Some simple explicit results for the elastic dielectric properties and stability of layered composites

Abstract

A string of partial results—aimed at shedding light on the behavior of dielectric elastomer composites—have been recently reported in the literature for the macroscopic electroelastic response and stability of layered composites with ideal elastic dielectric phases. Such results have been restricted to two phases and plane-strain loading conditions. It is the purpose of this paper to place on record simple explicit expressions for the macroscopic electroelastic response and stability of layered composites with any number of ideal elastic dielectric phases under general electromechanical loading conditions. Inter alia, these expressions provide insight into a variety of practical and theoretical issues in relation to the modeling of elastic dielectric composites with anisotropic microstructures, ranging from the choice of invariants to describe their free energy function to the effects of interphasial phenomena.This paper also places on record the conditions of ordinary and strong ellipticity for elastic dielectrics in full generality.