A k-elliptical local enrichment strategy with weighted-superposition shape functions for efficient modeling of interacting multiple crack tips

Abstract

The simulation of interacting multiple cracks in elastic solids remains a challenging problem in computational fracture mechanics, especially when crack tips are closely spaced. Continuum-based numerical methods often rely on global superposition or enrichment strategies that become computationally expensive for complex multi-crack configurations. This paper proposes a novel local enrichment approach that efficiently captures the overlapping crack-tip fields through weighted-superposition shape functions confined to k-elliptical domains around interacting tips. The method constructs the approximation by separately enriching for each tip within its local elliptical region and then applying a weighted superposition, thereby avoiding the cost of global nodal processing. The formulation is implemented within an element-free Galerkin framework and validated on several benchmark problems in isotropic and orthotropic media. Results show that the proposed technique accurately evaluates stress intensity factors for the investigated interacting-crack problems while exhibiting potential computational advantages compared with existing global superposition schemes. The strategy is general and can be readily integrated into other continuum-based discretization frameworks such as FEM, XFEM and IGA.