Stress state of a half-plane with cracks under rigid punch action

Abstract

A contact problem in elasticity theory for an isotropic half-plane with a set of curvilinear cracks, into which a rigid punch with the foundation of convex shape is indented, is considered. Coulomb friction is assumed to exist between the punch and the half-plane, while the crack faces are under conditions of either stick or smooth contact on contact parts. On the basis of integral representation for Kolosov-Muskhelishvili complex potentials by derivatives of displacement discontinuities along the crack contours and pressure under the punch, the problem is reduced to a system of complex Cauchy type singular integral equations of first and second kind. An algorithm is proposed to find solution of these equations by the method of mechanical quadratures using an iterative procedure. Two numerical examples are presented.