Abstract：An adaptive mesh refinement method based on the quadtree structure is proposed to model the fracture problem of heterogeneous material. By introducing the shape functions of the virtual node polygonal elements into the approximation of standard extended finite element method (XFEM), a regulatable multi-level refined mesh in the vicinity of the discontinuities can be created. Especially for the cracks, the dynamic mesh refinement and coarsening near the crack tips can be realized by the proposed method. According to above schemes, a novel crack growth computational method is thus formulated as VP-XFEM in the framework of linear elastic fracture mechanics. To verify the computational accuracy and efficiency of VP-XFEM, two fracture problems of structures containing cracks and holes are simulated using this method. The results show that the VP-XFEM can achieve better accuracy and efficiency compared with the standard XFEM.
2019, Vol. 40 
