Convergence of domain integrals for stress intensity factor extraction in 2‐D curved cracks problems with the extended finite element method

Abstract

SUMMARY The aim of this study is the analysis of the convergence rates achieved with domain energy integrals for the computation of the stress intensity factors (SIF) when solving 2‐D curved crack problems with the extended FEM (XFEM). Domain integrals, specially the J ‐integral and the interaction integral, are widely used for SIF extraction and provide high accurate estimations with FEMs. The crack description in XFEM is usually realized using level sets. This allows to define a local basis associated with the crack geometry. In this work, the effect of the level set local basis definition on the domain integral has been studied. The usual definition of the interaction integral involves hypotheses that are not fulfilled in generic curved crack problems, and we introduce some modifications to improve the behavior in curved crack analyses. Despite the good accuracy of domain integrals, convergence rates are not always optimal, and convergence to the exact solution cannot be assured for curved cracks. The lack of convergence is associated with the effect of the curvature on the definition of the auxiliary extraction fields. With our modified integral proposal, the optimal convergence rate is achieved by controlling the q ‐function and the size of the extraction domain. Copyright © 2013 John Wiley & Sons, Ltd.