Micromechanics of Nanocomposites with Interface Energy Effect

Abstract

In this paper, a fundamental framework of micromechanics for predicting the effective properties of a composite is generalized to include the interface energy effect. In this framework, both the interface constitutive relations for multi-phase hyperelastic solids at finite deformation and the Lagrangian and Eulerian descriptions of the generalized Young-Laplace equations are presented. Then, by taking into account the change of the “residual” elastic field due to the change of configuration, the difference of the governing equations across the interface is derived. A discussion of the infinitesimal deformation approximation of these governing equations is also given, and analytical expressions of the size-dependent effective moduli of a particle-filled nanocomposite are obtained. It is shown that the liquid-like interface tension influences the effective properties of the nanocomposite. Thus some misunderstandings of the interface energy effect in the existing literature are clarified.