ON VARIATIONAL PRINCIPLES FOR POLARIZATION RESPONSES IN ELECTROMECHANICAL SYSTEMS

Electromechanical systems can be found in many physical and biological applications, such as ion transport in membranes, batteries, and dielectric elastomers. Classical electrodynamics uses a dielectric constant to describe the polarization response of an electromechanical system to charges in an electric field. We generalize that description to include a wide variety of responses to charges in the electric field by a unified, thermodynamically consistent, variational framework. This framework is motivated and developed using the classical energetic variational approach (En VarA). The coupling be-tween the electrical part and the chemo-mechanical parts of the system is described either by Lagrange multipliers or various energy relaxations. The classical polarization and its dielectrics and dielectric constants appear as outputs of this analysis. The Maxwell equations then become universal conservation laws of charge and current, conjoined to an electromechanical description of the polarization of materials.