On rate-dependent dissipation effects in electro-elasticity

Abstract: This paper deals with the mathematical modelling of large strain electro-viscoelastic deformations in electro-active polymers. Energy dissipation is assumed to occur due to mechanical viscoelasticity of the polymer as well as due to time-dependent effective polarisation of the material. Additive decomposition of the electric field $\mathbb{E} = \mathbb{E}_e + \mathbb{E}_v$ and multiplicative decomposition of the deformation gradient $\mathbf{F} = \mathbf{F}_e \mathbf{F}_v$ are proposed to model the internal dissipation mechanisms. The theory is illustrated with some numerical examples in the end.