1. NLISO Material Model Workshop Four REFERENCE: Training Manual Rate-Independent Plasticity (3-65)

2. Workshop Supplement September 30, 2001 Inventory #001492 W4-2 Workshop Four: Nonlinear Isotropic Hardening Tensile Specimen Purpose Compare multilinear isotropic hardening and nonlinear isotropic hardening laws. Goal Solve a nonlinear analysis of two tensile specimens, one with multilinear isotropic hardening (MISO) and other with nonlinear isotropic hardening (NLISO). Model Description 2D axisymmetric models, PLANE182 elements Use of MISO and NLISO hardening laws. Symmetry boundary conditions MISO NLISO

3. Workshop Supplement September 30, 2001 Inventory #001492 W4-3 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 1.Read in the input file named “ANL_W04_NLISO.inp” Use the GUI menu method: –Utility Menu > File > Read Input From… Select the file “ANL_W04_NLISO.inp” Click on [OK] or Command Input method: –/INPUT,ANL_W04_NLISO,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 2 axisymmetric models of a tensile specimen. The current database will be erased, and the jobname will be changed to “Exercise_4”. The graphics and other settings will also be set to be consistent with these slides.

4. Workshop Supplement September 30, 2001 Inventory #001492 W4-4 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 2.Verify the element options for PLANE182 (4-node quad) Use the GUI menu method: –Main Menu > Preprocessor > Element Type > Add/Edit/Delete … Select “Type 1 PLANE182” Click on [Options] Verify element options, then click on [OK] Select [Close] or Command Input method: –/PREP7 –ETLIST Notes: Element type 1 will use an axisymmetric, “Full Integration” element formulation (a.k.a. B-Bar method). B-Bar is used because this problem will have large plastic strains (nearly incompressible). This problem is dominated by bulk deformation, so shear locking is not an issue.

5. Workshop Supplement September 30, 2001 Inventory #001492 W4-5 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 3.Verify existing material property 1 Use the GUI menu method: –Main Menu > Preprocessor > Material Props > Material Models … Select “Material Model Number 1 > Linear Isotropic” Look at linear materials, then click on [OK] Select “Material Model Number 1 > Multilinear Isotropic” Look at MISO properties. Click on [Graph] to see stress-strain curve, then click on [OK] Select “Material > Exit” or Command Input method: –MPLIST,1 –TBLIST,ALL,1 Notes: Similar to Step 2, there is nothing to input in this step. MISO properties have already been input for the user. It is always a good idea, however, to review input for any model.

6. Workshop Supplement September 30, 2001 Inventory #001492 W4-6 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 4.Input NLISO as material property 2 Use the GUI menu method: –Main Menu > Preprocessor > Material Props > Material Models … Select “Materials GUI > Material > New Model” Click on [OK] Select “Structural > Nonlinear > Inelastic > Rate Independent > Isotropic Hardening Plasticity > Mises Plasticity > Nonlinear” You will be prompted to input linear properties first. Click on [OK] Enter “6.4e6” for “EX” and “0.3” for “PRXY” Click on [OK] Enter “128000” for “Sigy0”, “40691” for “R0”, “120305” for “Rinf”, and “68” for “b” Click on [OK] Select “Material > Exit” or Command Input method: –MP,EX,2,6.4E6 –MP,PRXY,2,0.3 –TB,NLISO,2,1,4 –TBDATA,1,128000,40691,120305,68

7. Workshop Supplement September 30, 2001 Inventory #001492 W4-7 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 5.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 “20” for “Number of substeps” Enter “100” for “Max no. of substeps” Enter “20” for “Min no. of substeps” Select “Write N number of substeps” for “Frequency” Enter “-20” for “where N=“ Click on [OK] or Command Input method: –/SOLU –NLGEOM,ON –NSUBST,20,100,20 –OUTRES,ALL,-20 Notes: For this problem, we have entered the value of “-20” for “Write N number of substeps”. The negative value tells ANSYS to write 20 results as evenly spaced apart as possible. Under the “Nonlinear” tab, we could have also specified a maximum equivalent plastic strain limit (CUTCONTROL) to ensure greater accuracy in capturing the path-dependent response.

