Antiplane Deformation of a Perfectly Elastoplastic Body with Rigid Rectangular Inclusion

Abstract

We solve the problem of plastic exfoliation of a rigid rectangular inclusion in a perfectly elastoplastic medium loaded at infinity by shear forces parallel to the horizontal sides of the inclusion. It is assumed that plastic strains are concentrated on the boundary of the inclusion, in layers whose thickness is equal to zero starting from the vertices of the inclusion. We find the length of plastic strips and the degree of exfoliation (i.e., the jump of displacements) at the vertex of the inclusion as functions of the acting load. It is shown that the complete exfoliation of the horizontal sides of the inclusion occurs under a certain load (which increases with the width of the inclusion) but its vertical sides never exfoliate completely. We prove that the solution of the elastic problem represents the limiting case of the solution of the corresponding elastoplastic problem as the yield limit tends to infinity. By using this limit transition, we obtain the elastic solution of the analyzed problem.