Simple Technique of Stress Analysis in Elastic Solids with Many Cracks

摘要

It is well known that the problem of a linear elastic solid with many cracks can be reduced to a system of integral equations. Approximate methods of solution of this system constitute a possible approach to the crack interaction problems. A simplier method based on the superposition technique and the ideas of self-consistency applied to the average tractions on individual cracks is proposed here. It is applicable to arbitrary two- and three-dimensional arrays of cracks (penny-shaped, in the 3-D case) of arbitrary geometry. It is not restricted to remotely located cracks: the accuracy remains good when the distance between cracks is much smaller than the crack length. In the case of weak interactions the method is asymptotically exact. The method is demonstrated on test problems and then formulated for the general case.