Finite deformations of thin plates made of dielectric elastomers: Modeling, numerics, and stability

In this article, we present a nonlinear theory for thin plates, which are made of incompressible electroded dielectric elastomer layers. The layers are assumed to exhibit a neo-Hookean elastic behavior, and the effect of the electrostatic forces is taken into account by means of the electrostatic stress tensor. A plane state of stress is imposed on the total stress tensor, based on which two-dimensional constitutive relations for the plate are derived. A geometrically nonlinear formulation for the plate as a material surface is devloped, and solutions are computed using nonlinear finite elements. The numerical results are compared to available results from the literature verifying our approach, and an additional nonsymmetric example problem is studied with respect to stability.