Modeling quasi-static crack growth with the extended finite element method Part II: Numerical applications

In Part I [Int. J. Solids Struct., 2003], we described the implementation of the extended finite element method (X-FEM) within Dynaflow™, a standard finite element package. In our implementation, we focused on two-dimensional crack modeling in linear elasticity. For crack modeling in the X-FEM, a discontinuous function and the near-tip asymptotic functions are added to the finite element approximation using the framework of partition of unity. This permits the crack to be represented without explicitly meshing the crack surfaces and crack propagation simulations can be carried out without the need for any remeshing. In this paper, we present numerical solutions for the stress intensity factor for crack problems, and also conduct crack growth simulations with the X-FEM. Numerical examples are presented with a two-fold objective: first to show the efficacy of the X-FEM implementation in Dynaflow™; and second to demonstrate the accuracy and versatility of the method to solve challenging problems in computational failure mechanics.