v6.04.104 SSNV104 - Contact of two spheres

Summary:

The calculation consists in crushing two hemispheres on top of each other to test the unilateral contact algorithm statically. The solution is compared to the Hertz analytical result.

The models implement axisymmetric calculations as in \(\mathrm{3D}\) with linear/quadratic elements and different contact resolution methods (dualization, penalization, continuous formulation, Mortar pairing).

This classical test, for which an analytical solution is available, is also used to validate several options of the matching algorithm.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Reference quantities and results
  • 2.3. Uncertainties about the solution
  • 2.4. Bibliographical reference
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
  • 3.4. notes
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
  • 4.4. notes
• 5. D modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
  • 5.4. notes
• 6. E modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
  • 6.4. notes
• 7. F modeling
  • 7.1. Characteristics of modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
  • 7.4. notes
• 8. G modeling
  • 8.1. Characteristics of modeling
  • 8.2. Characteristics of the mesh
  • 8.3. Tested sizes and results
  • 8.4. notes
• 9. H modeling
  • 9.1. Characteristics of modeling
  • 9.2. Characteristics of the mesh
  • 9.3. Tested sizes and results
  • 9.4. notes
• 10. Modeling I
  • 10.1. Characteristics of modeling
  • 10.2. Characteristics of the mesh
  • 10.3. Tested sizes and results
  • 10.4. notes
• 11. J modeling
  • 11.1. Characteristics of modeling
  • 11.2. Characteristics of the mesh
  • 11.3. Tested sizes and results
  • 11.4. notes
• 12. K modeling
  • 12.1. Characteristics of modeling
  • 12.2. Characteristics of the mesh
  • 12.3. Tested sizes and results
• 13. L modeling
  • 13.1. Characteristics of modeling
  • 13.2. Characteristics of the mesh
  • 13.3. Tested sizes and results
• 14. M modeling
  • 14.1. Characteristics of modeling
  • 14.2. Characteristics of the mesh
  • 14.3. Tested sizes and results
• 15. N modeling
  • 15.1. Characteristics of modeling
  • 15.2. Characteristics of the mesh
  • 15.3. Tested sizes and results
• 16. Summary of results