Nonlinear Modelling Of Dielectric Elastomer Single Layer Plates Using A Multiplicative Decomposition Of The Deformation Gradient To Account For Electrostriction

Abstract

In this paper we study dielectric elastomers accounting for constitutive cou- pling by means of electrostriction using a multiplicative decomposition of the deformation gradient tensor. The resulting constitutive relations are reduced to the special case of thin single layer plates made of incompressible dielectric elastomers. As an example problem we study the electro-mechanically coupled behavior of such a single layer plate in the ab- sence of mechanical forces with special emphasis on the effect of electrostriction on the breakdown instability.