AN ALTERNATING METHOD BASED ON THE VNA SOLUTION FOR ANALYSIS OF DAMAGED SOLID CONTAINING ARBITRARILY DISTRIBUTED ELLIPTIC MICROCRACKS

This paper presents the development of an alternating method for the i nteraction analysis of arbitrary distributed numerous elliptical micro cracks. The complete analytical solutions (VNA solutions) for a single elliptical crack in an infinite solid, subject to arbitrary crack-fac e tractions, are implemented in the present alternating method, togeth er with the coordinate transformations for stress tensors. First, the present method is verified by solving the problems of two interacting cracks for which accurate numerical solutions have been obtained previ ously. Next, the present method demonstrates obtaining efficient and a ccurate solutions for the problems of many interacting elliptical crac ks, which cannot be solved in a practical sense by the ordinary numeri cal methods such as the finite element method. Furthermore, damaged so lids containing periodically distributed elliptical microcracks are an alyzed by the present alternating method. The effective elastic moduli are evaluated for varying microcrack density. Detailed structures of the interactions in the damaged solids are visualized and clarified.