A hybrid micro–macro BEM formulation for micro‐crack clusters in elastic components

Local analysis schemes capable of detailed representations of the micro‐features of a problem are integrated with a macro‐scale BEM technique capable of handling complex finite geometries and realistic boundary conditions. The micro‐scale effects are introduced into the macro‐scale BEM analysis through an augmented fundamental solution obtained from an integral equation representation of the micro‐scale features. The proposed hybrid micro‐macro BEM formulation allows decomposition of the complete problem into two sub‐problems, one residing entirely at the micro‐level and the other at the macro‐level. This allows for investigations of the effects of the micro‐structural attributes while retaining the macro‐scale geometric features and actual boundary conditions for the component or structure under consideration. As a first attempt, elastic fracture mechanics problems with interacting cracks at close spacings are considered. The numerical results obtained from the hybrid BEM analysis establish the accuracy and effectiveness of the proposed micro–macro computational scheme for this class of problems. The proposed micro–macro BEM formulation can easily be extended to investigate the effects of other micro‐features (e.g. interfaces, short or continuous fibre reinforcements, voids and inclusions, in the context of linear elasticity) on macroscopic failure modes observed in structural components.