Fiber-constrained, dielectric-elastomer composites: Finite-strain response and stability analysis

This paper presents homogenization estimates for the finite-strain effective response of a certain class of dielectric elastomer composites (DECs) subjected to electromechanical loading conditions. The DECs consist of a dielectric elastomer matrix phase constrained to undergo plane strain deformations by means of aligned, long, rigid-dielectric fibers of elliptical cross section that are also aligned but randomly distributed in the transverse plane. The estimates for the effective electro-active response are obtained by means of available estimates for the purely mechanical response of such composites, together with a partial decoupling strategy/approximation. Such homogenization estimates can then be used to assess the effect of various microstructural parameters, such as the concentration and cross-sectional shape of the fibers, on the overall electromechanical response of the DECs, when subjected to an electric potential difference across suitably positioned soft electrodes. In addition, three different instability and failure mechanisms are investigated: loss of positive definiteness, loss of strong ellipticity and dielectric breakdown, with the objective of finding an optimal design of the microstructure and constituent properties for maximal electrostriction before failure.