8. Workshop Supplement September 30, 2001 Inventory #001492 W4-8 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen Before solving the model, you can also examine the mesh and the boundary conditions on the two tensile specimens to become more familiar with the model. There are symmetry boundary conditions for axisymmetry (UX constrained along X=0) and half-symmetry constraints (UY constrained along Y=0) There are coupled sets at the end. The “master” node of the coupled sets is pulled 0.4 units (direction shown with red arrow on right). Material 1 is on the top (MISO), Material 2 is on the bottom (NLISO). Notice that the mesh is biased near the half- symmetry plane of the models. This is where necking is expected to occur, so the mesh is concentrated in that area to capture the high stress gradients. MISO NLISO

9. Workshop Supplement September 30, 2001 Inventory #001492 W4-9 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 6.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.

10. Workshop Supplement September 30, 2001 Inventory #001492 W4-10 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 7.Review equivalent plastic strains 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 “Strain-plastic” on left side, then select “vonMises EPPLEQV” on right Click on [OK] to plot equivalent plastic strains or Command Input method: –/POST1 –SET,LAST –PLESOL,EPPL,EQV Notes: Note that there is some difference in the amount of plastic strains between the two specimens.

11. Workshop Supplement September 30, 2001 Inventory #001492 W4-11 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 8.Review force vs. deflection response Use the GUI menu method: –Main Menu > TimeHist Postpro > Variable Viewer... Select “Exercise_4.rst” results file. –Variable Viewer > “+” Icon (Add Data) … Select “Reaction Forces > Structural Forces > Y-component of force”. Click on [OK] Select upper-left corner node of top specimen (node 573). Click on [Apply] Repeat for upper-left corner node of bottom specimen (node 232). Click on [OK] In the Variable Calculator, Shift-Click both “FY_2” and “FY_3”. Then, click on the “Plot” icon (Graph Data). The force-deflection curves will then be plotted (see next slide).

12. Workshop Supplement September 30, 2001 Inventory #001492 W4-12 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 8.Review force vs. deflection response (cont’d) or Command Input method: –/POST26 –RFORCE,2,node(0,9,0),f,y,FY_2 –RFORCE,3,node(0,4,0),f,y,FY_3 –PLVAR,2,3 Notes: The force vs. deflection curves for the two tensile specimens (MISO and NLISO) are shown on the right. Note the similarity between the curves. However, as we will see next, this is due to the fact that the NLISO and MISO materials used for this exercise are close but not exactly the same. In the command-input method, a *GET function node() was used to retrieve the node numbers corresponding to coordinates of (0,9,0) and (0,4,0). You can also use the node numbers directly (573 and 232) instead. MISO (top specimen) is in light blue, NLISO (bottom specimen) is in purple.

13. Workshop Supplement September 30, 2001 Inventory #001492 W4-13 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen 9.Use a pre-existing macro “EX4PLOT” to plot stress-strain curves at necking region. Use the Command Input method: –EX4PLOT Notes: Although the stress-strain curves are similar, they are not exactly the same. Hence, there is also some difference in results between the two specimens during the analysis. Although the procedure done with the EX4PLOT macro could be accomplished manually through the GUI menu or through commands, this is left as an exercise to the reader. MISO (top specimen) is in light blue, NLISO (bottom specimen) is in purple.

14. Workshop Supplement September 30, 2001 Inventory #001492 W4-14 Workshop Four: Nonlinear Isotropic Hardening... Tensile Specimen Note that if the model was run with a larger load, the stress-strain behavior will differ more. The MISO input assumes perfectly-plastic behavior beyond the defined points, as shown by the blue line. On the other hand, NLISO continues with slope defined by R0, illustrated by the purple line. MISO (top specimen) is in light blue, NLISO (bottom specimen) is in purple.