Stability of two bodies interface under compression along the cracks distributed on the interface. 3. Exact solutions for a combined case of unequal and equal roots

The stability loss problem for the interface of two bodies is considered in case when some plane cracks are located in the interface and bodies are compressed along the crack (along the interface of two various materials). The investigations have been performed for the problems using the three-dimensional linearized theory of deformable bodies stability. Complex variables and potentials of above mentioned linearized theory are applied. This problem is reduced to the problem of linear conjugation of two analytical functions of complex variable. Exact solution of the above mentioned stability loss problem was obtained for the case when the first material had unequal roots and second material had equal roots of main equation on determination of complex roots (parameters) as applied to the plane problem of three-dimensional linearized theory of deformable stability. In earlier published author's articles the exact solutions have been obtained for the cases when the first material and the second one have unequal roots or when the first material has equal roots and the second one has equal roots. Some mechanical effect have been analyzed under general conditions (elastic, elasto-plastic compressible and incompressible isotropic and orthotropic bodies). It was pointed out that in accordance with the exact solutions the main result and conclusions have general view for the above mentioned various cases of roots.