Modeling and analysis of finite-strain visco-elastic materials with electrostatic interaction

Abstract

We develop a thermodynamically consistent model for the viscoelastic deformation of electrically charged bodies in the Lagrangian frame, incorporating a Jeffreys-type rheology and flow of free charge-carriers within the framework of the General Equations for Non-Equilibrium Reversible?Irreversible Coupling (GENERIC). The formulation couples mechanical, electrostatic, and dissipative effects in a structure that ensures compatibility with the principles of nonequilibrium thermodynamics. Furthermore, in the isothermal and mechanically quasistatic regime, i.e., where inertial effects are neglected, we establish the existence of weak solutions to a reduced version of the governing system. The proof relies on a Galerkin approximation combined with suitable regularizations of the degenerate mobilities of the free charge carriers and of the free energy. A typical application is the description of conductive hydrogels used in biomedicine.