Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method

Abstract

This paper presents a new extended isogeometric boundary element method (XIGABEM) for the analysis of cracks in two-dimensional bimaterial interfaces. The classical NURBS approximations used in isogeometric formulations are augmented with functions based on the first two terms of the crack-tip stress and displacement series expansions. The first term is related to the complex stress intensity factor (SIF) and allows the numerical method to capture the singular and oscillatory near-tip behaviour, while the second accounts for the T-stress contribution to the solutions. The proposed enrichment strategy only introduces three additional degrees of freedom per crack tip, which are accommodated in a square linear system by a crack tip tying constraint and a novel condition on the stress parallel to the tip. These supplementary relations also cause the enrichment parameters to become proxies for the SIFs and T-stress. Therefore, the crack-tip factors can be obtained directly from the solution vector given by XIGABEM, eliminating the need for costly computational post-processing techniques. Several benchmark examples, including both straight and curved cracks, are presented to demonstrate the accuracy and convergence of the proposed method. The direct XIGABEM solutions for the SIFs and T-stress compare favourably against those from the literature.