The discontinuity-enriched finite element method for multiple intersecting discontinuities

We extend the Discontinuity-Enriched Finite Element Method (DE-FEM) to simulate intersecting discontinuities, such as those encountered in polycrystalline materials, multi-material wedge problems, and branched cracks. The proposed hierarchical enrichment functions capture weak and strong discontinuities at junctions within a single formulation. Several numerical applications to branched cracks and polycrystalline microstructures under both thermal and mechanical loads are presented to demonstrate the proposed method. Results indicate that DE-FEM can accurately capture complex discontinuous primal and gradient fields and attain convergence rates comparable to those of standard FEM using fitted meshes. The main advantages of DE-FEM equipped with the proposed junction enrichment functions lie in the method's ability to model intersecting discontinuities using meshes that are completely decoupled from them and its robustness in reproducing correct displacement and strain jumps across them, as demonstrated by a patch test. This work thus highlights the potential of DE-FEM for applications to problems characterized by the presence of multiple intersecting discontinuities, posing a valid alternative to traditional FEM and eXtended/Generalized Finite Element (X/GFEM) Methods.