Thermoelastic plane problem for material with circular inclusions

Abstract

We consider two-dimensional thermoelastic composite materials in the case when the temperature is constant. Using complex potentials and applying a method of functional equations, we construct a simple algorithm to solve the corresponding boundary value problem. The stress tensor is written with the accuracy of up to the term O(R²), where R = max_k,m r_k d_km^-1, r_k is the radius of the k-th inclusion, d_km is the distance between centers of the k-th and m-th inclusion (k ≠ m). The effective elastic constants and the coefficient of thermal expansion are written in analytic form up to O(R⁴).