A novel crack-tip singular element for extended finite element analysis

The traditional extended finite element method (XFEM) is suitable for simulating crack growth, but the crack-tip stress field analysis still depends on the enriched function. In this paper, based on the numerical eigensolution of the singular displacement and stress field together with the Hellinger-Reissner (H-R) variational principle, a novel crack-tip singular element is established to replace the enriched element in the crack-tip region in the traditional XFEM. The stress field inside the element adopts a series expression instead of only including the leading-order terms. The element only requires Gaussian integration at the element boundary and avoids mesh refinement in the crack-tip region. The element can be used to analyze cracks in anisotropic materials, interface cracks, and cracks terminating at the bimaterial interface. The numerical solutions of the singular stress field in various crack forms are presented through numerical examples, which proves the effectiveness and versatility of the novel crack-tip singular element.