Improved implementation of the extended finite element method for stress analysis around cracks

Although the extended finite element method (XFEM) allows for modelling arbitrary discontinuities, its low order elements often means that frequent improvements on accuracy are required. The generalized finite element method (GFEM), the extension of the conventional FEM, improves the approximation accuracy of the FEM by introducing generalized degrees of freedom and re-interpolating nodal degrees of freedom. This paper enhances the implementation of the XFEM for stress analysis around cracks by coupling the GFEM and XFEM. The generalized node shape functions are used in a cluster of nodes around the cracks, and the conventional finite element shape functions are adopted at nodes outside the cracks, thereby reducing costs and improving the accuracy of stresses in the vicinity of the cracks. Several numerical examples show that the proposed approach generates higher accuracy for stress intensity factor computations at affordable costs.