The stability of the interface between two bodies compressed along interface cracks. 3. Exact solutions for the combined case of equal and unequals roots

The problem of the stability 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 them (along the interface of two different materials). The study is carried out for a plane problem by using the three-dimensional linearized theory of stability of deformable bodies. 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 complex variable. The exact solution of the above-mentioned problem is derived for the case where the basic equation has unequal roots for the first material and equal roots for the second material. In earlier authors' publications, the exact solutions were obtained for the cases where both materials have either equal or unequal roots. Some mechanical effects are analyzed for the general formulation of the problem (elastic, elastoplastic compressible and incompressible isotropic and orthotropic bodies). It is pointed out that, in accordance with the exact solutions, the main result and conclusions have a general form for the above-mentioned cases of roots.