Interphase Model for Effective Moduli of Nanoparticle-Reinforced Composites

Abstract

A novel interphase model is constructed based on the double-inclusion theory and the Eshelby tensor in a finite domain, which can be used to calculate the effective material properties of three-phase composites. The refinement of the double-inclusion theory takes into account the effect of a finite matrix and that of a finite interphase. In the model proposed, the multiphase composites are reinforced by different material fillers, which are embedded in a matrix with finite size. The general formulations are derived following the method of Eshelby’s equivalent inclusion. The Dirichlet and Neumann Eshelby tensors for a spherical inclusion in a finite spherical domain are applied to the homogenization of composite materials. By the explicit inversions of the fourth-order tensors involved, the relationships between the elastic moduli of transversely isotropic and orthotropic materials are derived, which are then validated through numerical results from the homogenization of several