAL_ORIENTATION gt name flow lt FLOW gt kinematic lt CRYSTAL_KINEMATIC gt isotropic lt ISOTROPIC gt interaction lt SLIP_INTERACTION gt rotate lt ROTATION gt store_all ct i a OE a 0 a ee E a E y ys y continued 13 80 lt POTENTIAL gt e The criterion is always 7 z ri with x D X and r ip RE where the term k 0 refers to the isotropic hardening of the current potential specified with the xisotropic command and the other terms k gt 0 reflect the contributions due to SLIP_INTERACTION see page 13 92 or inter potential INTER
226. rithm 15 16 angles 15 17 anisotropic 13 11 13 95 anisotropic elasticity 13 11 anisotropic thermal strain 13 95 armstrong_frederick 13 38 asaro 13 39 auto_init_from_file 16 23 auto_step 14 8 automatic_time 6 5 15 16 behavior 9 13 behavior aging theta 11 3 behavior veil_theta 11 3 by_point 13 55 cast iron 13 41 class 9 3 19 3 19 4 compaction 10 18 compare g_file_file 16 13 component 15 9 15 17 constant 13 55 constant_parameter 15 8 conventions 1 5 creep 13 36 criterion 15 17 cubic 13 11 cubic elasticity 13 11 debonding 12 4 12 6 12 8 12 10 debug 6 4 default 13 52 degrees 15 17 DEPVAR 3 9 3 17 dimension 6 6 directionl 15 9 direction2 15 9 divergence 2 8 14 8 15 16 dont_use_e_bar 13 3 double_norton 13 45 elastic 13 35 ELASTICITY 13 9 Elasticity modules 13 10 eps 14 7 15 18 error_plot 15 9 exponential_crystal 13 45 factor 15 18 file 15 10 15 13 15 14 find_offset 15 18 flow_sum_inv 13 45 forceit 14 8 format 16 25 frequency 15 14 full_step_jacobian 14 8 function 17 3 Gurson 10 18 init_from_file 16 24 initialize_variable 2 17 integration 2 15 15 13 Interface files automatic_time 2 8 behavior 2 9 debug 2 10 external storage 2 11 material 2 12 Darameter 2 18 save_energies 2 19 skip_cycle 2 20 interface_control 13 45 inv_exp 13 45 1so 13 52 iso_table 13 55 isotropic 13 9 13 95 iso
227. s This page summarizes the conventions used for the Z set input files An overview of the general command syntax command hierarchies is given in the beginning of the Examples Training manual e Running of Z set modules generally requires that a problem name be given Most input and output data files are based on this name with a variety of suffixes attached Henceforth problem will often be used to indicate the problem name given while running the commands e The characters and indicate that the rest of the line is a comment For example kload external problem loading e There are no abbreviations allowed in the use of keywords All keywords and command names must be written entirely e The admissible characters for the names of user variables are a z A Z gt gt y gt E 7 e The text entry is always case sensitive e The use of braces in the syntax descriptions indicates an option with a default definition e All parameter values used in the input files and described as real in the syntax de scriptions must have a decimal point All standard specifications of floating point values are accepted Two examples of real values are 3 0 4 2e 5 e The use of parenthesis indicates data input of real values in vector form An example is 0 1 0 2 1 0 In most cases the size of such vectors must be compatible with the overall problem dimension The symbol indicates a section whe
228. s 10 1 lin arveldsti o sor cp eu a adia aaa a a we 10 3 damage_elasticity ee ee 10 4 hyper elastiG 2 pos mobi dace a ge haa bk ee eee Sia a he ga 10 5 linear_viscoelastic a 10 6 viscoelastic_spectral ooo ee 10 9 hyperviscoelastic ee 10 12 PEN EVD o het e A RAE AREA Oe ES Ee eR RA 10 13 reduced_plastic 10 16 porous_plastic s se 2 ee 10 18 mechanical_step_phase e 10 24 A take aoe Betis doers oe a oats A a oe Bhs de eer a Sb ee o i 10 25 Secondary Models 11 1 ASME 2 RGR ER Re Dae a Be ee A we oe a 11 3 aniso damage 1 ee ee 11 5 becker_needleman 2 2 a 11 7 CAST TOM A a e al eld oie Aia F 11 9 bodner_partom ooa 41 11 finite_strain_crystal a 11 13 matmod 24 a a a a AA ee ee es a es 116 MALMOdZ e urea ee ea ee ee Roe A a ed AL MOCMOLY sz pho OW ew eR ee a Ee Be ae 11 19 non_associated ooo a 11 20 visco_aniso damage ooo a 11 22 Other Models 12 1 coeihicient diffiision p e a e Bak A ee oe 123 needleman_debonding oaoa aa a 12 4 crisfield debonding a 12 6 chaboche_debonding 2 ee 12 8 generalized_debonding 02 00 eee ee ee ee 12 10 diffusion i sans pororaa ea SO we ee ee ee a ea 12 14 linear Spring A E Ge de ko dee RL ae SS a Re ae eS 12 15 thermal s o som ss ba ee 12 16 variable friction e ee me ida os a we SO lc 12 17 Material Components 13 1 ANISOTROPIC_DAMAGE e 1333 ANISOT
229. s a simple whole example to give an indication of overall syntax The user will please refer to the different applicable porous potentials for further examples and details behavior porous_plastic lagrange_rotate_no_J elasticity isotropic young 210000 poisson 0 3 porous_potential porous_criterion gurson fs f qi 1 5 q2 1 shear_anisotropy mises isotropic_hardening constant RO T 200 50 200 O 150 100 100 500 flow norton K 01 n 5 radiabatic_heating 9 x coefficient capacity 3 6 return 10 22 behavior porous plastic porous_potential porous_potential Description porous_criterion shear_anisotropy flow isotropic strain nucleation kinematic 10 23 x behavior mechanical_ste behavior mechanical step phase Description This behavior is given to model materials which undergo a a phase change Syntax behavior mechanical_step_phase integer_steps parameter phase_id phase Oxide 0 file step mat 2 rotation lt rot definition gt phase Alu 1 file Alu mat return Example behavior mechanical_step_phase kinteger_steps parameter phase_id phase Oxide 0 file step mat 2 rotation lt rot definition gt phase Alu 1 file Alu mat return 10 24 specify integer step values to be used the parameter defining the step phases use this phase if phase_id O int value This file 2nd beh
230. s are at the time of this writing available for ABAQUS 6 3 6 4 MARC Ansys version 7 x LS Dyna 970 and COSMOS M 2 7 Machine platforms for ABAQUS include Solaris 32 bit IRIX 64 bit HP UX 11 HP UX 11 Ttanium AIX 5 OSF1 Linux i86 Linux Itanium and windows NT4 2000 XP The COSMOS interface is available on windows platforms only Z mat for Ansys is available on Windows SunOS 64 bit and IRIX64 Z mat for MARC is available on 64 bit IRIX only at this time Some of the platforms have limitations due to the methods of the different solvers Infor mation on these is described in the different Z mat chapters Normally we find the interface for ABAQUS the most robust with Ansys next then Cosmos followed by MARC The library is compiled as a dynamic shared object which can be linked to other programs The library is entirely programmed in C but only a system linker 1d is required for basic use of the program Again some specifics relating to the different platforms are relevant In particular for Ansys and Cosmos the user needs to compile a custom executable because we are not allowed to distribute a pre linked Z mat executable To have user routines attached to the basic library plug ins a C compiler is necessary Which C to use is determined by the requirements of the interfacing code e g ABAQUS and one should seek information from that vendor for compatibility For use with Z set only a g version is available for all plat
