Griffith formulae for elasticity systems with unilateral conditions in domains with cracks

In this paper we consider the elasticity equations in nonsmooth domains in Rn, n=2,3. The domains have a crack whose length may change. At the crack faces, inequality type boundary conditions describing a mutual nonpenetration of the crack faces are prescribed. The derivative of the energy functional with respect to the crack length is obtained. The Griffith formulae are derived in 2D and 3D cases and the other properties of the solutions are established. In two-dimensional case the Rice–Cherepanovʹs integral over a closed curve is constructed. The path independence of the Rice–Cherepanovʹs integral is shown.