Extended Finite Element Method

In the extended finite element method (XFEM), a standard displacement based finite element approximation is enriched by additional (special) functions using the framework of partition of unity. In the XFEM, the finite element mesh need not conform to the internal boundaries (cracks, material interfaces, voids, etc.), and hence a single mesh suffices for modeling as well as capturing the evolution of material interfaces and cracks. This book mainly focuses on the application of XFEM in modeling dynamic fracture in thin plates and shells. New crack tip enrichment functions are extracted from analytical solutions and several enrichment schemes are introduced for various elements. As an application, the problem of cracked thin tubes under gaseous detonation loading is simulated by the introduced Dynamic-XFEM formulation and the obtained response of the tube to moving detonation loading is compared with ANSYS-LS DYNA results.