Numerical modeling of interactions between a macro-crack and a cluster of micro-defects

The interactions between a macro-crack and a cluster of micro-defects are studied numerically by using a series of special finite elements each containing a defect. These special finite elements, which contain defects such as holes, cracks, and inhomogeneities, are developed based on the hybrid displacement, complex potential and conformal mapping techniques. These hybrid-type elements can be used together with the conventional finite elements without any difficulty. Thus, simple finite element models can be devised to study the interactions between a macro-crack and a cluster of micro-defects. In this paper, the mathematical and finite element modeling procedures for the study of the above-mentioned problems are presented.