Input Parameters for Springback Simulation using LS-DYNA
Contents
1. CONTROL_ COARSEN icoarse angle nseed 1 8 0 0 nl n2 n3 n4 n5 n6 n7 n8 0 0 0 0 0 0 0 0 An optional number of boxes may also be defined which protect regions of the mesh from coarsening using the keyword DEFINE BOX COARSEN The parameter iflag indicates whether elements lying inside or outside the box will be protected DEFINE BOX COARSEN boxid xmin xmax ymin ymax zmin zmax iflag 0 0 0 0 0 0 0 0 Implicit Springback Creating an input deck for implicit springback using a dynain file is simple Keywords are required to activate the implicit method and to select the time step size and the termination time Extra constraints can be added using nodal SPCs to eliminate free rigid body motion of the sheet when the tools are removed For difficult springback jobs optional keywords are available to request multi step springback unloading to automatically adjust the time step size according to the difficulty of each step and to control the linear and nonlinear equation solvers A short template file can be used to save typical values for these keywords Other necessary input such as part material and section definitions can be taken directly from the original forming input deck Activating The Implicit Method Since springback is a static process the implicit solver should be used This solver is activated using the first parameter imflag 1 on CONTROL_ IMPLICIT GENERAL The time step size is also input here2. Figure 1 shows a diagram of the location of these nodes on the model Figure 1 Diagram showing location of constraint nodes on a typical springback model Node A is the reference node where all displacements are constrained This eliminates the three translational rigid body motion of the part Selected translational degrees of freedom are constrained at nodes B and C to eliminate the three rigid body rotations of the part about node A Constraints For Symmetric Models Some stamping models include only one half of a symmetric panel such as a hood or deck lid In these cases Symmetry constraints are applied along one edge of the mesh To eliminate rigid body motion during springback for these parts constraints need only be added to two nodes chosen on the symmetry plane completely constraining all translations for the first node and eliminating one additional in plane motion for the second node Over constraining a symmetric model by choosing three nodes according to figure 1 can lead to incorrect results Figure 2 shows an example for the case of symmetry in the X Z plane X Z symmetry plane 1 L L I I Figure 2 Diagram showing location of constraint nodes for a symmetric part The plane of symmetry in this example is the X Z plane Constraints must be added to two nodes on the symmetry plane to eliminate rigid body motion during static springback analysi
3. 98 196 98 196 an INCORE solution will be performed Initialization CPU 7 220E 00 seconds Symbolic Factorization CPU 1 065E 01 seconds Numeric Factorization CPU 8 539E 02 seconds Forward Backward CPU 5 060E 00 seconds Figure 4 By selecting Iprint 1 on CONTROL_ IMPLICIT SOLVER or by interactively typing lt ctrl c gt lprint the memory and CPU requirements for the linear equation solver will be displayed to the screen Output is shown for a production size springback model This job will run in core memory since the total memory available 98 196 Mwords is larger than the total required for incore solution 87 648 Mwords The option memory 100m was used on the command line to request 100 000 000 words of memory Difficult Springback Simulations The following section offers suggestions for solving difficult springback simulations These typically involve very flexible parts on which experimental springback measurements are also often difficult In simulation these parts usually present convergence trouble for the nonlinear equilibrium iteration process A method is presented below for using several steps to simulate springback unloading followed by a troubleshooting checklist with other modeling suggestions Multi Step Springback for Difficult Parts The applied load in a springback simulation results from the initial stress in the sheet which is no longer in equilibrium once the tools have been removed For difficult
