Invariant Integrals in the Problem of a Crack on the Interface between Two Media

The equilibrium problem for an elastic body containing a crack on the interface between two media is considered. It is proved that there exist invariant (independent of the integration surface) integrals in this problem. The existence of invariant integrals is also established in the problem of a contact between an elastic body and a rigid stamp. Nonlinear boundary conditions of mutual non-penetration are prescribed on the contact boundaries. The physical meaning of invariant integrals is established.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 123–137, September–October, 2005.