r7.02.13 Crack propagation algorithms with X- FEM

Summary:

This document presents crack propagation algorithms as part of the X- FEM method [R7.02.12]. The crack is then represented by level-sets. The propagation of the crack therefore consists in updating the level-sets taking into account the advance of the crack front.

• 1. Introduction
• 2. Calculation of the propagation speed field
  • 2.1. Rate of advance of the bottom of the crack
  • 2.2. Velocity field extended to the mesh
  • 2.3. Calculating the speeds for each node in the mesh
  • 2.4. Calculating the local base
  • 2.5. Adjusting the normal speed field
  • 2.6. Consideration of the spill
  • 2.7. Determination of bifurcation angles
• 3. Level-set update
  • 3.1. Update equations
• 4. Resetting and reorthogonalizing level-sets
  • 4.1. Introduction
  • 4.2. Resolution by the fast marching method
  • 4.3. Calculating level-sets near iso-zeros
• 5. Location of the level-set calculation domain
  • 5.1. Selection of nodes/points and elements of the localized computing domain
  • 5.2. Displacement of the localized domain following the propagation of the crack
  • 5.3. Limitations on the value of the radius of the localized domain between two successive propagations
• 6. Direct calculation of new level-sets after advanced
  • 6.1. Level-set calculation method
  • 6.2. Treatment of problem areas
  • 6.3. Normal level-set discontinuity and calculation limitations
  • 6.4. Domain location
• 7. Mesh method for updating level-sets
  • 7.1. Presentation of the method
  • 7.2. Algorithm
• 8. Separation and fusion of crack fronts
  • 8.1. Meshing method
  • 8.2. Upwind method: introduction of a virtual background
  • 8.3. Geometric and simplex method
• 9. Bibliography
• 10. Description of the versions