Robust and direct evaluation of J(2) in linear elastic fracture mechanics with the X-FEM

International audienceThe aim of the present paper is to study the accuracy and the robustness of the evaluation of J(k)-integrals in linear elastic fracture mechanics using the extended finite element method (X-FEM) approach. X-FEM is a numerical method based on the partition of unity framework that allows the representation of discontinuity surfaces such as cracks, material inclusions or holes without meshing them explicitly. The main focus in this contribution is to compare various approaches for the numerical evaluation of the J(2)-integral. These approaches have been proposed in the context of both classical and enriched finite elements. However, their convergence and the robustness have not yet been studied, which are the goals of this contribution. It is shown that the approaches that were used previously within the enriched finite element context do not converge numerically and that this convergence can be recovered with an improved strategy that is proposed in this paper