231. s associated with the stress 7 attained at the end of the first part of the damage process Figure 1 These both parameters depend on the shape of the cohesive law which is defined using two shape parameters ag and as determined by _ E _ 6 60 Ao gt as 5 60 12 Figure 4 Shape of the tri linear model for a constant mixed mode ratio in the T plane The damage variable Amaz which is the maximum value of A reached up until the current instant increases from 0 no damage to 1 for a broken element The normal and shear this behavior is Z set specific and therefore does not apply for Z mat for other codes SVandellos T Huchette C and Carrere N Proposition of a framework for the development of a cohesive zone model adapted to Carbon Fiber Reinforced Plastic laminated composites Comp Struct 105 2013 199 206 Z set Non linear material amp structure analysis suite behavior generalized debonding components of the cohesive traction T ie Ty T it n Ty and Tp T Ty are defined by Ty Kuy 1 A Tr K r 1 A 13 where K is the interfacial stiffness For the compressive case where uy lt 0 the normal component of the traction is modified to Tn a Kun 14 with a a penalization factor Figure 5 illustrates the typical response of the cohesive zone model under specific loads for the parameters as given in the example Remarks e the parameter a
232. s is not required with the bi linear shape e the parameter a has to be defined only with the tri linear law e two stress criteria puissance and reinforcement and three propagation laws puissance benzeggagh and vandellos are available e the option turon is required for applying the modification proposed by Turon continued Turon A Camanho P P Costa J and Renart J Accurate simulation of delamination growth under mixed mode loading using cohesive elements Definition of interlaminar strengths and elastic stiffness Comp Struct 92 2010 1857 1864 Z set Non linear material amp structure analysis suite 12 11 behavior generalized debonding Syntax behavior generalized_cohesive_zone strength Zt Zt Sc Sc toughness Gic Gic G2c Gric stiffness K K alphac Qe propagation propagation law puissance or benzeggagh or vandellos n n initiation stress criterion puissance or reinforcement softening shape of the cohesive law bi_linear or tri_linear or trapezoidal alpha_delta aj alpha_sigma a turon optional Example behavior generalized_cohesive_zone strength Zt 100 Sc 100 toughness Gic 0 0005 G2c 0 0005 stiffness K 1 e8 alphac 1 e3 propagation benzeggagh n 1 142 initiation puissance softening tri_linear alpha_delta 0 4 alpha_sigma 0 8 return continued 12 12 Z set Non amp structure a behavior general
233. s of the order of the flow stress this law will make the transition to rate independence Many uses of this equation include explicitly the activation energy term to scale the flow viscosity according to thermally activated mechanisms In Z mat the activation term should be entered in using the coefficient mechanism either as tables or functions for the value of de0 Syntax The flow law accepts coefficients de0 m sigma0 Example An example input using the coefficient mechanism to add thermal activation is given below flow sellars_tegart de0 function 0 202e 2 exp 401 0 8 3144e 3 temperature 273 0 sigma0 120 0 m 1 44 Z set Non linear material amp structure analysis suite lt FLOW gt lt FLOW gt sum Description i This law provides a summation of different flow rates A 5 A where the A are the rates given by other flow objects other than sum_flow or flow_sum_inv Syntax The syntax is the following flow flow_sum lt FLOW gt lt FLOW gt Similar kind of syntax applies to flow_sum_inv law also Example A simple example is given below which uses the Norton law as one of the flow rule behavior gen_evp xelasticity isotropic young 260000 poisson 0 3 potential gen_evp ev criterion mises flow flow_sum norton K 140 0 n 5 0 isotropic constant RO 130 0 13 51 lt INTERACTION gt lt INTERACTION gt Description This option allows addition of various variab
234. same and therefore only one optimization unknown is created If the initial value file is given it will be copied to a new file with the suffix bak to save the values Syntax This command is generally a one liner where it only takes the file name bases for optimization files file fl fn where fl fn are filenames where variables are The software searches these variables in template files named fl tmpl fn tmpl It then creates files fl fn with the actual values of the variables Example The following statement declares that file file1 contains the data to be optimized files filel where filel tmpl could for example be behavior gen_evp elasticity young 260000 poisson 0 3 potential gen_evp ev flow norton n 7 0 K Visco Z set Non linear material amp structure analysis suite x xoptimize xfiles xisotropic constant RO RRR return The lines Visco and RRR indicate that two variable values are to be substituted in their places during the optimization Z set Non linear material amp structure analysis suite 16 19 optimize x xfunction function Description The function is used to declare functions with variables to be optimized The functions use a similar format for declaring places for optimization variables as in the files option That is parameters within the function syntax which are named a z A Z 0 9 x are taken to be variables f
