Cracked coating problem in nanomaterials and seismology

A method for studying the stress-strain state of block structures typical of materials with coating, including nanomaterials, is presented under the assumption that the coating consists of two-dimensional horizontally arranged different-type blocks contacting with each other along their boundaries. The coating is located on the surface of a three-dimensional linearly deformable substrate. The block structures in question are subjected to an external action (in particular, vertically harmonic). This is also typical of lithospheric plate structures, whose stress-strain state can be studied to obtain information about the seismicity of territories. In the present paper, the topological approach in [1] is refined and used to derive new integral equations, which permit studying the stress-strain state of such block structures.