3D Punch (Rounded Edges) (NAFEMS Contact Benchmark 2)


The aim of this test case is to validate the following functions:

  • penalty contact
  • augmented lagrange contact
  • friction

The simulation results of SimScale were compared to the results presented in [NAFEMS_R94]. The mesh used in (A) was taken from [SSNA122] and extruded in 3D hexahedral elements. The mesh in (B) was created with the tetrahedralization-with-refinements tool on the SimScale platform.

Import validation project into workspace



Geometry of the sphere

Due to the symmetry of the problem only a quarter of the model is used for the simulation. The punch (DGHJKL) is on top of the foundation (ABCDEF).

Punch diameter 100 mm
Punch height 100 mm
Foundation diameter 200 mm
Foundation height 200 mm
Fillet radius at the edge of the punch contact 10 mm

Analysis type and Domain

Tool Type : Code_Aster

Analysis Type : Dynamic

Mesh and Element types :

Case Mesh type Number of nodes Element type
(A) linear hexahedral 7803 3D isoparametric
(B) linear tetrahedral 19353 3D isoparametric

Mesh used for the SimScale case (A)


Mesh used for the SimScale case (B)

Simulation Setup


All displacement and load components are referred to the coordinate system in the figure of the geometry section.


  • Punch: isotropic: E = 210 GPa, \(\nu\) = 0.3
  • Foundation: isotropic: E = 70 GPa, \(\nu\) = 0.3


  • Face ABC fixed
  • Face ACDF and DHJL zero x-displacement
  • Face ABDE and DGJK zero y-displacement


  • Uniform pressure \(p\) = 10⁸ Pa on face JKL
  Contact I Contact II Contact III
Solution method Augmented Lagrange Penalty Penalty
Contact smoothing on on on
Coefficient of contact 100 10¹⁴ 10¹⁴
Coefficient of friction \(\mu\) 0 0 0.1


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


Comparison of the axial displacement on edge DE


Comparison of the radial displacement on edge DE


Normal pressure on edge DE