XFEM elements with regularized cohesive laws and path-following methods

by G. Ferte, EDF R&D / LaMSID

Modelisation of fracture is a major issue for the lifetime assessment of structures and components. Authors generally distinguish between three distinct methods. While a diffuse damage law is introduced in the bulk in the first one, so as to account for gradual deterioration of the material, this deterioration is concentrated on a default surface in both others. Among the latter, the first one relies on global energy minimization principles, which provide some propagation information if characteristic threshold values are overstepped. The second one introduces cohesive zones, with cohesive forces acting in between the crack sides, following a softening interface law triggered by stress-based local criterion.

The first method is expensive but it provides an accurate description of the initiation process while the second one fails short to modelize it. Such
information may be obtained from the third one, since both crack initiation and propagation may be predicted as soon as the location of the original
defect and its propagation direction are known a priori. Eventually, we would like this approach to not require an a priori knowledge of the crack path by means of the combined use of the X-FEM formulation and some criterion over the propagation direction.

For now, regularized CZM_EXP_REG and CZM_LIN_REG cohesive laws are available in the X-FEM, extension of the classical finite element method to computation with non-conforming meshes. To activate them on an X-FEM interface, information ALGO_CONT=’CZM’ and RELATION=’CZM_LIN_REG’ should be entered within the DEFI_CONTACT command.

In order to perform quasi-static brutal failure computation, some path-following methods have been implemented in the X-FEM. The existing elastic
prediction method was extended and two dedicated methods SAUT_IMPO and SAUT_LONG_ARC were created, in which the average jump across the interface in controlled, along a specified direction or by controlling the jump norm, respectively. Computation of some brutal failure is presented hereafter.

This work results from a collaboration with Pr. Nicolas Moës, from the Ecole Centrale Nantes.