1. Volumetric Locking Workshop Two REFERENCE: Training Manual Element Technology (2-64)

2. Workshop Supplement September 30, 2001 Inventory #001492 W2-2 Workshop Two: Volumetric Locking Axisymmetric Billet Purpose Demonstrate, detect, and alleviate volumetric locking. Goal Solve a nonlinear analysis of a forging of a billet. Model Description 2D axisymmetric billet, elasto-perfectly-plastic material (BISO) Rigid Piece Deformable Billet

3. Workshop Supplement September 30, 2001 Inventory #001492 W2-3 Workshop Two: Volumetric Locking... Axisymmetric Billet 1.Read in the input file named “ANL_W02_VoluLock.inp” Use the GUI menu method: –Utility Menu > File > Read Input From… Select the file “ANL_W02_VoluLock.inp” Click on [OK] or Command Input method: –/INPUT,ANL_W02_VoluLock,inp Notes: This will read in an input file which will generate the geometry, loads, and boundary conditions for the current exercise. We will have one rectangular mesh for the billet and a rigid target surface. The current database will be erased, and the jobname will be changed to “Exercise_2”. The graphics and other settings will also be set to be consistent with these slides.

4. Workshop Supplement September 30, 2001 Inventory #001492 W2-4 Workshop Two: Volumetric Locking... Axisymmetric Billet 2.Verify the element options for PLANE42 (4-node quad) Use the GUI menu method: –Main Menu > Preprocessor > Element Type > Add/Edit/Delete … Select “Type 1 PLANE42” Click on [Options] Verify element options, then click on [OK] Select [Close] or Command Input method: –/PREP7 –ETLIST Notes: Element type 1 is PLANE42 without “extra displacement shapes.” This will provide a fully- integrated, conventional displacement-based element - recall that this element is susceptible to shear and volumetric locking.

5. Workshop Supplement September 30, 2001 Inventory #001492 W2-5 Workshop Two: Volumetric Locking... Axisymmetric Billet 3.Add elastic and nonlinear plasticity properties Use the GUI menu method: –Main Menu > Preprocessor > Material Props > Material Models … Select “Structural > Nonlinear > Inelastic > Rate Independent > Isotropic Hardening Plasticity > Mises Plasticity > Bilinear” You will be prompted to input linear properties first. Click on [OK] Enter “200” for “EX” Enter “0.3” for “PRXY” Click on [OK] Enter “0.7” for “Yield Stss” Enter “0” for “Tang Mod” Click on [OK] Select “Material > Exit” or Command Input method: –MP,EX,1,200 –MP,PRXY,1,0.3 –TB,BISO,1,1 –TBDATA,1,0.7,0.0

6. Workshop Supplement September 30, 2001 Inventory #001492 W2-6 Workshop Two: Volumetric Locking... Axisymmetric Billet 4.Specify Solution Options for nonlinear run. Use the GUI menu method: –Main Menu > Solution > -Analysis Type- Sol’n Control … Select “Large Displacement Static” under “Analysis Options” Enter “100” for “Number of substeps” Enter “1e5” for “Max no. of substeps” Enter “20” for “Min no. of substeps” Select “Write every substep” under “Frequency” Click on [OK] or Command Input method: –/SOLU –NLGEOM,ON –NSUBST,100,1e5,20 –OUTRES,ALL,ALL Notes: We will save all intermediate results for debugging purposes.

7. Workshop Supplement September 30, 2001 Inventory #001492 W2-7 Workshop Two: Volumetric Locking... Axisymmetric Billet Before solving the problem, it is a good idea to look at the mesh, boundary conditions, and other elements present to become more familiar with the model. There is a rigid target surface which is controlled with a pilot node at the tip. An imposed displacement is applied on the pilot node. The deformable mesh is covered with contact elements as shown by the arrows. Axisymmetry boundary conditions (UX=0 along X=0) and symmetry plane boundary conditions (UY=0 along Y=0) are also applied in the model. We will solve the model using (a) PLANE42 without extra displacement shapes and (b) PLANE182 with B-Bar method. Rigid Target Deformable Billet Pilot Node Contact Elements

8. Workshop Supplement September 30, 2001 Inventory #001492 W2-8 Workshop Two: Volumetric Locking... Axisymmetric Billet 5.Solve the nonlinear model Use the GUI menu method: –Main Menu > Solution > -Solve- Current LS After reviewing the status window, close it by selecting “File > Close” To start the analysis, click on [OK] or Command Input method: –SOLVE Notes: Since this is a nonlinear analysis, the solution may take a few minutes, depending on the hardware used. It is always a good idea to review the solution window (/STAT,SOLU) to ensure that the solution settings are correct. In this case, the problem dimensionality (2D with UX, UY DOF), the use of nonlinear geometric effects, the number of substeps, and the frequency of output results are the most important settings.

