Discontinuities such as voids, cracks, material interfaces, and joints widely exist in nature. Conventional finite element method (FEM) requires the finite element mesh to coincide with the discontinuities, which often complicates the meshing task. When evolution of discontinuities are necessary, remeshing is inevitable, which makes the simulation tedious and time-consuming. In order to overcome such inconveniences, the extended finite element method (XFEM) and the generalized finite element method (GFEM) were developed by incorporating special functions into the standard finite element approximation space based on partition of unity. The finite element mesh is allowed to be totally independent of the discontinuities and remeshing is totally avoided for discontinuity evolution. The numerical manifold method (NMM) can also be viewed as an extension or generalization to the conventional FEM. Different from the XFEM/GFEM, the approximation in the NMM is based on covers. The NMM models discontinuities by its dual cover system. In this paper, a detailed comparison between the NMM and the XFEM in discontinuity modeling is presented. Their advantages and disadvantages are pointed out. How the dual cover system in the NMM favors the complex crack modeling is emphasized. Potential extensions to the XFEM and the NMM are suggested.
- Extended finite element method (XFEM)
- generalized finite element method (GFEM)
- numerical manifold method (NMM)