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Documentation

# 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
• 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: Figure 1: Punch and foundation geometry for the present validation case

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

Find below the mesh used for cases B and D. It’s a standard mesh with second-order tetrahedral cells. Figure 2: Second-order standard mesh used for cases B and D

## 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: Figure 3: Axial displacements on the DE edge, showing good agreement with reference values

Now, comparing axial displacement from the cases with the friction and the reference values. Similarly to the previous case, a very good agreement is observed here: Figure 4: Axial displacements on the DE edge, with friction being modeled

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

Figure 6 shows contours for $$y$$ displacement, in meters, for case D: