Thermoelastic analysis of infinite space containing ellipsoidal inhomogeneities

This article conducts a thermoelastic analysis of an infinite space embedded with multiple ellipsoidal inhomogeneities, which exhibit different thermal conductivity, stiffness, and thermal expansion ratios. Using the dual equivalent inclusion method (DEIM), the inhomogeneities are replaced by a matrix containing two continuously distributed eigen-fields: eigen-temperature-gradient (ETG) and eigenstrain. Unlike conventional numerical methods that rely on the volume integrals of temperature, the thermo-mechanical fields are expressed by volume integrals of eigen-fields and three Green’s functions over the inhomogeneity domains only, which exhibit significant improvement in computational efficiency. Through the DEIM, this article proves that the uniform ETG and linear eigenstrain, and linear ETG and quadratic eigenstrain are the exact solutions when an ellipsoidal inhomogeneity is subjected to a uniform far-field temperature gradient and a uniform volumetric heat source, respectively. The accuracy of the DEIM is verified via the finite element method through comparisons of thermoelastic fields.