235. sing the file command This allows to separate the interface commands that may be specific to the FEA code and the material coefficients Default is to look for the behavior definition in the interface file dimension dim Second order tensors passed in by SAMCEF as arguments of the user material subrou tine OVMAXX always have 6 components storage of a 3D symmetric second order tensor in a vector regardless of the problem dimension Theorically the particular kinematic hypothesis used in the calculation 3D axisymetric plane strain plane stress can be known at the level of the OVMAXX routine by means of the IHYP argument Unfortunately in the current SAMCEF version SAMCEF v10 1 this argument is not correctly initialized during the loading phase of the Z mat behavior Therefore by default all Z mat objects will be initialized with a 3D size A dimension 2 command may then be used to bypass this problem and cut down material state variables storage requirements for 2D problems Note also that for the same reason it is currently necessary to add an explicit plane_stress modifier to the behavior or a plane_stress switch in the gen_evp assembly in order to properly take into account the plane stress hypothesis Z set Non linear material amp structure analysis suite Chapter 7 Z mat Cosmos 7 1 7 2 Z set Non linear material amp structure analysis suite Zcosmos interface Z mat Cosmos M
236. sive it is advisable to set this to a fairly low value e g 5000 One can also use file_management to control the parameter Z7_TMP_DIR directory where the temporary files are to be stored Default is the problem directory This can also be set with file management Z7_LICENSE fully qualified path to a license file Extremely useful when there are multiple versions or for running Zebulon directly off a CD ROM where one can t put the license file in a read only lib dir Example In the C shell these variables are set using the setenv command The variables may be directly in the user s cshrc file or in a separate file For the later case one may add the line to the cshrc file if f lib Z7_vars source lib Z7_vars Examples of variable settings are given below Z set Non amp structure an Environment Variables cat lib Z7_vars setenv Z7_TMP_DIR home disk me Z7 setenv Z7_MAX_NB_DOF 5000 setenv Z7_PRINTER_COLOR_A3 HPDESKJET 17 6 Z set Non linear material i amp structure analysis suite Chapter 18 Bibliography 18 1 Z set Non linear material 18 2 amp structure analysis suite Back91 Bely00 Bone97 Cont89 Cail92 Cail94 Cail95 Croi92 Delo96 Flec92 Gree65 Gir92 Hjel94 Jose95 Lade80 Lema85 Leve44 T F B ck A survey of evolution strategies In R K Belew and L B Booker editors Proc of the 4th International Conference on Gene
237. sotropic nonlinear_sum RO 50 Q1 30 b1 2000 Q2 10 b2 20 Q3 40 b3 2 The next example shows the use of isotropic by point Between two data points inter polation is linear potential gen_evp ep criterion mises flow plasticity isotropic by_point sigeq epcum 130 0 0 0000 140 0 0 0001 145 0 0 0002 150 0 0 0004 160 0 0 0009 170 0 0 0017 180 0 0 0028 The following gives a point by point specification of an isotropic harding Between two data points interpolation is linear as with all Z set tables For p gt 0 1 it uses the values of 0 1 because that was the last specified isotropic table O temperature temp table for epcum 0 220 23 0 100 200 0 1 temperature temp table for epcum 0 1 300 23 0 120 200 13 56 Z set No amp structure lt KINEMATIC gt lt KINEMATIC gt Description This object defines the model of kinematic hardening tensorial back stresses applicable in behaviors or potential objects in the gen_evp behavior The models generally store an additional tensorial internal variable and therefore may support static recovery and state coupling without modification The name of this internal variable will be determined normally by the object to which it belongs a POTENTIAL for example Kinematic hardening acts as a translation of the yield surface in stress space often deviatoric Syntax The syntax consists of specifying the type of kinematic object supplyi
238. ss condition with R being the current isotropic yield radius The general porous viscoplastic material is therefore described by the following plastic multiplier p blox R with being any of the Z mat flow laws given under lt FLOW gt see page 13 44 The evolution of plastic strain is found via an equivalence of plastic work between the matrix stress plastic This behavior is programmed only for the 0 method No plane stress is available The coefficients can depend on porosity notably of which is the f for the Gurson potential Z set Non linear material amp structure analysis suite behavior porous plastic strain and the macroscopic stress and strain of the composite porous medium 00x 1 fob i g fE A The evolution of porosity is given via conservation of mass given that the plastic strain has a volumetric part due to the pore growth or compaction f 1 f Trace p In the case of multiple criterions Hp and Hf are used to specify interaction between potential so that p J HY p j F SOAR SD j fi Y HH A fa j continued Z set Non linear material amp structure analysis suite 10 19 behavior porous plastic 10 20 Syntax The whole behavior keyword summary is given below behavior porous_plastic modifier thermal_strain lt THERMAL_STRAIN gt elasticity lt ELASTICITY gt porous_potential name porous_cr
239. te 13 95 lt THERMAL_STRAIN gt 13 96 Z set Non linear material amp structure analysis suite Chapter 14 Modifiers 14 1 Z set Non linear material 14 2 amp structure analysis suite lt MODIFTER gt lt MODIFIER gt Description This class is used as a behavior wrapper in order to modify the integration method or the formulation in some way Primarily these modifiers are used to transform the domain of application for the behavior by providing some translation of the primal dual variable combination such as is found for corotational large strain modifications CODE DESCRIPTION lagrange_polar lagrange_rotate lagrange_polar_no_J lagrange_rotate_no_J bifurcation auto_step runge_jacobian runge_rollover plane_stress perturbation corotational finite strain equivalent to a Green Naghdi stress rate formulation polar decomposition of the deformation gradient corotational modification for updated Lagrangian finite strain using an integrated rotation polar corotational formulation without a density correction integrated corotational formulation without a density correction bifurcation of mechanical solution analysis activates automatic sub stepping for implicit theta_method_a integration mixed integration method associating explicit runge_kutta integration of behavior differential equa tions with a final Jacobian call as in theta_method_a for the
