Micromechanical Analysis of Macroscopic Elastic Moduli and Coefficients of Thermal Expansion for a Composite Material Containing Ellipsoidal Reinforcements

Abstract

Micromechanical analysis of a composite material containing many ellipsoidal reinforcements is performed by using the equivalent inclusion method combined with the Mori-Tanaka theorem. Eshelby tensor for the reinforcement is rearranged as a function of Poisson's ratio of the matrix multiplied by the geometrical factor and is used in the analysis. The geometrical factor is only a function of the aspect ratios of reinforcement and is named by the authors. Since all reinforcements are assumed to align along the same direction in the modeling, the composite material has three perpendicular two-fold rotational symmetries. Therefore, nine components of the macroscopic elastic constant of the composite are derived as a function of the geometrical factor of reinforcement. Moreover, macroscopic coefficients of thermal expansion for the composite are also expressed successfully.