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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. [ABSTRACT FROM AUTHOR]

We study the thermoelastic problem of an inclusion of general shape surrounded by a foreign elastic matrix under plane deformation and the influence of an in-plane far-field heat flux. The small-scale interface effects, related to not only interface conductivity, interface stretching rigidity and interface thermal expansion but also (residual) interface tension, are incorporated in the corresponding analysis. We establish general boundary value formulations in both heat conduction and thermoelasticity for an arbitrary inclusion shape, allowing for analytic or at least semi-analytic treatment of the problem. Specially, we derive closed-form solutions for the case of circular inclusion and obtain concise expressions for describing the remote heat flux-induced thermal stress near the interface (at both the inclusion side and matrix side). Surprisingly, it is shown that for the case of circular inclusion, interface tension plays the same role as interface stretching rigidity in determining the full thermal stress field, or in other words, the full thermal stress field depends on only the sum of interface tension and interface stretching rigidity but not on the specific value of either of them. Numerical examples are also given to illustrate the influence of interface tension on the von Mises stress distribution in the vicinity of the interface. [ABSTRACT FROM AUTHOR]