A hybrid BEM formulation for multiple cracks in orthotropic elastic components

Local analysis schemes capable of detailed representations of micro-features (e.g. micro-crack interactions) of a problem are integrated with a macro-scale BEM technique capable of handling orthotropic elastic components with 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 proposed micro-macro BEM formulation can easily be extended to investigate the effects of other micro-features (e.g. interfaces, short or continuous fiber reinforcements, voids, and inclusions, in the context of linear elasticity) on macroscopic failure modes observed in structural components.