# Constitutive equations for an electro-active polymer

## TL;DR

This paper develops constitutive equations for ionic electro-active polymers, modeling their coupled electro-mechanical behavior using a two-phase continuum approach and thermodynamic principles.

## Contribution

It introduces a comprehensive thermodynamic model for electro-active polymers, deriving constitutive equations that couple mechanical deformation with electrochemical effects.

## Key findings

- Stress-strain relations follow a Kelvin-Voigt model
- Derived generalized Fourier's and Darcy's laws
- Formulated Nernst-Planck equation for ion transport

## Abstract

Ionic electro-active polymers (E.A.P.) can be used as sensors or actuators. For this purpose, a thin film of polyelectrolyte is saturated with a solvent and sandwiched between two platinum electrodes. The solvent causes a complete dissociation of the polymer and the release of small cations. The application of an electric field across the thickness results in the bending of the strip and vice versa. The material is modelled by a two-phase continuous medium. The solid phase, constituted by the polymer backbone inlaid with anions, is depicted as a deformable porous media. The liquid phase is composed of the free cations and the solvent (usually water). We used a coarse grain model. The conservation laws of this system have been established in a previous work. The entropy balance law and the thermodynamic relations are first written for each phase, then for the complete material using a statistical average technique and the material derivative concept. One deduces the entropy production. Identifying generalized forces and fluxes provides the constitutive equations of the whole system : the stress-strain relations which satisfy a Kelvin-Voigt model, generalized Fourier's and Darcy's laws and the Nernst-Planck equation.