240. ted One can use the prn2 to make certain debug selections See the developer manual for more information limit_debug time Limit the time for debug output Give the start and end time for debug output in the solution time scale Example The following example is taken from material input file e3danis located in test database directory Z mat umat_v61 x debug material integration runge_kutta 1 e 3 1 e 3 2 10 Z set No amp structure Interface files external_storage external storage Description This option is used to specify that the state variable storage is to be made in a separate file instead of using the FEA solver s internal database The command currently works with the ABAQUS and ANSYS interfaces With this command there is no limit to the number of state variables which can be used in a Z mat model In some cases we find that the codes efficiency can be improved as well by using external storage because of the buffering and relief from some copying operations Syntax external_storage buffer_size sz file db tmp file full_path db tmp file vars list buffer_size The buffer size determines the file buffering given in number of integration points This means that only every sz integration points will the storage be serialized to disk file Specifies the external file to be used for the storage This file name is relative to the current working directory full_path Spe
241. temperature has for temperature Example The following example illustrates the use of parameter keyword It is an excerpt of file ts1 located in test database in Z mat umat_v61 parameter ambient_temperature 125 0 field_variable humidity 2 initial_value 0 25 2 18 Z set No amp structure Interface files save_energies save_energies Description This command indicates stores the elastic energy for output The command is a bit simplistic but extracts from the material the variable eel and returns sse O Eel if e does not exist in the material not normally the case for standard materials but possible an error will occur and the option should be removed Z set Non linear material amp structure analysis suite Interface files x skip_cycle skip_cycle Description The skip_cycle command is used to give cyclic based extrapolation of the material state to allow skipped cycles for structures loaded with many cycles Syntax x skip_cycle check_with_component list of components file sdv file 2 20 Z set Non linear material i amp structure analysis suite Zmaster interfaces Zmaster interfaces Description Many of the different Z mat platforms have integrated functionality for their mesh input and results files within the other Z set products including the Zmaster GUI program This software is what NW Numerics uses exclusively for validation a
242. temperature such that the state variable id given by Zpreload must be incremented by one to select the proper material variable Finally note that this shift in the state variable id is automatically taken into account for the post command the shift is done in the plotv user subroutine included in the Zmarc release Z set Non li amp structure an Chapter 6 Z mat SAMCEF 6 1 6 2 Z set Non linear material amp structure analysis suite Zsamcef interface Z mat SAMCEF interface Description The command described in this chapter allows to use a Z mat behavior within a SAMCEF MECANO analysis The interface makes use of the OVMAXX user subroutine that allows to implement user defined behavior within SAMCEF Syntax Zsamcef problem lt lt where problem dat is the name of a SAMCEF input data file The Zsamcef script activates a non standard MECANO executable with name Z7PATH Zsamcef mecano_zmat_ Z7MACHINE Please verify that this file is indeed included in your Zset distribution A new user module module mecano_zmat associated to module Id zm should be declared in the SAMCEF environment by means of the samrc ini configuration file The samrc ini file in the user home directory is automatically updated by the Zsamcef script with the command required to declare this new user module module zm me mecano_zmat Z7PATH Zsamcef mecano_zmat_ Z7MACHINE Note that a MECANO calculation with a Z mat b
243. tes the definition of intrinsic coefficients which are not specific to ma terial laws These coefficients are applicable to all the material models The allowable global coefficients are summarized below CODE DESCRIPTION masvol volumetric mass of the material capacity volumetric heat capacity pC 3Note that we frequently find this the advisable approach for production runs as well as it avoids confusion or possible version conflicts when numerous runs are to be made Older definitions with the coefficient command outside the behavior and return commands are no longer allowed Z set Non linear material amp structure analysis suite 9 11 Material file Units should be coherent within the problem definition For example if using SI system masvol is in kg m and capacity in J m K but if using the mm MPa s unit system masvol is in ton mm and capacity in J mm K7 plane_stress indicates that a plane stress behavior is to be used 033 0 This is not available with all material behaviors Z bulon plane stress must not use this option save_coefficients list coefficient names which are to be saved as output variables New var aux variables are created and therefore increase the total storage for each material integration point This option is extremely useful when the variation of coefficients is important such as in coupled problems Example Another example of material file input
244. th these tensors are non symmetric The stretch rate D and rotation rate Q are symmetric and non symmetric respectively These methods require elements of the type updated_lagrangian specified with the option mesh in the inp file Z set Non linear material amp structure analysis suite lt MODIFTER gt lt MODIFIER gt lagrange_polar The lagrange polar modifier is a corotational formulation for finite strain leading to an equivalent Green Naghdi stress rate in elastic problems Gree65 Nagt82 The stretch rate tensor is transformed into a local strain rate measure through the following expression R DR where the rotation tensor R is found by the polar decomposition of the deformation gradient F RU with R being a pure rotation and U a pure stretch tensor Using the transformed material strain rate e the behavior may be evaluated as in small deformation An conjugate stress results from the material behavior integration S which is transformed to the global Cauchy stress as o det F RSR Z set Non linear material amp structure analysis suite 14 5 lt MODIFIER gt 14 6 lt MODIFIER gt lagrange_rotate The lagrange rotate modifier is a corotational finite strain formulation based on an integrated rotation tensor Lade80 This method yields an equivalent stress strain response to a Jaumann rate formulation but allows tensorial internal variables and anisotropic relations to be used as was in
