The Contact of a Cuspidal Crack

Abstract

A simplified airfoil mapping is used to define a cuspidal crack. The objective is to investigate the effects of compressive loads on an infinite solid containing crack-like flaws. Such an objective cannot be achieved by using the conventional line crack to characterize the flaws. The associated contact problem is solved exactly by assuming that the contact region is small in comparison to the crack length. It is shown that the well-known Barenblatt model is just the present contact problem in reverse. Moreover, a specific functional form is determined to describe the so-called cohesive force which was assumed to be a material function by Barenblatt.