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]\(^1\).

Geometry

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

The plate dimensions are tabulated below:

	A	B	C	D	E	F
x	0	0.004	0.005	0.005	0	0
y	0	0	0.001	0.005	0.005	0.001
z	0.0001	0.0001	0.0001	0.0001	0.0001	0.0001

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.

Case	Element Type	Number of Nodes	Element Technology
(A)	2nd Order Tetrahedral	44211	Standard
(B)	2nd Order Tetrahedral	44211	Reduced integration

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

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 case A, where element technology is set to standard:

Similarly, for case B, 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: November 7th, 2023