245. the evolution optimizer care should be taken not to misinterprete the order of the variables THE REAL ORDER is given in the msg files for instance Example this is very useful for variables which span orders of magnitude A classical example is a creep law of the form Ao where A much change orders of magnitude in response to small changes in n for similar values of Sometimes a better approach is to re formulate for example with o K Z set Non linear material amp structure analysis suite 16 21 xxkkoptimize value x values auto_init_from_file levenberg best C1 fixed 200 min 1 e 5 max 1 e6 f_trans fixed 1 min 0 3 max 1 1 m 0 2 min 0 05 max 20 M 2 01 min 0 01 max 40 f_crit 0 85 min 0 0 max 0 95 16 22 Z set Non linear material amp structure analysis suite x xoptimize x value auto_init_from file auto_ init_from file Description This option is used to conveniantly re start an optimization from the last best values Syntax The syntax takes the name of an ascii file which has the format of the problem best file This file is written each time a trial of the function is less than the previous best value kauto_init_from_file file Example Supposing the following values entry is given x values kauto_init_from_file levenberg best K 700 min 600 max 5000 n 4 47 min 1 2 max 20 K2 500 min 200 max 5000 n2 35 min 3 max 75 Ci 290 min 3 0 max
246. the interpolated value from the smaller file and ys the test value from the smaller file ys is the points value in the reference file experiment file which may be an interpolated point if that file was smaller Syntax g file file sim file sx sy exp file ex ey weight vweight sim file is the simulation file which the optimization variables x should be changing exp file is the reference which is the goal should not change during optimization sx and sy are the x and y columns of the simulation file and ex and ey are the x and y columns of the reference file Note One is advised to make sure that the x variables are continuously increasing as a comparison of multi valued functions or data curves are not allowed In normal use time makes a very useful x variable although a control parameter such as strain could be used as well The measure of error may differ quite significantly from the t_file_file output so if it is desired to mix the two types of comparison use of the weight values will be very useful Z set Non linear material amp structure analysis suite 16 13 xxkkoptimize compare i_file_file compare i file file Description allows to compare two files names fnamel et fname2 Files are columns files containing doubles Column cl of file fhamel is compared with column c2 of file fname2 Both files must have the same number of lines The function to be optimized is given
247. the polar decomposition case Lade80 The principle of this method is to always evaluate the material within a local material referential Passing from the global to material referential is made using a rotation tensor in the following relations Q Q Q 1 Got Q DQ local strain o det F QSQ 2 This method requires additional storage at each Gauss point for the non symmetric ro tation tensor and the local material strain The name of strain used in the material law is therefore changed to ETO in place of eto This strain is also observed to be a logarithmic strain For the two methods the nonlinear material tangent D describing the JAS 0Ae rela tionship is modified for the additional large strain non linearities as follows Di det F AD A Aijkl Qik Qj which relates Ao AtD The polar decomposition method will of course use R in the place of Q in the above One may note an improved convergence for conditions where the material behavior cal culation of D is best i e implicit 0 method integration with 0 1 The calculation of the stress is also noted to depend on the determinant of the total value of the deformation gradient F from time to to the current time Nonlinearity in this term especially in trial solutions during iterations may limit the convergence of the method Z set Non linear material amp structure analysis suite lt MODIFTER gt lt MODIFIER gt plane_stress Descriptio
248. this model are the total strain code etoxx the tensorial variables X code kip xx prefix size description default eto T 2 total small deformation strain yes sig T 2 Cauchy stress yes eel T 2 elastic strain yes ean T 2 anelastic strain yes kip T 2 X variable no The code names will replace the symbol with a sequential number from 1 to nt The default saving of variables in the output files are only those marked by yes in the previous table Example behavior viscoelastic_spectral kelasticity isotropic young 2800 poisson 0 3 spectrum n1 30 n2 30 nt 50 nc 7 n0 3 viscous_effects lrt 0 6 lrc 0 6 reversible_asymptote beta 1 p 1 return 10 11 behavior hyperviscoe behavior hyperviscoelastic Description This behavior is a general Hyper viscoelastic form with both shear and volumetric recovery components The model is based on the discussions from Simo and Hughs Simo98 The model uses the same hyperelastic potential components as in the hyper_elastic behavior Also any number of shear and volumetric terms can be added to the model Syntax behavior hyperviscoelastic thermal_strain lt THERMAL_STRAIN gt hyperelasticity lt HYPERELASTIC_LAW gt hyperelasticity lt ISOTROPIC_HYPERELASTIC_LAW gt model_coefficients possible level commands for hyper law Example The following example comes from the validation tests More e
249. tic Algorithms volume I pages 2 9 USA Morgan Kauffmann 1991 T Belytschko W K Liu B Moran Nonlinear Finite Elements for Con tinua and Structures John Wiley amp Sons 2000 J Bonet and R D Wood Nonlinear Continuum Mechanics for Finite Ele ment Analysis Cambridge University Press Cambridge United Kingdom 1997 E Contesti and G Cailletaud Description of Creep Plasticity Interaction with Non Unified Constitutive Equations Application to Austenitic Stainless Steel Nuclear Engineering Design 116 265 280 1989 G Cailletaud A Micromechanical Approach to Inelastic Behavior of Metals Int J Plasticity 8 55 73 1992 G Cailletaud P Pilvin Utilisation de modeles polycristallins pour le calcul par l ments finis Revue europ enne des l ments finis 515 542 1994 G Cailletaud and K Sai Study of Plastic Viscoplastic Models with various Inelastic Mechanisms Int J Plasticity 10 1995 D Croizet L M ric M Boussuge G Cailletaud General Formulation of a Plasticity Viscoplasticity Algorithm in Finite Element Num Meth Eng 92 ed C Hirsch et al Bruxelles 741 747 1992 P Delobelle P Robinet P Geyer and P Bouffioux A Model to De scribe the Anisotropic Viscoplastic Behavior of Zircaloy 4 Tubes J Nuclear Materials 238 135 162 1996 N A Fleck L T Kuhn and R M McMeeking Yielding of metal powder bonded by isolated contacts J Mech P
