中文摘要：

扩展有限元（extended finite element method，XFEM）是近年来发展起来的、在常规有限元框架内求解不连续问题的有效数值计算方法，其基于单位分解的思想，在常规有限元位移模式中加入能够反映裂纹面不连续性的跳跃函数及裂尖渐进位移场函数，避免了采用常规有限元计算断裂问题时需要对裂纹尖端重新加密网格造成的不便。在推导扩展有限元算法的基础上，分析了应力强度因子的，积分计算方法及积分区域的选取。采用XFEM对I型裂纹进行了计算，有限元网格独立于裂纹面，无需在裂纹尖端加密网格；分析了积分区域、网格密度对应力强度因子计算精度的影响，指出了计算应力强度因子的合适参数，验证了此方法的可靠性和准确性。

英文摘要：

The extended finite element method （XFEM） is a numerical method for modeling discontinuities within the classical finite element framework developed in recent years. In XFEM, jump functions and asymptotic crack-tip fields were added to enrich the finite element displacement using the framework of partition of unity to model the discontinuities of cracks. A key advantage of XFEM is that in fracture problems the finite element mesh does not need to be updated and remeshed. Based on the algorithm of XFEM, the J integral methods which calculate the stress intensity factor（SIF） are introduced. A numerical case with model I fracture is analyzed by XFEM. The results illustrate that the FEM mesh is independent of the crack interface. The major factors which influence the accuracy of SIF are discussed, such as integral domain and mesh density. Proper parameters to calculate the SIF are given; and the feasibility and accuracy of XFEM are validated.