The stability of the interface between two bodies compressed along interface cracks. 2. Exact solutions for the case of equal roots

The problem of buckling of the interface between two bodies is considered for the case where several plane cracks are located in the interface and the bodies are compressed along the cracks (along the interface of two different materials). The studies were carried out for a plane problem using the three-dimensional linearized theory of stability of deformable bodies. The complex variables and potentials of the above-mentioned linearized theory are used. This problem is reduced to the problem of linear conjugation of two analytical functions of a complex variable. The exact solution of the above-mentioned buckling problem is obtained for the case where the roots of the basic equation are equal. Some mechanical effects are analyzed under general conditions (elastic, elastoplastic, compressible, incompressible, isotropic, and orthotropic bodies).