On the Effective Moduli of Anisotropic Composites with Aligned Ellipsoidal Inclusions

Abstract

The effective elastic and shear moduli of a 3-D composite containing aligned ellipsoidal inclusions are evaluated in this paper. The material considered is transversely isotropic due to the uniform dispersion of inclusions in plane sections normal to their major axis. The method followed for the solution of the problem is based upon Eshelby's theory. We evaluate the strain field around a single ellipsoidal inhomogeneity surrounded by the effective anisotropic medium. Considering the mutual interaction of the neighbouring inclusions inside the matrix, we may evaluate the effective stiffness of composites with inclusions at dilute concentrations by using Mori-Tanaka's concept. The parameters involved in the analysis are the aspect ratio of the inclusions, their volume fraction and the ratio of the elastic moduli of the constituent phases forming the composite. The results show that the anisotropy of the composite is rather affected by the hardness of the inclusions relatively to the matrix than by the aspect ratio of inclusions. On the other hand, the stiffness of the composite is rather greater in models with inclusions of a needleshape form than in composites with spheroidal inclusions.