Modeling crack in orthotropic media using a coupled finite element and partition of unity methods

The problem of crack modeling in 2D orthotropic media is considered. The extended finite element method has been adopted for modeling and analyzing a crack and its domain numerically. In this method, first the finite element model without any discontinuities is created and then the two-dimensional asymptotic crack–tip displacement fields with a discontinuous function are added to enrich the finite element approximation using the framework of partition of unity. The main advantage is the ability of the method in taking into consideration a crack without any explicit meshing of the crack surfaces, and the growth of crack can readily be applied without any remeshing. Mixed-mode stress intensity factors (SIFs) are evaluated to determine the fracture properties of domain. The results of proposed method are compared with other available numerical or (semi-) analytical methods. The SIFs are obtained by means of the interaction integral (M-integral).