Griffith's Formula and Cherepanov–Rice's Integral for a Plate with a Rigid Inclusion and a Crack

The model problem for a plate with rigid inclusion, describing a biharmonic equation, is considered. There is a crack between the inclusion and an elastic part of the plate. The derivative of the energy functional with respect to a small perturbation of the crack length is found. Moreover such derivative can be represented by an invariant integral. The derivative and the invariant integral are corresponding analogues of Griffith's formula and Cherepanov–Rice's integral in the brittle fracture theory.