The stability of the interface between two bodies compressed along interface cracks. 1. Exact solutions for the case of unequal roots

The buckling of the interface between two bodies is considered in the case where the interface contains several plane cracks and the bodies are compressed along them (along the interface of two different materials). The investigation is carried out for a plane problem using the three-dimensional linearized theory of stability of deformable bodies. Complex variables and potentials of the mentioned linearized theory are applied. This problem is reduced to the problem of linear conjugation of two analytical functions of complex variables. The exact solution is derived for the case of unequal roots of the basic equation. Some mechanical effects are analyzed for the general formulation of problems (elastic, elastoplastic, compressible, incompressible, isotropic, and orthotropic bodies).