4. model during implicit springback are treated with the S R Hughes Liu element formulation 6 This option allows the user to reproduce previous results which were obtained using LS DYNA3D for forming simulation and LS NIKE3D for springback simulation when default element formulations were chosen in both software For best springback accuracy however it is recommended to use the Fast Shell element 16 for both the forming and springback simulations so the element formulation switching option is not required The DYNAIN File Method At the end of the forming simulation LS DYNA can output a keyword formatted file named dynain containing the deformed mesh stress and strain state The dynain file is requested using the keyword INTERFACE SPRINGBACK DYNA3D Input the id psid of a part set containing a list of parts to be included in the output file usually just the sheet workpiece An optional list of extra node constraints can be included which are applied as the dynain file is written These constraints provide a convenient way to eliminate rigid body motion in springback calculations Required constraints are discussed later in this document INTERFACE SPRINGBACK DYNA3D psid 0 S nid tcode rcode 0 0 0 0 0 0 The dynain file can be used to perform many follow on simulations such as springback trimming or additional forming It can be included into a new LS DYNA input deck so that each simulation is performed indep
5. springback problems this load must be applied slowly over several steps in order to divide the nonlinear springback response into manageable pieces Artificial stabilization is the method used in LS DYNA to distribute springback response over several steps In this method springs are artificially introduced to the model which restrict the motion of the sheet nodes As the solution proceeds the spring stiffnesses are reduced allowing more springback When the termination time is reached the springs are completely removed allowing completely unrestrained springback It is important to reach the termination time completely otherwise some artificial stabilization will remain in the model and the results will not be accurate To use multiple steps in a springback solution the termination time must be extended A good starting point for difficult jobs is four steps so if the step size on CONTROL_IMPLICIT_GENERAL is dt0 0 001 then the termination time on CONTROL TERMINATION should be term 0 004 Artificial stabilization is activated using ias 1 on CONTROL IMPLICIT STABILIZATION When active a message is printed to the screen at the start of each time step showing how much stabilization remains in the model At the termination time the message reports that artificial stabilization has been completely removed CONTROL IMPLICIT STABILIZATION S ias scale tstart tend 1 0 001 0 0 The initial stiffness of these springs can b
6. the INTERFACE SPRINGBACK keywords or when the dynain file method is used constraints can be added to the springback input deck using BOUNDARY_SPC_NODE Parameter nid indicates the constrained node ID and a value of one is entered for each degree of freedom dx dy dz to be constrained BOUNDARY SPC _NODE nid cid dx dy dz rx ry LZ 0 0 0 0 0 0 0 0 Enough constraints must be defined to eliminate six rigid body motions in the model three translations and three rotations In theory this could be accomplished by constraining all six degrees of freedom at a single shell element node point In practice numerical truncation error is introduced when rotational degrees of freedom are used to eliminate rigid body motion The recommended method is therefore to constrain selected translational degrees of freedom at three nodes The three constraint nodes should be chosen well separated from each other and away from edges and flexible areas in the part The first node A receives constraints to all three translational degrees of freedom and defines the reference point in the model where springback displacements are zero The second node B is located away from node A along the global X direction Constraints are applied at node B to eliminate global Y and Z translation The third node C is located away from node A along the global Y direction Only the global Z translation is constrained at node C
7. the seamless method LS DYNA begins by performing an explicit forming simulation When the termination time is reached LS DYNA automatically and seamlessly switches to the implicit method and continues with the springback simulation At the time of switching a user specified list of parts the sheet blank are retained as active and the remaining parts the rigid tools are deleted from the model All contact interfaces are also automatically deleted An optional list of nodal constraints are activated to eliminate rigid body motion after the tools are removed for the static springback simulation Required constraints are discussed later in this document INTERFACE SPRINGBACK SEAMLESS psid 0 S nid tcode rcode 0 0 0 After switching seamlessly LS DYNA proceeds to perform a static implicit springback simulation A special set of defaults are used which eliminate all requirements for CONTROL_ IMPLICIT keyword input These alternate springback defaults are identified clearly in the user s manual and affect the time step size artificial stabilization and automatic time step control parameters Default parameter values can be overridden by including optional CONTROL_ IMPLICIT keywords into the forming input deck Element Formulation Switching An option is available to automatically switch shell element formulations when using the seamless springback method When activated all shell elements which are retained in the
