A dynamic finite element method for inhomogeneous deformation and electromechanical instability of dielectric elastomer transducers

We present a three-dimensional nonlinear finite element formulation for dielectric elastomers. The mechanical and electrical governing equations are solved monolithically using an implicit time integrator, where the governing finite element equations are given for both static and dynamic cases. By accounting for inertial terms in conjunction with the Arruda–Boyce rubber hyperelastic constitutive model, we demonstrate the ability to capture the various modes of inhomogeneous deformation, including pull-in instability and wrinkling, that may result in dielectric elastomers that are subject to various forms of electrostatic loading. The formulation presented here forms the basis for needed computational tools that can elucidate the electromechanical behavior and properties of dielectric elastomers that are used for engineering applications.