A linear complete extended finite element method for dynamic fracture simulation with non-nodal enrichments

A linear complete extended finite element method for arbitrary dynamic crack is presented. In this method, strong and weak discontinuities are assigned to a set of non-nodal points on the interface, whereby the discontinuous functions across the interface are reproduced by extended interpolation. The enrichments are described to reproduce both the constants and linear functions on sides of the interface, which are critical for finite element convergence. A key feature of this method is that the enrichment descriptions and the finite element mesh are optimally uncoupled; the element nodes are not enriched facilitating the treatment of crack modeling in object-oriented programs. The enrichment variables are physically-based quantities which lead to a strong imposition of both the Dirichlet boundary conditions and the interface conditions. The convergence of the method is validated through static simulations from linear elastic fracture mechanics. The efficacy of the method for modeling dynamic crack propagation is demonstrated through two benchmark problems.