9. Workshop Supplement September 30, 2001 Inventory #001492 W2-9 Workshop Two: Volumetric Locking... Axisymmetric Billet 6.Review hydrostatic pressure final result Use the GUI menu method: –Main Menu > General Postproc > -Read Results- Last Set This command loads in the last results set. –Main Menu > General Postproc > Plot Results > -Contour Plot- Element Solu … Select “Stress” on left side, then select “HydrostPres HPRE” on right Click on [OK] to plot hydrostatic pressure or Command Input method: –/POST1 –SET,LAST –PLESOL,NL,HPRES Notes: There is significant variation of hydrostatic pressure in each element. This checkerboard pattern indicates that volumetric locking is a problem.

10. Workshop Supplement September 30, 2001 Inventory #001492 W2-10 Workshop Two: Volumetric Locking... Axisymmetric Billet 7.List the reaction force at the pilot node Use the GUI menu method: –Main Menu > General Postproc > List Results > Reaction Solu … Click on [OK] to list reaction forces. The pilot node for the rigid contact surface is Node 6. or Command Input method: –PRRSOL Notes: Please make note of the reaction force at the pilot node, which is -596 in the Y-direction. Because we imposed a displacement on the rigid surface, the reaction force indicates how much force would be required to move the rigid surface -7 units in the y-direction. Next, we will switch the element type to PLANE182 with B-Bar method.

11. Workshop Supplement September 30, 2001 Inventory #001492 W2-11 Workshop Two: Volumetric Locking... Axisymmetric Billet 8.We will now use PLANE182 B-Bar method. Reenter Preprocessor to change element type Use the Command Input method: –/PREP7 –ET,1,182,,,1 Notes: For this operation, it is much easier to use command method, so no GUI menu equivalent is presented here. We have switched Element Type 1 from PLANE42 to PLANE182, using the axisymmetric option. By default, PLANE182 uses B-Bar method which handles volumetric locking well for nearly incompressible problems.

12. Workshop Supplement September 30, 2001 Inventory #001492 W2-12 Workshop Two: Volumetric Locking... Axisymmetric Billet 9.Resolve the nonlinear model Use the GUI menu method: –Main Menu > Solution > -Solve- Current LS After reviewing the status window, close it by selecting “File > Close” To start the analysis, click on [OK] or Command Input method: –/SOLU –SOLVE Notes: After switching element types to an element formulation which can handle volumetric locking, we will rerun the same problem.

13. Workshop Supplement September 30, 2001 Inventory #001492 W2-13 Workshop Two: Volumetric Locking... Axisymmetric Billet 10.Review hydrostatic pressure final result Use the GUI menu method: –Main Menu > General Postproc > -Read Results- Last Set This command loads in the last results set. –Main Menu > General Postproc > Plot Results > -Contour Plot- Element Solu … Select “Stress” on left side, then select “HydrostPres HPRE” on right Click on [OK] to plot hydrostatic pressure or Command Input method: –/POST1 –SET,LAST –PLESOL,NL,HPRES Notes: This time, we do not see any “checkerboard pattern” when plotting hydrostatic pressure. B-Bar method of PLANE182 is one way to prevent volumetric locking in nearly incompressible problems (i.e., finite strain plasticity).

14. Workshop Supplement September 30, 2001 Inventory #001492 W2-14 Workshop Two: Volumetric Locking... Axisymmetric Billet 11.List the reaction force at the pilot node Use the GUI menu method: –Main Menu > General Postproc > List Results > Reaction Solu … Click on [OK] to list reaction forces. The pilot node for the rigid contact surface is Node 6. or Command Input method: –PRRSOL Notes: Please make note of the reaction force at the pilot node, which is -488 in the Y-direction. If we compare PLANE42 without extra shape functions with B-Bar method, we see that B-Bar takes less force to move the rigid surface by the same amount. In fact, there is a 22% difference in required force. To put another way, the PLANE42 mesh encounters volumetric locking, making it too stiff. More force is required to deform the mesh by the same amount.

15. Workshop Supplement September 30, 2001 Inventory #001492 W2-15 Workshop Two: Volumetric Locking... Axisymmetric Billet Resulting animation of hydrostatic pressure for fine mesh with symmetry expansion on.