Thermal Expansions of Heterogeneous Solids Containing Aligned Ellipsoidal Inclusions

A theoretical study has been made to predict overall thermal expansion characteristics of a two-phase material consisting of a matrix and aligned ellipsoidal inclusions. The calculation is based on Eshelby's theory on the transformation problem; an approximate method is Introduced to account for the effect of finite concentrations of the inclusions. The following two cases are treated: elastic matrix-elastic inclusions and elastoplastic matrix- elastic inclusions. The results are explicitly obtained when shapes of the inclusions are spherical, disc-shaped, and fiber-shaped. The calculated over all thermal expansion coefficient for the case of elastic matrix-elastic spheres agrees with Kerner's prediction.