Compression of a layered composite with sliding components along two parallel interface structural cracks

The problem of the linearized stability theory on compression of a piecewise-homogeneous body consisting of a nonlinearly elastic strip that slides frictionlessly between two nonlinearly elastic half-planes and weakened by two parallel cracks located on the rectilinear interface was studied. A proven analytical-numerical method is used, which consists in reducing the original boundary value problem using general representations of solutions of linearized equilibrium equations through potential harmonic functions to the Fredholm integral equation of the first kind. The specified solving integral equation of the problem was obtained in a general form for a wide class of combinations of two compressible or incompressible materials for which the case of equal roots of the characteristic equations is realized. The critical values of the load parameters corresponding to the start of the fracture of such a body were determined and the nature of their dependence on the physical-mechanical and geometrical parameters of the body was investigated.