A Solid Shell Finite Element Formulation for Dielectric Elastomers

This paper is concerned with a solid shell finite element formulation to simulate the behavior of thin dielectric elastomer structures. Dielectric elastomers belong to the group of electroactive polymers. Due to efficient electromechanical coupling and the huge actuation strain, they are very interesting for actuator applications. The coupling effect in the material is mainly caused by polarization. In the present work, a simple constitutive relation, which is based on an elastic model involving one additional material constant to describe the polarization state, is incorporated in a solid shell formulation. It is based on a mixed variational principle of Hu-Washizu type. Thus, for quasi-stationary fields, the balance of linear momentum and Gauss' law are fulfilled in a weak sense. As independent fields, the displacements, electric potential, strains, electric field, mechanical stresses, and dielectric displacements are employed. The element has eight nodes with four nodal degrees of freedom, three mechanical displacements, and the electric potential. The surface oriented shell element models the bottom and the top surfaces of a thin structure. This allows for a simple modeling of layered structures by stacking the elements through the thickness. Some examples are presented to demonstrate the ability of the proposed formulation.