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# Elastoplastic Notched Plate

This validation case belongs to solid mechanics. It aims to validate the following parameters:

• Plastic material behavior
• Reduced integration element type

The simulation results of SimScale were compared to the reference values presented in [SSNP123]$$^1$$.

## Geometry

Find below the notched plate geometry used for this validation case:

The plate dimensions are tabulated below:

The corresponding nodes marked with an apostrophe (‘) are translated 0.0001 $$m$$ along the negative z-direction.

## Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Nonlinear static

Mesh and Element Types: The meshes used for cases A and C were created in SimScale with the standard algorithm. The mesh used for cases B and D is a hexahedral mesh that was created locally.

Find below the mesh used for cases A and C. It’s a standard mesh with second order tetrahedral cells.

Cases B and D are run on a 2nd order hexahedral mesh, which is shown below:

## Simulation Setup

Material:

• Steel (plastic behavior)
• $$E$$ = 200 $$GPa$$, $$v$$ = 0.3
• $$\rho$$ = 7870 $$kg/m^3$$
• $$\sigma_y$$ = 200 $$MPa$$, $$E_T$$ = 1000 $$MPa$$, as shown below:

Boundary Conditions:

• Constraints
• $$d_x$$ = 0 on face AA’E’EF
• $$d_y$$ = 0 on face AA’B’B
• $$d_z$$ = 0 for all nodes
• Face EE’D’D: displacement of 0.0001 $$m$$ in the positive y-direction

## Result Comparison

The results obtained from SimScale for the Cauchy stress $$\sigma_{yy}$$ along the FC line are compared to the values of reference from [SSNP123]$$^1$$. These values of reference were extracted with WebPlotDigitizer. Figure 5 shows the results for cases A and B, where element technology is set to standard:

Similarly, for cases C and D, where reduced integration was used:

In both Figures 5 and 6, SimScale’s results show good agreement with the reference values.

Inspecting the Cauchy stress $$\sigma_{yy}$$ for case B in the post-processor:

Last updated: August 4th, 2020