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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]\(^1\).


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:

3d punch foundation 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:

x \([mm]\)000.1000.100.04000.05
y \([mm]\)-0.2-0.2-0.2000000.10.10.1
z \([mm]\)00.1000.100.4000.50
Table 1: Coordinates of points A through K in the CAD model

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

Geometry FeatureDimension \([mm]\)
Punch diameter100
Punch height100
Foundation diameter200
Foundation height200
Fillet radius at the edge of the punch contact10
Table 2: Punch and foundation dimensions, in meters

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.

CaseMesh TypeNodesElement TypeSolution MethodContact SmoothingContact CoefficientCoefficient of Friction
A1st order hexahedral7803StandardAugmented LagrangeOn1000
B1st order hexahedral7803StandardPenaltyOn1e140
C1st order hexahedral7803StandardPenaltyOn1e140.1
D1st order standard32101StandardAugmented LagrangeOn1000
E1st order standard32101StandardPenaltyOn1e140
Table 3: Mesh characteristics and contact settings for cases A through E

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

first-order hex mesh validation
Figure 2: First-order hexahedral mesh used for cases A, B, and C

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

first order standard mesh for validation
Figure 3: First-order standard mesh used for cases D and E

Simulation Setup


  • 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.
  • Surface loads
    • 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:

axial displacements 3d punch no friction
Figure 4: Axial displacements on the DE edge, showing good agreement with reference values

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

axial displacements 3d punch with friction
Figure 5: 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.

radial displacements 3d punch no friction
Figure 6: Radial displacements on the DE edge, for the cases with no friction

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

radial displacements 3d punch with friction
Figure 7: Radial displacements on the DE edge, for cases involving friction

Lastly, the normal pressures observed for cases A through E, on the edge DE, are compared to reference values.

normal pressure plot over line
Figure 8: Comparing normal pressure levels on the DE edge for all cases

Figure 9 shows contours for \(y\) displacement, in meters, for case D:

y displacement contours in simscale post processor
Figure 9: Contours for the displacements observed in the y-direction

Last updated: May 19th, 2021

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