8. using dt0 and can be chosen arbitrarily in most cases since the solution is static A physically reasonable time step size should be chosen so use dt0 0 001 seconds CONTROL IMPLICIT GENERAL imflag dto iefs nstepsb igso 1 0 001 0 0 0 Choosing The Number Of Time Steps The termination time and time step size determine the total number of springback steps Springback of most reasonably stiff panels can be performed in a single step so select the termination time term dt0 using CONTROL_ TERMINATION Some difficult parts require several steps A reasonable starting point for a difficult multi step analysis is four steps or term 4 dt0 CONTROL_ TERMINATION term 0 001 Required Constraints All static simulations including implicit springback analysis require that rigid body motions be eliminated by defining constraints These constraints are required since dynamic inertia effects are not included in a static analysis Without constraints a tiny applied load would cause the entire workpiece to move rigidly an infinite distance without creating any stresses Mathematically this means that without any constraints the global stiffness matrix for the model is singular and the inverse can not be computed When constraints are properly chosen this rigid body motion will be eliminated and the model will deform freely without developing any reaction forces at the constraint points Constraints can be applied using
9. Input Parameters for Springback Simulation using LS DYNA Bradley N Maker Xinhai Zhu Livermore Software Technology Corporation June 2001 LS DYNA has been applied to springback simulation by a large number of users with generally mixed results Some results have demonstrated 70 accuracy or better while others have been entirely misleading In order to eliminate inconsistent results this report presents a standard procedure for conducting springback simulations with LS DYNA The seamless and dynain methods for springback are described followed by a description of general implicit springback problem set up Recommendations are given for anticipating and improving springback prediction accuracy Wherever possible LS DYNA keyword input data is shown to clarify the presentation Recommended input parameters are identified in boldface type and included in boxed keyword input syntax for quick reference A boldface zero value is entered for required input data which is model specific such as the termination time term The Forming Simulation Results from the forming simulation provide the starting point for the springback simulation The most important factor in springback accuracy is the accuracy of the forming simulation This is essential If trouble occurs during springback look for the cause in the forming analysis In explicit forming simulations run time can and should be greatly decreased using mass scaling and or artific
10. d the scope of standard stamping simulation Clearance and Home Gap Many springback simulations and experiments are very sensitive to sidewall clearance in tools and the home gap left at the bottom of the punch stroke Carefully verify that your model accurately represents these details by making measurements directly on the model using the post processor Errors of less than one millimeter can have substantial effects on accuracy References Maker B N and Zhu X Input Parameters for Metal Forming Simulation Using LS DYNA April 2000 available at www feainformation com forming parameters2 pdf or by email from support Istc com 11
11. e scaled using the input parameter scale This parameter must be chosen using some engineering judgement about the flexibility of the panel being studied Table 1 gives some guidelines on choosing scale type of panel example application scale stiff heavy gage frame crossmember 1 000 default stiff standard gage reinforced inner panel 0 100 flexible curved fender outer panel 0 010 flexible flat hood outer panel 0 001 Table 1 When artificial stabilization is used for multi step springback the stabilization stiffness scale factor must be chosen according to the panel type Note that stiff panels generally do not require multi step springback so the default value scale 1 000 must nearly always be reduced A small value for scale gives softer springs allowing more springback in the first few steps of the simulation If convergence of the first step is difficult use a larger value for scale If the first few steps converge in very few iterations but the last step is difficult use a smaller value for scale If convergence trouble is encountered during the iteration process automatic time step control is available to repeat a failed step using a smaller step size Automatic time step control is activated using iauto 1 on the CONTROL_IMPLICIT_ AUTO keyword For difficult springback simulations an aggressive time step control strategy can be used Increase the optimum number of iterations using iteopt 200 and restrict the maximum time step s
12. endently This procedure avoids cumbersome binary restart databases and separates multi stage forming and springback jobs into more manageable pieces For this reason the dynain file method is the recommended method for springback simulation In the dynain file method the input deck for springback simulation is easily constructed using the part section and material information from the original forming model and the node element and initial stress and strain information from the dynain file A few additional keywords must be added to control the implicit springback process Mesh Coarsening Accurate forming simulation requires a very fine mesh over tool radii typically at least four elements are needed around a ninety degree radius Surprisingly much of this mesh refinement can be removed prior to springback analysis without significant loss of springback accuracy Mesh coarsening is the procedure used in LS DYNA to automatically combine neighboring elements in flat regions of the mesh Mesh coarsening can be applied to both uniform and adapted meshes Mesh coarsening provides three significant benefits for implicit springback analysis improved convergence behavior during nonlinear equilibrium iteration due to reduced numerical truncation error and reduced memory and cpu requirements due to the reduced model size The coarsening procedure is performed at the beginning of a simulation Coarsening is applied to the input mesh and then
13. fective stress effective plastic strain curve must be carefully checked Q The first data point must be at zero effective plastic strain and yield stress 0 0 oy Q Stress and strain must increase monotonically Q Slope of each segment must vary smoothly Q Data must fully include the range of strain seen in the part including very large strains seen at the outer surface in sharp corners Do not rely on LS DYNA to extend your curve Q Avoid too many data points Rely on at most four significant digits 10 Incomplete Solution Beware that if convergence fails LS DYNA will issue an error termination message and a d3plot state will be generated containing the last trial equilibrium geometry These results are not accurate Similarly if the final step of a multi step solution is not completed successfully artificial stabilization will not be completely removed an error termination message will be written and the d3plot results will not be accurate Accurate results can only be obtained after a normal termination Incorrect Constraints The model must be adequately constrained to remove rigid body motion but should not be over constrained Review the above section Required Constraints Gravitational Effects The shape of large flexible panels can be affected by gravity Gravity effects can be easily included in springback simulations using LOAD_ BODY and DEFINE CURVE keywords Be careful to employ a consistent syste
14. ially high tool velocity Both these methods introduce artificial dynamic effects which must be minimized to reasonable levels in an engineering sense A single independent parameter describing artificial dynamic effect is the number of explicit time steps cycles taken per millimeter of tool motion Relatively more cycles per millimeter are required when the forming process allows large unrestrained sheet motion An example is the crash forming process which uses no binders Relatively fewer cycles per millimeter are necessary when the sheet is heavily constrained with binders and punch support For most simulations values of between 100 and 1000 cycles per millimeter produce reasonable results If possible or when it is otherwise necessary to repeat a simulation use two different values and compare results to estimate sensitivity to artificial dynamic effects For an extensive description of input parameters for the forming simulation see Maker and Zhu 1 Springback Methods LS DYNA springback simulations can be performed by several methods A standard explicit dynamic method may not be used since the objective is to obtain a static springback solution free from dynamic oscillations Explicit dynamic relaxation is a viable method The preferred approaches to springback employ the static implicit method The two most common implicit approaches the seamless and dynain methods are described below Seamless Springback Method In
