The Griffith formula and Cherepanov–Rice integral for a plate with a rigid inclusion and a crack

Abstract

We consider the model problem for a plate described by a biharmonic equation. The plate contains a rigid inclusion separated from the elastic part by a crack. We show that the target energy functional is differentiable with respect to a small perturbation of the crack length and the derivative can be represented as an invariant integral — a contour integral along a contour surrounding a crack vertex. The formula for the derivative and the invariant integral are analogues of the Griffith formula and Cherepanov–Rice integral known in the brittle fracture theory. Bibliography: 34 titles.