基于XFEM与自适应网格的非均质材料裂纹扩展模拟

针对含有间断的非均匀材料的断裂问题，本文将虚节点多边形单元的形函数引入到扩展有限元（XFEM）中，提出了一种基于四叉树结构的动态网格细化方法，该方法可对间断面附近单元实现可调控的多层级细化，特别是对于裂纹扩展问题，可实现裂尖附近单元的动态网格细化与粗化。基于以上网格细化方法，本文提出了针对非均匀材质裂纹扩展问题的计算方法VP-XFEM。为验证算法的准确性与计算效率，针对含有孔洞及材料界面的断裂问题，本文给出了相应的算例。结果显示，与传统的一致性网格的XFEM相比，VP-XFEM能够明显改善计算精度与计算效率。

Crack growth simulation in heterogeneous material using the adaptively refined XFEM

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.