On rate-dependent dissipation effects in electro-elasticity

•Rate-dependent effects in the mechanical deformation and electric polarisation of electro-active solids.•Multiplicative decomposition of deformation gradient and additive decomposition of electric field.•Numerical examples presented to illustrate the non-linear coupling between deformation and electric field.

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 E=Ee+EvE=Ee+Ev and multiplicative decomposition of the deformation gradient F=FeFvF=FeFv are proposed to model the internal dissipation mechanisms. The theory is illustrated with some numerical examples in the end.