A three-scale generalized finite element method for the simulation of three-dimensional crack propagation

A three-scale Generalized Finite Element Method (GFEM 3 ) is proposed for the simulation of three-dimensional crack propagation in domains where the characteristic crack size is substantially smaller than the structural dimensions. The approach integrates the Generalized Finite Element Method (GFEM) with global-local enrichments (GFEM gl ) and classical submodeling. Within this framework, the GFEM gl decomposes the problem into two scales and provides boundary conditions for a set of submodels created along the crack front. These submodels are solved in parallel to recover high-fidelity displacement fields, enabling accurate computation of stress intensity factors (SIFs). The SIFs obtained along the crack front are assembled into a continuous profile that drives the crack propagation. Three numerical studies of increasing complexity demonstrate that the GFEM 3 achieves SIF accuracy comparable to single-scale GFEM, offers a reduction in computational cost relative to two-scale GFEM gl analyses, and enables the simulation of three-dimensional crack propagation problems that are beyond the practical reach of both single-scale GFEM and two-scale GFEM gl . Overall, the method provides a robust and scalable framework for multiscale modeling of three-dimensional fracture where crack features are small compared to the overall structure.