r7.02.12 eXtended Finite Element Method: General

Summary:

This document presents the X- FEM method (eXtended Finite Element Method) which mainly makes it possible to consider cracks that do not respect the mesh to treat 2D and 3D crack problems. The crack is defined by the DEFI_FISS_XFEM [U4.82.08] command and can be used for linear and non-linear static calculations.

Other documents dedicated to specific issues are available:

• touch-friction on the lips of the crack in small slips with X- FEM [R5.03.54],

• touch-friction on the lips of the crack in large swings with X- FEM [R5.03.53],

• crack propagation with X- FEM [R7.02.13]

• 1. Introduction
• 2. Representation of the crack by « level sets »
  • 2.1. Theoretical aspect of level sets
  • 2.2. Calculation of level sets
  • 2.3. Local base at the bottom of a crack
  • 2.4. Determination of the crack background
• 3. Cracking problem with X- FEM
  • 3.1. General problem
  • 3.2. Enrichment of the displacement approximation
  • 3.3. Sub-division
  • 3.4. Retrieving contact facets
  • 3.5. Integrating stiffness
  • 3.6. Integration of the second surface members
• 4. Linear thermal with X- FEM
  • 4.1. Introduction
  • 4.2. Restrictions
  • 4.3. Problem treated
  • 4.4. X- FEM approximation of the temperature field
  • 4.5. Integration of matrices and elementary vectors
• 5. Energy calculation of Stress Intensity Factors
  • 5.1. G-theta method for calculating G
  • 5.2. G-theta method for calculating KI, KII and KIII with level sets
  • 5.3. G-theta method with X- FEM
• 6. Bibliography
• 7. Description of the versions