Elastic Properties of Composite Material with Randomly Distributed Anisotropic Ellipsoidal Inhomogeneities

—2nd Report: Basic Theory Based on Reuss Model and Its Numerical Examples—

Abstract

In this study, first, we obtain the elastic modului of the overall composite material based on the Eshelby/Mori-Tanaka model in the case where anisotropic ellipsoidal inhomogeneities with three-dimensional orientations are regularly distributed in an isotropic homogeneous matrix. Then, the elastic moduli of the overall a composite material are determined when anisotropic ellipsoidal inhomogeneities are distributed randomly based on Reuss model and an equivalent model using the concept of local regions in the previous paper. Furthermore, using the analytical equations obtained, concrete numerical examples under the assumption of a ceramic matrix composite material (SiO₂/Al₂O₃) are studied. As a result, we have succeeded in the theoretical determination of the elastic moduli of the overall composite material containing anisotropic ellipsoidal inhomogeneities of arbitrary volume fraction and shape.