Abstract
In the present study, the problem of an infinitely extended elastic solid containing a doubly periodic rectangular array of cracks is considered. The analysis is made based on the method of pseudo-tractions, and a first-order approximate but explicit solution is obtained. The study reveals the fundamental difficulty of the problems of doubly periodic cracks which gives rise to the discrepancies between the results of the previous works. The stress intensity factors of mode I and mode II and the overall compliance are derived as functions of the crack density and geometry of the crack array. The overall compliance of solids with randomly distributed, unidirectional cracks is evaluated by the self-consistent method. The validity of the self-consistent method is discussed in terms of the results of the doubly periodic cracks.
