XFEM modeling for curved fracture in the anisotropic fracture toughness medium

The materials with anisotropic fracture toughness are familiar in nature, e.g., anisotropic rocks, woods, and crystals. The deflecting crack propagation behaviors are often observed in these materials due to the anisotropic fracture toughness property. In this paper, the extended finite element method (XFEM) is developed for modeling the crack extending behavior in anisotropic fracture toughness medium. First, anisotropic fracture toughness profiles are introduced and embedded into XFEM, and the crack deflecting direction is predicted based on maximum energy release rate criterion. To capture the details of the twisting crack path as accurate as possible in XFEM, a mesh independent piecewise linear crack model is developed numerically. Then several numerical examples in studying the curved crack path in a material with the anisotropic fracture toughness property are given. With the techniques of XFEM embedded with anisotropic fracture toughness, the crack path in such anisotropic materials could be predicted and designed.