Study of fracture problem with extended finite element method

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.