Simulation of partial closure of a crack-like cavity with cohesion between the faces in an isotropic medium

A mathematical model for the closure of a crack-like cavity with cohesive end zones in an isotropic medium is constructed using methods of elastic theory. It is assumed that the interaction between the surfaces of the crack-like cavity under the action of body and surface forces can lead to the formation of contact zones on their surfaces. Determination of the unknown parameters characterizing the closure of the crack-like cavity reduces to a system of singular integrodifferential equations. The integral equations are converted to a system of nonlinear algebraic equations which is solved by the method of successive approximations. The contact stresses, the interaction forces between the faces of the crack-like cavity, and the size of the contact zone in which the faces of the crack-like cavities are closed are determined.