A Discontinuity-Enriched Finite Element Method (DE-FEM) for modeling quasi-static fracture growth in brittle solids

Enriched finite element methods (e-FEMs) have become a popular choice for modeling problems containing material discontinuities (e.g., multi-phase materials and fracture). The main advantage as compared to the standard finite element method (FEM) remains the versatility in the choice of discretizations, since e-FEMs resolve discontinuities by completely decoupling them from the finite element mesh. However, modeling complex kinematics such as branching and merging of discrete cracks remains challenging. This article extends previous research on the Discontinuity-Enriched Finite Element Method (DE-FEM) for simulating quasi-static crack propagation in brittle materials. In DE-FEM enrichments are added to nodes created directly along discontinuities. Most notably, we demonstrate DE-FEM can resolve complex kinematics, namely the modeling of multiple cracks propagating and merging—and with a straightforward computer implementation. We validate the formulation with experimental results carried out on a compact tension specimen. Other numerical examples show the capability of DE-FEM in capturing crack paths similar to those observed in the literature.