As a paradigm for non-interpenetrating crack models, the Poisson equation in a nonsmooth
domain in R2 is considered. The geometrical domain has a cut (a crack) of variable length.
At the crack faces, inequality type boundary conditions are prescribed. The behaviour of
the energy functional is analysed with respect to the crack length changes. In particular, the
derivative of the energy functional with respect to the crack length is obtained. The associated
Griffith formula is derived, and properties of the solution are investigated. It is shown that
the Rice–Cherepanov integral defined for the solutions of the unilateral problem defined in
the nonsmooth domain is path-independent. Finally, a non-negative measure characterising
interaction forces between the crack faces is constructed.