A Complete Direct Approach to Modeling of Dielectric Elastomer Plates as Material Surfaces

Abstract

In this paper we present a complete direct approach to modeling nonlinear plates, which are made of incompressible dielectric elastomer layers. In particular, the layers are assumed to exhibit a neo-Hookean elastic behavior and the effect of electrostatic forces is incorporated by a purely electrical contribution to the Helmholtz free energy. In our previous work on this subject, two-dimensional constitutive relations for the plate were derived by numerical integration of the three-dimensional augmented free energy through the plate thickness imposing a plane stress assumption and an a-priori assumption concerning the distribution of the strain through the thickness of the plate. In contrast, we directly postulate the form of the two-dimensional augmented free energy for the structural plate problem in this paper. Results computed within the framework of this novel approach are compared to results from our previous work, which are well tested against existing solutions in the literature. A very good agreement is found.