15. ize using dtmax 0 001 In this way the stepsize will always be increased after successfully converging until the maximum stepsize is reached CONTROL IMPLICIT AUTO iauto iteopt itewin dtmin dtmax 1 200 0 0 0 0 001 Troubleshooting Checklist The following sections offer suggestions for common springback problems Poor Accuracy Most accuracy problems result from errors which were introduced during the forming simulation By closely examining the forming model and results it may be possible to identify problems and anticipate poor springback predictions before they are submitted Follow the guidelines described in Maker and Zhu 1 In particular look for Q Insufficient mesh refinement At least four elements are needed around ninety degree tool radii Poor element aspect ratio Use elements which are as nearly square as possible Artificial explicit dynamic effects Running the forming simulation too slowly or too quickly can introduce error Check the number of cycles taken per millimeter of tool motion Q Changes in element formulation For best accuracy the more expensive element 16 must be used in the forming simulation as well as during springback even though this adds significant cost to the forming simulation Q Changes in thickness integration points The number of thickness integration points must never be changed between forming and springback simulation Incorrect or Insufficient Material Data The ef
16. m of units when defining gravitational acceleration Loose Convergence Tolerance Nonlinear convergence tolerances can be increased to allow premature convergence leading to poor accuracy The default tolerance values for dctol and ectol on CONTROL_ IMPLICIT SOLUTION are generally adequate and should not be increased Decreasing these tolerances to enforce equilibrium more strictly can be beneficial especially when a double precision executable is used Single vs Double Precision Use of a double precision version of LS DYNA improves convergence behavior in many implicit simulations Merely activating a double precision linear equation solver has marginal benefit in an otherwise single precision executable Contact LSTC to see if a double precision executable is available for your computer platform Mesh Coarsening Mesh coarsening should be applied to most production size jobs to combine small elements into larger ones reducing cpu time memory requirement and numerical truncation errors If the number of elements in the formed workpiece exceeds 50 000 consider using mesh coarsening Extrusion and Coining Significant errors result from situations where the workpiece is pinched between upper and lower tools to the extent that it is extruded or coined This does not include the normal action of binders Accurate simulation of extruded and coined parts may require layers of 8 node solid elements and advanced friction models which are beyon
17. rium convergence summary for time step 3 at time 1 0999005E 00 Number of iterations to converge 13 Number of stiffness reformations 2 Figure 3 By selecting nlprint 1 on CONTROL_ IMPLICIT SOLUTION or by interactively typing lt ctrl c gt nlprint the progress of the iterative equilibrium search will be displayed to the screen Output is shown for a typical implicit step The equilibrium search is performed using a Newton based method By default the BFGS method is used where a new stiffness matrix is formed after every 11 iterations For difficult springback problems flexible parts with large springback deformation the Full Newton method is better since this method forms a new stiffness matrix after every iteration To activate the Full Newton method set the iteration limit between stiffness reformations to ilimit 1 and increase the maximum allowable stiffness reformations per time step to maxref 100 In some cases the full Newton method will perform better if the line search is disabled using Istol 99999 CONTROL IMPLICIT SOLUTION nlsolvr ilimit maxref dctol ectol retol lstol 0 1 100 0 0 0 0 0 99999 dnorm divflag inistif nlprint 0 0 0 1 Solving The Linear System K x f The stiffness matrix formed during implicit analysis requires a large amount of memory and computing its inverse requires most of the CPU time These operations are performed by the linear equation solver whose con
18. s Node A is the reference node where all displacements are constrained This eliminates the three translational rigid body motion of the part In addition to the standard symmetry constraints selected translational degrees of freedom are constrained at node B to eliminate the three rigid body rotations of the part about node A Other LS DYNA Input Parameters The remaining necessary input parameters can be taken directly from the forming simulation input deck and should not be modified for springback analysis These include the PART MAT_ and SECTION keywords which describe the workpiece For recommended values of these parameters see Maker and Zhu 1 Running The Nonlinear Implicit Springback Simulation Unlike explicit simulations where tiny time steps are completed very quickly a large implicit simulation may take many minutes to complete a single time step By default LS DYNA issues very little screen output information when running in implicit mode Optional input parameters and interactive controls are available to produce more information about the progress of the simulation as described below Equilibrium Iterations and Convergence During each time step the nonlinear solver searches iteratively to find static equilibrium Activate the nonlinear solver print flag nlprint 1 using the CONTROL_ IMPLICIT SOLUTION keyword or interactively type lt ctrl c gt nlprint to see the progress of these iteration
