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