On modeling generally periodic crack arrays: Low-cost computational techniques. Edge effects. Application to evolving damage

A number of computational techniques have been developed for solving generalized periodic problems of interaction of multiple cracks. Although sufficiently accurate, these techniques are mostly time-consuming. This article presents an extension of the simple method of crack interaction analysis proposed by M. Kachanov to problems of multiple periodic collinear crack arrays under in-plane and anti-plane loading. Despite certain limitations (discussed in the article), this method enables a substantial reduction in computational complexity, especially for evolving cracks (e.g. stress corrosion damage). For evolutionary problems involving periodic or doubly periodic crack arrays, a periodization procedure is proposed that avoids the accumulation of the edge effect during time-step simulation and reduces computational costs. Focusing on crack propagation under mode I loading, the edge effects caused by the finiteness of periodic crack arrays are examined. In particular, it is shown that in a material weakened by several collinear crack arrays, this effect may lead to splitting along the outermost rows of cracks.