Arc Crack in a Homogeneous Electrostrictive Material

Abstract

We consider the problem of determination of the stress-strain state of an elastic electrostrictive plane containing an arc crack and subjected to the action of electric and mechanical forces applied at infinity, which may be arbitrarily oriented relative to the crack axis. This problem is reduced to the problem of linear conjugation for a piecewise analytic function of complex variable. We obtain its exact analytic solution and deduce analytic expressions for the stresses at any point of the medium, crack opening displacements, and the stress intensity factors at the crack tips.