volumetric locking workshop two reference: training manual element technology (2-64)

Volumetric Locking

Workshop Two

REFERENCE: Training ManualElement Technology (2-64)

September 30, 2001

Inventory #001492

W2-2

Advanced Structural Nonlinearities 6.0


Workshop Supplement

Workshop Two: Volumetric LockingAxisymmetric 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

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Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet1. 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.

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Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet2. 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.

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Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet3. 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

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Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet4. Specify Solution Options for nonlinear run.


– 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.

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Workshop Supplement

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

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Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet5. Solve the nonlinear model


– 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.

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Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet6. Review hydrostatic pressure final result


– 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.

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Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet7. List the reaction force at the pilot node


– 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.

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Workshop Two: Volumetric Locking ... Axisymmetric Billet8. We will now use PLANE182 B-Bar method.

Reenter Preprocessor to change element typeUse 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.

September 30, 2001

Inventory #001492

W2-12



Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet9. Resolve the nonlinear model


– 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.

September 30, 2001

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Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet10. Review hydrostatic pressure final result


– 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).

September 30, 2001

Inventory #001492

W2-14



Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet11. List the reaction force at the pilot node


– 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.

Reaction ForcePLANE42 w/o extra shape functions -596PLANE182 with B-Bar method -488Percent difference 22%

September 30, 2001

Inventory #001492

W2-15



Workshop Supplement

Workshop Two: Volumetric Locking ... Axisymmetric Billet

Resulting animation of hydrostatic pressure for fine mesh with symmetry expansion on.

volumetric locking workshop two reference: training manual element technology (2-64)

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