Numerical analysis of the inclusion-crack interaction by the extended finite element method

One of the partition of unity methods, the extended finite element method (XFEM), is applied to study the inclusion-crack interactions in an elastic medium. Both the inclusions and the crack are modelled within the XFEM framework. A structured quadrilateral mesh is used and the influence of crack length, the number of inclusions, and the geometry of the inclusions on the crack tip stress field are numerically studied. The interaction integral for non-homogeneous materials is used to compute the stress intensity factors ahead of the crack tip. The accuracy and flexibility of the XFEM is demonstrated by various numerical examples