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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]\(^1\).


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

    CaseElement TypeNodesElement TechnologySolution MethodContact SmoothingPenalty CoefficientCoefficient of Friction
    A1st Order Tetrahedral32101StandardPenalty On1e14 0
    B2nd Order Tetrahedral 50226Reduced IntegrationPenaltyOn1e140
    C1st Order Tetrahedral 32101StandardPenaltyOn1e140.1
    D2nd Order Tetrahedral 50226Reduced IntegrationPenalty On1e14 0.1
    Table 3: Mesh characteristics and contact settings for cases A through D

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

    second order standard mesh for validation
    Figure 2: Second-order standard mesh used for cases B and D

    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 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:

    axial displacements 3d punch with friction
    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.

    radial displacements 3d punch no friction
    Figure 5: Radial displacements on the DE edge, for the cases with no friction

    Figure 6 shows contours for \(y\) displacement, in meters, for case D:

    y displacement contours on a punch on a cylinder case in simscale post processor
    Figure 6: Contours for the displacements observed in the y-direction

    Last updated: September 30th, 2021