Longitudinal Shear of Bimaterials with Interphase Thin Physically Nonlinear Layered Functional-Gradient Inhomogeneities

An analytical–numerical method for solving the class of problems of determining mechanical fields in composite structures with interfacial ribbon-like deformable multilayer physically nonlinear inhomogeneities under combined force and dislocation loading is proposed. The mathematical model of thin inclusion of material with arbitrary mechanical properties is constructed. The possibility of the existence of an imperfect contact along the part of the interface between the inclusion and the matrix, as well as between the layers of the inclusion, where there is surface energy or sliding with dry friction, is provided. Based on the method of jump functions, the stress–strain field in the vicinity of the inclusion at its interaction with concentrated forces and helical dislocations is calculated. The values of the generalized stress intensity coefficients for the asymptotic of the stress–strain fields in the vicinity of the ends of thin inhomogeneities are calculated, which can be used to calculate the stress concentration and local strength of the structure. Several new effects that can be used in the design of the structure of layers and modes of operation of such composites are revealed.