Thermoelastic problem of two arbitrarily-shaped inclusions

In this paper, we study the plane thermoelastic problem of an infinite matrix containing two interacting inclusions of arbitrary shapes for a uniform heat flux applied on the matrix remotely. We propose a numerical scheme for calculating the temperature and stress fields in the inclusion-matrix system by using the principle of superposition and the Faber series method. A group of numerical examples is given to demonstrate the stress field around two soft inclusions (softer than the matrix) of triangular and square shapes. The results show that the interfacial thermal stress concentration may be relieved by improving the thermal conductivities of the soft inclusions. In particular, we find that for soft inclusions with higher thermal conductivities (higher than the matrix), the interfacial thermal stresses could even reduce slightly when the inclusions approach each other. Additionally, it is shown that the thermal load-induced interaction between the inclusions decays much slower than the mechanical load-induced interaction between the inclusions as the inclusions move away from each other.