A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries

摘要

An interface-enriched generalized finite element method (GFEM) is introduced for 3D problems with discontinuous gradient fields. The proposed method differs from conventional GFEM by assigning the generalized degrees of freedom to the interface nodes, i.e., nodes generated along the interface when creating integration subdomains, instead of the nodes of the original mesh. A linear combination of the Lagrangian shape functions in these integration subelements are then used as the enrichment functions to capture the discontinuity in the gradient field. This approach provides a great flexibility for evaluating the enrichment functions, including for cases where elements are intersected with multiple interfaces. We show that the method achieves optimal rate of convergence with meshes which do not conform to the phase interfaces at a computational cost similar to or lower than that of conventional GFEM. The potential of the method is demonstrated by solving several heat transfer problems with discontinuous gradient field encountered in paniculate and fiber-reinforced composites and in actively-cooled micro-vascular materials.