Micromechanics of randomly oriented ellipsoidal inclusion composites. Part I: Stress, strain and thermal expansion

Abstract

A framework for micromechanics investigation of randomly oriented ellipsoidal inclusion composites has been proposed and established, based on the eigenstrain concept introduced by Eshelby, and the equivalent inclusion method. The average residual stress and strain and the average stress and strain, in both the matrix and the inclusions, have been derived relative to the mismatch of elastic moduli, thermal‐expansion coefficients, and the shape of the ellipsoid. The inclusion shape has a significant effect on the stress and strain field, with the smallest effect generated by a spherical inclusion. An expression for the relationship between the average stress and strain and the inclusion shape has been formulated. The multiphase inclusion composite model has also been established. As an example, the thermal‐expansion coefficient for randomly oriented ellipsoidal inclusion composites has been derived and related to the inclusion content, shape and elastic moduli. In Part II of this work, the elastic moduli of the inclusion composites are formulated and discussed.