v6.04.182 SSNV182 — Block with interface in friction contact with X- FEM

Summary

The purpose of this test is to validate the consideration of contact on the lips of the crack, by limiting itself to the case where the crack completely crosses the structure. Contact is taken into account by the continuous method [bib1] adapted to the framework of the X- FEM method [bib2]. Two contact algorithms are tested: the augmented Lagrangian method and the penalized method [bib2].

This test involves a parallelepipedic block in compression modelled in \(\mathrm{2D}\) and \(\mathrm{3D}\). The interface crossing it is represented by a level-set as part of the X- FEM method. Several angular positions of the interface are taken into account: the interface follows the faces of the elements (\(\theta =0°\)) and the interface cuts the elements (\(\theta =26.56°\) in \(\mathrm{3D}\) and \(\theta =30°\) in \(\mathrm{2D}\)). By taking a Coulomb coefficient of friction high enough for there to be adhesion, we find the solution of the same problem without an interface. The d, e and f models make it possible to validate the method also in \(\mathrm{2D}\).

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. Characteristics of the mesh
  • 1.5. Bibliography
• 2. Modeling A: right interface, augmented Lagrangian method
  • 2.1. Analytical resolution
  • 2.2. Features tested
  • 2.3. Tested sizes and results
  • 2.4. Comments
• 3. B modeling: leaning interface, augmented Lagrangian method
  • 3.1. Analytical resolution
  • 3.2. Tested sizes and results
  • 3.3. Comments
• 4. C modeling: right interface and sub-integration, augmented Lagrangian method
  • 4.1. Tested sizes and results
  • 4.2. Comments
• 5. D modeling: right interface in plane constraints, augmented Lagrangian method
  • 5.1. Analytical resolution
  • 5.2. Tested features
  • 5.3. Tested sizes and results
  • 5.4. Comments
• 6. E modeling: leaning interface under plane constraints, augmented Lagrangian method
  • 6.1. Analytical resolution
  • 6.2. Tested sizes and results
• 7. F modeling: leaning interface in plane deformations, augmented Lagrangian method
  • 7.1. Tested sizes and results
• 8. G modeling: right interface, penalized method
  • 8.1. Analytical resolution
  • 8.2. Features tested
  • 8.3. Tested sizes and results
  • 8.4. Comments
• 9. H modeling: slanted interface, penalized method
  • 9.1. Analytical resolution
  • 9.2. Tested features
  • 9.3. Tested sizes and results
  • 9.4. Comments
• 10. Modeling I: right interface in plane constraints, penalized method
  • 10.1. Analytical resolution
  • 10.2. Features tested
  • 10.3. Tested sizes and results
  • 10.4. Comments
• 11. J modeling: leaning interface in plane constraints, penalized method
  • 11.1. Analytical resolution
  • 11.2. Features tested
  • 11.3. Tested sizes and results
  • 11.4. Comments
• 12. K modeling: right interface in plane constraints, augmented Lagrangian method on a quadratic mesh
  • 12.1. Analytical resolution
  • 12.2. Tested features
  • 12.3. Tested sizes and results
  • 12.4. Comments
• 13. L modeling: leaning interface under plane constraints, augmented Lagrangian method on a quadratic mesh
  • 13.1. Analytical resolution
  • 13.2. Tested features
  • 13.3. Tested sizes and results
  • 13.4. Comments
• 14. M modeling: 3D leaning interface, augmented Lagrangian method on a quadratic mesh
  • 14.1. Analytical resolution
  • 14.2. Tested features
  • 14.3. Tested sizes and results
  • 14.4. Comments
• 15. Summaries of results