Efficient large-deformation shell elements for the simulation of electromechanical coupling effects in incompressible dielectric elastomers

So-called electro-active polymers are not only capable of undergoing very large deformations, but they also exhibit different electromechanical coupling effects due to their dielectric or electrostrictive characteristics. In the present paper the sub-class of dielectric elastomers is studied; in particular, we focus on thin dielectric elastomer shells, which undergo large deformations under an applied electric field. We develop a framework for the modeling and subsequent efficient simulation of thin structures made from incompressible dielectric elastomers. A thermodynamically consistent phenomenological continuum model based on the free energy density is adapted imposing the kinematic assumptions of Kirchhoff-Love shells in combination with including the thickness deformation and the electric field as independent unknown fields. To make the formulation accessible to finite element simulations, existing non-linear elastic shell mixed finite elements are extended to the present hyperelastic electromechanically coupled formulation for dielectric elastomer shells. Computational results of the shell theory are compared to three-dimensional results validating the proposed modeling and numerical simulation methodology, and showing high accuracy already for coarse finite element discretizations of the shell.