A polarisation based approach to model the strain dependent permittivity of dielectric elastomers

A wide-spread lumped parameter model describing the electrostatic pressure present in dielectric elastomer actuators is presented by Pelrine et al. in 1998. In Pelrine's model, the electrostatic pressure is affected by the relative permittivity of the material, also known as dielectric constant. However, many researchers found that the dielectric constant of dielectric elastomers is not constant at all, but decreasing with increasing pre-stretch of the material. This holds especially for acrylic materials such as VHB 4910 from 3M. From a physical point of view, polarisation within the dielectric material is responsible for the material's permittivity and in general, polarisation is deformation dependent. In this work, an alternative modelling approach is presented, explaining the stretch dependent electrostatic pressure. It is shown that Pelrine implicitly assumes that the polarisation of the material is linear in the imposed electric field strength. If this assumption is modified to allow for a more general polarisation field that is based on invariants of the electromechanically coupled problem, a new polarisation based lumped parameter model is obtained. It is shown that this new model fits experimental data found in literature quite well. (C) 2017 Elsevier B.V. All rights reserved.