Electrostatic–viscoelastic finite element model of dielectric actuators

The aim of this work is to set up a numerical framework to characterise the deformation process and effective forces when voltage is applied to dielectric elastomer actuators. Based on an existing model for non-linear electro-elasticity that covers the static case only, inertia terms are included in order to obtain a description of the deformation process depending on time. A potential energy function that is composed of Neo-Hooke material behaviour, electric field energy and coupling terms covers the material properties. Combined with the kinetic energy, a Lagrange function forms the basis in a variational setting of the model. Viscoelastic effects are included using non-conservative forces and account for time dependent strains. The action is approximated using quadrature rules and discretising with finite elements in space. A discrete version of Hamilton’s principle leads to a structure preserving integration scheme for DEAs. The integration scheme is implemented as C++ code and applied to various examples.