Combined extended and superimposed finite element method for cracks

A combination of the extended finite element method (XFEM) and the mesh superposition method (s-version FEM) for modelling of stationary and growing cracks is presented. The near-tip field is modelled by superimposed quarter point elements on an overlaid mesh and the rest of the discontinuity is implicitly described by a step function on partition of unity. The two displacement fields are matched through a transition region. The method can robustly deal with stationary crack and crack growth. It simplifies the numerical integration of the weak form in the Galerkin method as compared to the s-version FEM. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed method.