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Validation Case: 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]\(^1\).


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

notched plate geometry validation simscale
Figure 1: Notched plate geometry used in the present validation case

The plate dimensions are tabulated below:

Table 1: Geometry dimensions in meters

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 in this project were created in SimScale with the standard algorithm.

CaseElement TypeNumber of NodesElement Technology
(A) 2nd Order Tetrahedral44211Standard
(B) 2nd Order Tetrahedral 44211Reduced integration
Table 2: Mesh characteristics

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

tetrahedral second order mesh notched plate
Figure 2: Second order standard mesh used for cases A and B

Simulation Setup


  • 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:
young's modulus plastic behavior
Figure 4: Dependency of the Young’s modulus

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 case A, where element technology is set to standard:

notched plate validation results standard elements
Figure 5: Comparison of case A with the reference values from [SSNP123]¹

Similarly, for case B, where reduced integration was used:

notched plate validation results reduced integration elements
Figure 6: Comparison of case B with the reference values from [SSNP123]¹

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:

notched plate validation post processing contours
Figure 7: Case B, showing the contours for Cauchy stress σyy, in SimScale’s post-processor

Last updated: September 24th, 2021