On the Thermoelastic Field in a Composite Material with Inhomogeneities

Abstract

This paper concerns ellipsoidal inclusion problems in a three-dimensional composite material subjected to a far-field uniform heat flow. The eigenstrain formulation is developed to examine the thermoelastic field that results from two sources: one induced by the inclusion of thermal properties alone, and the other intensified by the inhomogeneity of elastic material constants. When the thermal conductivity and the thermal expansion coefficient of the inclusion are different from those of the surrounding matrix, the eigenstrain is utilized to simulate the thermal expansion strain and thermal expansion mismatch strain, respectively. It is shown that the eigenstrain is a homogeneous function of first degree, and the resulting thermoelastic field inside the ellipsoidal inclusion is therefore a homogeneous function of first degree. With these results in hand, the equivalent inclusion method is further employed to obtain the total thermoelastic field in the inhomogeneity which has elastic constants differing from those of the matrix.