250. tically available to the simulation and optimization methods creating a coherent extensible modeling environment In order to make user additions to Z mat a custom shared library must be compiled and installed into the proper location with the proper name For running Z mat with other ABAQUS the shared library must be named libZmat so where is replaced by a user designated character filename On HP UX systems the suffix is sa and on AIX it is a Files fitting the above wildcard name will be automatically loaded using the system dlopen command or equivalent The search path is e the current working directory e the path pointed to by the environment variable ZEBU_PATH e the default binary location Z7PATH PUBLIC 1ib Z7MACHINE More detail about the compiling process is given in the developer handbook and there is always a pre configured user project in the installation directory Z7PATH User project ABAQUS user routines The Z mat package uses the ABAQUS UMAT function to interface with that FEA solver This does not prevent one from programming extra user routines to run along with Z mat If the user routines are unrelated to the material such as user loads or MPCs an extra Fortran file can simply be appended to the Z mat interface by using the Zmat option uf An example is provided in the Z7PATHtest Z mat UMAT directory as problem 4020201 The execution is for example Zmat fg uf mpc f 4020201 which will link in th
251. tress evolves with the following three coupled state variables a2 m T2x2 X2 p2 Q2 a m Ta x1 x2 x play m T x x1 Ar g T o x The last term is a static time based recovery mechanism in the x variable It uses a separate recovery potential CRITERION object for g and a flow rate magnitude to find A These are selected with the g_function and recovery_flow options for g and A respectively In these evolutions the matrix T is entered similarly to the T matrix but using the T2 command An additional isotropic hardening component can be added to handle supplemental hard ening in the case of non radial loading The variable is integrated using the following evolution me ER x pQq Yo Yt_in fy Yg f 1 abs Y btyo The potential function h is a CRITERION object which can be entered using the optional h_function command If it is not entered the g function will be used explicit forms of this model are available in the ZebFront files Edf modif z and Lma_cwsr z Z set Non l erial amp structure an 13 77 lt POTENTIAL gt Hardening variables will be stored in the following order h la a Q3 yo while yg is only included when the coefficient bt is given Syntax The syntax understood by this potential is summarized below kpotential delobelle name flow lt FLOW gt criterion lt CRIT
252. tropic_elasticity 13 9 isotropic thermal strain 13 95 iter 14 7 iter_optimal 15 16 iteration 15 16 KKK KKK K 13 4 K_coeffs 13 3 lagrange_rotate 14 3 limit 2 8 6 5 14 8 limit_output_var 15 14 linear 13 55 13 58 linear_nonlinear 13 55 linear_pp 13 55 load 15 10 local_debug 6 4 make_contour 15 9 MATERIAL 3 9 material 6 6 matmod 11 15 matmod_z 11 17 Matrix coefficients 13 10 max_dtime 15 16 min_dtime 14 8 15 16 model 15 13 monocrystal 13 80 needs_temperature 6 5 nonlinear 13 55 13 58 nonlinear_1 13 56 nonlinear_evrad 13 58 nonlinear_phi 13 58 nonlinear_sum 13 55 nonlinear_with_crit 13 59 normalization 16 21 norton 15 44 Z set Non linear material amp structure analysis suite norton exp 13 45 nucleation 13 93 number 15 9 object 9 3 offset 15 18 one sided 14 12 orthotropic 13 11 orthotropic elasticity 13 11 OUT 2 10 2 11 output 15 14 output simulation 15 14 perturb 14 12 perturbation 14 12 plane stress 14 7 plastic 13 36 plasticity 13 45 13 73 porous_potential 10 23 potential 15 17 power_law 13 55 precision 15 14 rate 15 10 15 18 ratio 15 16 resolve 14 8 ref temperature 13 94 reversible_asymptote 10 10 ROTATION 2 15 rotation 2 15 15 13 runge 14 11 runge_jacobian 14 10 runge_kutta 2 13 runge_rollover 14 11 salt 13 87 save_scalar save tensor scale 15 9 security 2 8 14 8 15 16 segment 15 10
253. ture analysis suite lt COEFFICIENT MATRIX gt lt COEFFICIENT MATRIX gt Description This object is used to enter coefficients for a desired form of 4th order coefficient matrix The use of these matrices is often as an elasticity matrix so we sometimes refer to the object as ELASTICITY Syntax These objects take a list of coefficient declarations after the type keyword is given There are no explicit restrictions on the types of coefficients or their dependencies The different types keywords available are the following CODE DESCRIPTION diagonal 1 or dim coefficients isotropic 2 coefficients cubic 3 coefficients transverse 5 coefficients orthotropic 9 coefficients anisotropic 21 coefficients The default type depends on its application For elasticity objects this is isotropic The anisotropic model represents the most general elasticity model Coefficient names follow the same convention to describe components of the coefficient matrix This sets the coefficient name for a component C 1 to Cijkl For example a component y1212 is named y1212 When using elasticity objects special care has to be taken with respect to the nomenclature of the components When representing a tensor of elasticity in 6x6 form the Voigt convention is assumed but with one important difference the order of storage is 11 1 22 2 33 gt 3 12 gt 4 23 gt 5 31 gt 6 Zebulon instead of the usual 11 1 22
