A two-scale generalized finite element method for interaction and coalescence of multiple crack surfaces

Abstract This paper presents the application of a two-scale generalized finite element method ( GFEM ) which allows for static fracture analyses as well as fatigue crack propagation simulations involving the interaction of multiple crack surfaces on fixed, coarse finite element (FE) meshes. The approach is based on the use of numerically-generated enrichment functions computed on-the-fly through the use of locally-defined boundary value problems (BVPs) in the regions of existing mechanically-short cracks. The two-scale GFEM approach is verified against analytical reference solutions as well as alternative numerical approaches for crack interaction problems, including the coalescence of multiple crack surfaces. The numerical examples demonstrate the ability of the proposed approach to deliver accurate results even in scenarios involving multiple, interacting discontinuities contained within a single computational element. The proposed approach is also applied to a crack shielding/crack arrest problem involving two propagating crack surfaces in a representative panel model similar in complexity to that which may be of interest to the aerospace community.