On rate-dependent dissipation effects in electro-elasticity

TL;DR

This paper develops a mathematical model for large strain electro-viscoelastic deformations in electro-active polymers, incorporating energy dissipation from mechanical viscoelasticity and time-dependent polarization, with numerical illustrations.

Contribution

It introduces additive and multiplicative decomposition frameworks to model internal dissipation mechanisms in electro-elastic materials.

Findings

Model captures rate-dependent dissipation effects.

Numerical examples demonstrate the model's applicability.

Provides a foundation for simulating electro-viscoelastic behavior.

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.