254. umps are oriented so as to be more efficient than a completely random search evolution still needs around 1000 calculations of the function to get near the optimum The advantage of evolution is that it can escape local optima in the search space A useful application of the evolution method is to generate a starting point for other optimization methods This is because the evolution method is not sensitive to the convexity of the problem which permits approaching optimization problems that are numerically ill conditionned that diverge that have discontinuous functions evolution is a steady state genetic algorithm that handles continuous variables It can handle constraints using a penalization scheme cf introduction of the optimization in Z set page 16 4 There is a rule of thumb when changing the parameters of evolution some parameters will make the search more random i e more robust but also less efficient others will increase the speed of convergence but the probability of getting trapped far from the global optimum simultaneously increases The tradeoff is clear and default parameters are supposed to represent a reasonable compromise between randomness and efficiency Based on its experience the user may decide to emphasize an aspect or another of evolution s search population_size and prob_muta should be increased to increase randomness The following files are generated by a run of evolution case evo log contains various
255. ut only a system linker 1d is required for basic use of the program The Zmat script prepares the proper link command in place of using the C or Fortran command lines On Windows platforms no development software is necessary at all To have user routines attached to the basic library a C compiler will be necessary as a second add on shared library must be prepared Since the standardization of C the compiler requirements are greatly reduced from what was previously the case In most systems The Z mat interface is also known as Z aba or ZeBaBa in some older circles The Z mat name is however the official product name and symbolizes an approach which is a step beyond classical single code UMAT solutions and one which is tied to the extensive Z set software actually there is no limit to the number of plugins which can be used There is a specific naming convention for Z mat plugins however For unix systems the user library should begin with 1ibZmat and on windows the DLL should start with zmat Z set Non amp structure an 3 3 Z mat interface 3 4 Z mat plugins can be made which whatever C compiler is convenient Normally the user would be best advised to use the most modern version possible The general compiler level requirements specified by ABAQUS Inc will most likely not be absolutely necessary though we validate that those compilers do in fact work so they can be used as a guideline User plugins will
256. values The matrix is read HF is q HF aig HYN with N the number of porous potentials Hp Interaction matrix for plastic strain influence between potentials The matrix is read H H dale HIN HS ar a with N the number of porous potentials porous potential detailed separately on page 10 23 Any number of potentials greater than or equal to 1 can be entered with repeated uses of this command Stored Variables define a potential which is part of the model The stored variables for this model are the following behavior porous plastic This command is prefix size description default eto T 2 Total small deformation strain yes sig T 2 Cauchy stress yes eel T 2 Elastic strain no broken S if broken yes seq S effective flow stress O yes p S equivalent plastic strain yes fg S growth porosity yes fn S nucleation porosity yes fncl S effective crack like nucleation porosity yes f S void volume fraction fy fn yes ft S total effective porosity fg fn fnel yes pe S effective plastic strain yes Xmic T 2 microscopic back stress no Xmac T 2 macroscopic back stress no alpha T 2 kinematic hardening internal variable no X T 2 sum of all macroscopic back stresses no Z set Non linear material amp structure analysis suite 10 21 behavior porous plastic Example As discussed above the porous plastic material behavior is a very broad code and encompasses many options and features The following i
257. was necessary to perform a user build and link process in order to generate a user executable of ansys The newer versions interface with ANSYS via shared libraries and henceforth the user needs to do nothing special for the interface to work There are some test cases in the 4Z7PATH test Zansys INP directory The Z mat material files are named 10 txt where is the material number selected in the test using ansys commands such as TB USER 4 0 0 TB STATE 4 40 MPCHG 4 1 which would set the Z mat material for element group 1 to be read in the file 104 txt Currently all the commands listed in the Z mat handbook for the ABAQUS interface are supported with ANSYS as well except the use of multiple field variables Temperature is available as a parameter and can be set using commands like BFUNIF TEMP 523 0 The name TEMP will be re mapped to temperature in the Z mat files To try the test cases do for example Z cd Z7PATH test Zansys INP Zansys plast3 which launches the ansys GUI from which the input file can be loaded INPUT plast3 inp Elements and output Z mat for ansys must be run using the 18x class elements In order to get output for the state variables in the Z mat material model an additional command must be issued to get the variables stored to the output database such as erial Z set Non l amp structure an 4 3 Zansys interface 4 4 OUTRES SVAR ALL To plot the variable one can use th
258. which are dependent on the model chosen The possible criterion types are CODE DESCRIPTION mises classical von Mises criterion 2M1C criterion 2M1C only for potential mises_2m1c hill Hill criterion ratio classical criterion useful as viscoplastic overstress function karafillis_boyce Karafillis Boyce criterion full_hill Hill criterion tensile mises acts as von Mises criterion nouailhas macroscopic model developed by ONERA modified_nouailhas linear_drucker_prager modified nouailhas model non associated drucker prager criterion anisotropic classical energy equivalent form due to von Mises cast_iron criterion which provides asymmetric tension compression bron modes anisotropic behavior in the criterion and flow direction unsym non symmetric deviatoric hydrostatic criterion tresca Tresca criterion Some expressions which will be used are wm wm h No w 1 Sij Fj y Tudig where is the effective stress which may be displaced by a kinematic back stress 0 X The true form of this stress will be determined by the potential Stored Variables Criterion objects are not allowed to have any variables 13 14 Z set Non linear material amp structure analysis suite lt CRITERION gt lt CRITERION gt anisotropic Description This criterion is the classical energy equivalent form due to von Mises Here the effective stress is calculated based on the Jo stress invaria
