THE EXTENDED FINITE ELEMENT METHOD AND ITS APPLICATIONS--A REVIEW

The extended finite element method (XFEM) originally proposed in 1999 is very powerful for discontinuous problems in mechanics, such as crack growth, complex fluid, interface, and so on. The major difference between the XFEM and the conventional finite element method (CFEM) is that the mesh in XFEM is independent of the internal geometry and physical interfaces, such that meshing and re-meshing difficulties in discontinuous problems can be overcome. Based on the partition of unity concept, the XFEM relaxes the prohibitive requirements for mesh density by improving the shape functions with the basic knowledge of discontinuous problems. The XFEM retains all advantages of the CFEM, such as the single-field variational principle. symmetric banded and sparse system matrices, the ease of application to non-linear problems, anisotropic materials and arbitrary geometries. This paper presents an overview and comments on the XFEM, and is organized as follows. The partition of unity method (PUM) and Level Set Method (LSM) are briefly introduced in sections 2 and 3, respectively. Basic theory, implementation procedures and formulations of the XFEM are described in detail in sections 4 and 5, together with correction to several inaccurated points in literature The future investigations on XFEM are finally recommended in section 6.