A hybrid micro-macro BEM with micro-scale inclusion-crack interactions

Local analysis schemes capable of detailed representations of micro-features of a problem are integrated with a macro-scale BEM technique capable of handling finite geometries and realistic boundary conditions. This paper focuses on micro-scale interactions among cracks and inclusions as well as their ramifications on macro-scale damage evaluations. The micro-scale effects are introduced into the macro-scale BEM computations through an augmented fundamental solution obtained from an integral equation representation of the micro-scale features. The proposed hybrid micro-macro BEM formulation allows complete decomposition of the real problem into two sub-problems, one residing entirely at the micro-level while the other resides at the macro-level. This allows for investigations of the micro-structural attributes while retaining the macro-scale geometric features and actual boundary conditions for the structural component under consideration. As a first attempt, dilute inclusion densities with strong inclusion-crack and crack-crack interactions 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 be easily extended to investigate the effects of other micro-features (e.g., interfaces, short or continuous fibers, in the context of linear elasticity) on macro-scale failure modes observed in structural components.