259. with deviatoric and hydrostatic terms The criterion is written fer 1 a Seq a Trio R This criterion accepts a single coefficient a which must be input on a separate line from the unsym token This criterion is also non associated where the flow normal is written o X n8 2 o X with the X term being the summation of back stresses Often this criterion is used in con junction with the ziegler kinematic hardening options Croi92 but this is not necessarily so Z set Non linear material amp structure analysis suite lt CRITERION gt lt CRITERION gt 2M1C Description For this case the criterion is calculated in two parts using the following form fr y F Ep ak fi Aio Xj The coefficients gal and ga2 exist in order to define the localization parameters A Z set Non linear material amp structure analysis suite 13 29 lt CRYSTAL_KINEMATIC gt 13 30 lt CRYSTAL_KINEMATIC gt Description Because the crystal potential models takes into account the strains on the individual slip planes kinematic hardening represents a linear measure of a slip offset distance X or back stress on the slip line As described in the lt POTENTIAL gt crystal section see page 13 80 the yield criterion on each slip plane is of the form r gt gt 3 X ri where 7 is the resolved shear stress on slip plane i and r is the sum of all isotropic hardenings on that slip plane The
260. xamples can be found in test Viscoelastic_test INP behavior hyperviscoelastic khyperelasticity logarithmic kelasticity isotropic young 2 8125 poisson 0 40625 shear tau 1 0 omega 0 4 shear tau 10 0 omega 0 4 volumi c tau 3 omega 0 5 return 10 12 Z set Non amp structure a behavior gen_evp behavior gen _evp Description This material model is a generalized implementation of elastic elastic plastic or viscoplastic and multi potential constitutive equations The model is constructed entirely using object bricks For the moment the model will be constructed using an elasticity object a num ber of potentials and interactions between the potentials Potentials represent inelastic dissipations which describe the evolution of independent inelastic deformation mechanisms Hardening mechanisms are modeled with objects within the individual potentials type of hardening depending on the type of potential and are thus not yet specified This behavior is essentially a manager of sub model objects and will be discussed in general terms about the permissible variables The model s internal variables are determined by the sub objects which have been selected by the user The general storage form includes variables which are global to the material laws and therefore form relations with the imposed observable variables or apply to all the potentials Each potential may additionally contain
261. xwell model The model defines the stress a to the strain e by the following relation a t 201 rj lrjar 1 f K t T Trace dr with e the deviator of the strain tensor e The terms G and K are relaxation functions defined by Prony series G T G Go Go Vilr vir al wi exp T 7 K T Koo Koo Ko U2 T Va r 1 wi exp 7 71 1 Go and Goo are shear modulus coefficients Ko and K are bulk modulus coefficients Remark The sum of the coefficients w for modulus terms must equal one The implementation of the model is in differential form with the internal variables and 6 The state equations are written in the following form i na i ng o y X y Y 2G5e Ko Trace el i 1 i 1 with Xj 2 Goo Go wi e Qi 1 lt 1 lt Na Yi 3 Koo Ko wi Trace e 3 fi 1 1 lt i lt ng 2 The evolution equations for the internal variables are Qi L e aj 1 lt i lt ne 7 Traceg 3 Bi 1 lt i lt ng 3 It is necessary to define a single time the coefficients Ko Koo Go and Gy using the key words KO K_inf GO and G_inf respectively One may then define an arbitrary number of the variables and P using the key words omega and tau omega is a constant coefficient Syntax The syntax for this behavior model is the following 10 6 Z set Non linear material i amp structure analysis suite behavior linear _viscoel KO COEFFICIENT K_inf COEFFIC
262. zer but rather a convenience to test or re analyze a set of optimiza tion parameters It performs one single calculation of the cost function going through the principal routines of the optimizer It is particularly meant to be used in conjunction with the init_from_file command to choose a particular initial point There are no param eters in the convergence section and the reading of this algorithm will pass by entries there without an error message Example The following is an example where the variables cl b are read in the ASCII file init The values 1000 5 are in fact used for scaling only Only one simulation is performed and the objective function is calculated x optimize single files plast sim x shell Zrun S Q plast3 2 gt 1 gt dev null x values init_from_file init cl 1000 min 200 max cnl 140000 min 50000 dnl 100 min roO 260 min q 200 min b 5 min x convergence delta 0 005 eps 1 e 08 iter 100 compare t_file_file plast3 test 1 3 data_plast3 1 3 weight 1 return set Non linear material structure analysis suite ZE 8 50 50 20 2 max max max max 15000 max 200000 2000 500 500 20 16 37 x optimize single Z set Non linear material 16 38 amp structure analysis suite Chapter 17 Reference 17 1 Z set Non linear material 17 2 amp structure analysis suite Functions Functions Descriptio
263. zers are available in Z set Levenberg Marquardt simplex SQP and an evolutionary algorithm They span the different categories of optimizers mentioned earlier A rapid description of their principle can be found in the relevant sections Exceution proceedure Zrun o problem Z set Non linear material amp structure analysis suite x xoptimize optimize Description This keyword marks the start of an optimization command sequence which will be terminated by the next level command Syntax The syntax is as follows x optimize type files values shell XZIUN compare kkenforce function convergence evaluate constraint FAA EA AA FAA x linear_constraint return Different optimizer types are available by substituting keywords for type from the following CODE DESCRIPTION nelder_mead nelder mead aka simplex method slow but it gets there levenberg_marquardt Levenberg Marquardt method the classic for identifi cation augmented_lagrangian augmented lagrangian dual method for constrained optimization evolution evolutionary stochastic method slow but escapes local minima Anatomy of an optimization All the optimization methods rely on a centralized method of evaluating the error func tion and modifying the simulation using the variables being optimized Error functions will be computed using a we

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