r7.02.19 Cohesive elements with X- FEM

Summary:

This document presents the various cohesive elements available with the extended finite element method (X- FEM). Three types of cohesive laws are available. The law introduced first is a regularized law, available for linear elements, a function of the displacement jump only. Following the limits of this last one, two mixed laws were introduced: one for linear elements, the other for quadratic elements. A crack propagation procedure with cohesive elements is implemented. It is based on linear mixed elements.

Cohesive elements are implemented in*Code_Aster* in 2D and 3D. They can be used with two types of discontinuities: through interfaces (keyword TYPE_DISCONTINUITE =” INTERFACE “in DEFI_FISS_XFEM) and cohesive cracks (keyword TYPE_DISCONTINUITE =” COHESIF”) that are used for propagation studies on an unknown path. The cohesive law is defined in STAT_NON_LINE, the resolution is performed with the command STAT_NON_LINE [U4.51.03]. For a propagation study on an unknown path, the update of the cracked surface is done by the command PROPA_FISS, and the directional criterion is calculated by the command CALC_G.

Table of Contents

• 1. Introduction
• 2. Strong formulation of the cohesive problem
  • 2.1. Formulation of the equations of the general problem
  • 2.2. Cohesive laws
• 3. Variational formulations
  • 3.1. Formulation for the regularized cohesive law
  • 3.2. Disadvantages of a cohesive regularized law
  • 3.3. Reduced space for discretizing the interface constraint
  • 3.4. Formulation for a mixed cohesive law for quadratic elements
  • 3.5. Formulation for a mixed cohesive law for linear elements
• 4. Resolution strategy
  • 4.1. Newton-Raphson method
  • 4.2. Differentiation of cohesive law
  • 4.3. Linearization of the problem
• 5. Matrix expression of the problem
  • 5.1. Regularized cohesive law
  • 5.2. Mixed cohesive law for quadratic elements
  • 5.3. Mixed cohesive law for linear elements
• 6. Propagation of a cohesive crack
  • 6.1. Description of a cohesive crack
  • 6.2. Carrying out the mechanical calculation
  • 6.3. Forehead detection
  • 6.4. Determining the direction of propagation
  • 6.5. Extension of the potential cracking surface
  • 6.6. Expansion of the space of multipliers and initial internal variables
• 7. Bibliography
• 8. Description of the versions