u2.05.02 Instructions for using the X method- FEM

Summary

The objective of this note is to provide the information necessary for a user to perform calculations with*Code_Aster* using the extended finite element method (X- FEM for eXtended Finite Element Method) [1].

The first part introduces the objectives of the extended finite element method and recalls the basic principles of X- FEM and level sets.

The second part introduces the possibilities and limitations of using X- FEM in*Code_Aster*.

The following three parts detail the implementation of X- FEM in*Code_Aster*, for a calculation without or with contact on the lips of the crack, then for an underthickness calculation.

Finally, the last part gives a lot of practical advice.

• 1. Introduction
  • 1.1. Why use X- FEM?
  • 1.2. Specificity of a calculation with X- FEM
  • 1.3. Related documentation
• 2. Possibilities and limitations of X- FEM in Code_Aster
  • 2.1. Phenomenon, modeling, and enriched finite elements
  • 2.2. Law of behavior
  • 2.3. Definition of cracks
  • 2.4. Contact friction
  • 2.5. Cohesive zones
  • 2.6. Boundary conditions and loads
  • 2.7. Thermo-mechanical calculation
  • 2.8. Hydro-mechanical calculation with an HM- XFEM model
  • 2.9. Visualization post-treatments
  • 2.10. Mechanics of rupture
  • 2.11. Propagation in fatigue
  • 2.12. Various restrictions
• 3. Implementation: without contact on the lips of the crack
  • 3.1. Creating the healthy mesh and model
  • 3.2. Definition of crack
  • 3.3. Creating the rich model
  • 3.4. Resolution
  • 3.5. Visualization post-processing
  • 3.6. Post-treatment in fracture mechanics
  • 3.7. Various post-treatments
• 4. Implementation: with contact on an interface
  • 4.1. Interface definition
  • 4.2. Creating the rich model
  • 4.3. Bi-material
  • 4.4. Contact load
  • 4.5. Visualization post-processing
  • 4.6. Post-treatment in fracture mechanics
  • 4.7. Contact post-treatment
• 5. Implementation: hole or underthickness
• 6. Tips and recommendations on meshing
  • 6.1. The problem of mesh refinement in the X- FEM framework
  • 6.2. Definition of the size of a mesh
  • 6.3. Criteria for mesh sizes
  • 6.4. Techniques for mesh refinement in the X- FEM frame
  • 6.5. Methodology for mesh refinement with Lobster and level sets
  • 6.6. Summary of recommended mesh refinement methodology
• 7. Tips and recommendations on using X- FEM
  • 7.1. Enrichment
  • 7.2. CALC_G Settings
  • 7.3. POST_K1_K2_K3 Settings
  • 7.4. Post-treatment on several crack backgrounds
  • 7.5. Propagation
  • 7.6. Contact friction
• 8. Conclusions
• 9. Bibliography