Effective Elastic Characteristics of a Piecewise-Homogeneous Isotropic Body with a System of Rectilinear Thin Inclusions under Conditions of Longitudinal Shear

We study the problem of determination of effective elastic characteristics of a piecewise-homogeneous isotropic body containing a twice-periodic system of tunnel thin rectilinear inclusions. The body is subjected to antiplane strain, and the conditions of ideal mechanical contact between the matrix and inclusions are satisfied. We reduce the solution of the problem to a system of integro-differential equations which enable us to find the expressions for the effective elastic characteristics of the composite. We also present the results of numerical analysis of these characteristics for a rectangular grid of periods and for various geometric and mechanical parameters of the problem.