19. s appear on the screen The current displacement and energy norms are displayed each iteration as shown in figure 3 These must both be decreased below their respective tolerances detol and ectol before equilibrium is reached The default values of these tolerances 0 001 and 0 01 respectively are generally good and need not be changed BEGIN implicit time step 3 time 1 09990E 00 current step size 3 67821E 01 Iteration 1 dul u 1 0894498E 01 Ei EO 1 8731172E 00 DIVERGENCE increasing residual norm detected Fe Fi 1 0547507E 07 exceeds Fe 9 1389570E 06 automatically REFORMING stiffness matrix teration 2 ldul lu l 3 8969724E 03 Ei EO 3 3420090E 02 teration 3 dul lul 6 3582980E 03 Ei EO 3 3460971E 02 teration 4 dul lul 3780216E 03 Ei EO 6 2154527E 03 teration 5 dul lul 6 0081244E 03 Ei EO 7 7976128E 03 teration 6 dul lul 4377093E 03 Ei EO 8 9132953E 03 teration 7 dul lul 6 4089308E 03 Ei EO 1 7184228E 02 teration 8 ldul lul 8267103E 03 Ei EO 1 9337881E 03 teration 9 ldul lul 9491626E 03 Ei EO 2 3472405E 03 teration 10 dul lu 2 2147158E 03 Ei EO 1 5075735E 03 teration 11 ldul lul 8921960E 03 Ei EO 1 9947323E 03 teration 12 dul lul 5758326E 03 Ei EO 7 9428701E 04 TERATION LIMIT reached automatically REFORMING stiffness matrix teration 13 dul u 7 1106170E 04 Ei EO 3 0991789E 03 Equilib
20. the simulation proceeds using the coarsened mesh Ifa zero termination time is specified and the keyword INTERFACE SPRINGBACK DYNAS3D is included a new dynain file will be output containing the coarsened mesh and the simulation will terminate Be careful to rename the first dynain file to avoid overwriting it with the second dynain file This is the recommended procedure 1 forming simulation output dynain file at termination time 2 mesh coarsening with zero termination time output second dynain file 3 springback simulation using coarsened mesh Coarsening is activated using the keyword CONTROL_COARSEN The only required input parameter is the flatness tolerance angle which limits coarsening to areas of the mesh where the angle between normal vectors of adjacent elements is less than the input value A recommended value is angle 8 degrees although values of up to 12 degrees have been used successfully An optional list of nseed nodes are used to initialize the search for candidate groups of elements to be coarsened Seed nodes can be used to assist the automatic searching logic in finding isolated regions of mesh within a part which need to be coarsened Up to eight nodes may be defined A seed nodes identifies the center of a group of four elements which may be combined into one To avoid leaving a single row of fine elements around the perimeter in the coarsened mesh seed nodes should not be chosen on mesh edges or refinement boundaries
21. trol parameters are found on CONTROL_ IMPLICIT SOLVER The default linear solver Isolvr 0 is generally recommended A double precision solution to the linear system K x f can be selected using lsolvr 6 however this alone does not often improve results and does increase memory requirements by 2x Solver 6 is very efficient at utilizing scratch files on disk to run in out of core mode so it is recommended when computer memory resources are limited CONTROL IMPLICIT SOLVER lsolvr lprint negeig 0 0 0 A summary of memory and CPU usage is printed to the screen when the Iprint flag is activated either by input using Iprint 1 or interactively by typing lt ctrl c gt Iprint The interactive control can be issued a second time to stop printing the memory information Memory limits can be increased using the execution line argument memory where the default is memory 8500000 Note that 1 Mword 4 Mbytes in single precision and 1 Mword 8 Mbytes in double precision SPARSE LINEAR EQUATION SOLVER STORAGE data Mwords 225972 degrees of freedom pointer arrays initial 11 523 actual 6 413 stiffness coefficients 6 187 Factorization Workspace estimated symbolic 14 015 numeric 18 335 Final Storage Requirements 10 for pivoting incore out of core symbolic factorization 5 276 5 276 numeric factorization 69 772 5292 numeric solution 65 561 3 145 TOTAL 87 648 23 168 TOTAL available
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