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# Validation Case: 3D Punch With Rounded Edges (NAFEMS Contact Benchmark 2)

This 3D punch contact validation case belongs to solid mechanics. This test case aims to validate the following parameters:

• Penalty contact
• Augmented Lagrange contact
• Friction

The simulation results of SimScale were compared to the analytical results derived from [NAFEMS_R94]$$^1$$.

## Geometry

The geometry consists of a punch (DGHIJK) on top of a foundation (ABCDEF). The 3D punch has a 10 $$mm$$ radius fillet at the edge of the contact with the foundation. Figure 1 shows a wireframe of the geometry:

Due to the symmetry of the problem, only a quarter of the model is used for the simulations. These are the coordinates for each of the points:

The following dimensions are used in the creation of the geometry:

## Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Dynamic

Mesh and Element Types: The mesh for cases A through C was taken from [SSNA122]$$^2$$ and extruded in 3D hexahedral elements. It was created locally and imported to SimScale. For cases D and E, a first-order tetrahedral mesh was generated using the standard algorithm.

The mesh used for cases A through C has the following appearance:

Find below the mesh used for cases D and E. It’s a standard mesh with first-order tetrahedral cells.

## Simulation Setup

Material:

• 3D Punch
• Material behavior: Linear elastic
• $$E$$ = 210 $$GPa$$
• $$\nu$$ = 0.3
• $$\rho$$ = 7870 $$kg/m³$$
• Foundation
• Material behavior: Linear elastic
• $$E$$ = 70 $$GPa$$
• $$\nu$$ = 0.3
• $$\rho$$ = 7870 $$kg/m³$$

Boundary Conditions:

• Constraints
• $$d_x$$ = 0 on faces ABED and DGJI;
• $$d_z$$ = 0 on faces ACFD and DHKI;
• Fixed support on face ABC.
• Pressure = $$10^8 \ Pa$$ on face IJK.

## Result Comparison

Comparison of the displacements and the normal pressure of the nodes on edge DE. The values of reference in all figures were calculated with MSC.MARC and extracted from [NAFEMS_R94]$$^1$$ with WebPlotDigitizer.

The first plot is a comparison between the axial displacements from the cases without friction and the reference values:

Now, comparing case C results to the reference values, a very good agreement is also observed here:

Now, still analyzing the results over the DE edge, we will compare the radial displacements obtained with SimScale to the reference ones.

In Figure 7, we compare case C results for radial displacement with reference values:

Figure 9 shows contours for $$y$$ displacement, in meters, for case D: