A numerical method for dynamic fracture using the extended finite element method with non-nodal enrichment parameters

A modified extended finite element method (XFEM) for dynamic fracture is presented with a new methodology to construct the XFEM basis for discontinuities. In this method, the enrichment bases are defined to capture the characteristic discontinuities across the interface. The enrichments are vanished outside the element domain so that no blending of the local partition unity is required. The enrichment parameters effectively represent the physics of the discontinuity and are assigned to non-nodal points, which helps to impose Dirichlet boundary conditions on the interface. This feature successfully dissociates the finite element nodes from the extended finite element approximation; it facilitates the treatment of arbitrary crack propagation in explicit methods. The approach is applied to linear three-node triangular elements for element-by-element crack propagation modeling. The proposed method combined with explicit time integration and a cohesive law can successfully predict the dynamic fracture of ductile and brittle materials. Dynamic simulation results in terms of crack path and speed were effectively computed and match the experimental results. Through these numerical examples, the robustness and performance of the method were successfully demonstrated.