Equilibria of charged hyperelastic solids

TL;DR

This paper studies the equilibrium states of charged hyperelastic solids by analyzing an energy functional that couples elastic deformation with electrostatic effects, proving the existence of minimizers in this complex setting.

Contribution

It introduces a novel variational framework for charged hyperelastic materials with a capacitary coupling term, establishing existence results for equilibrium configurations.

Findings

Existence of minimizers for the electroelastic energy functional.

Development of a mathematical framework coupling elasticity and electrostatics.

Analysis of the continuity properties of capacitary terms under deformation convergence.

Abstract

We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This features the coupling of elastic response and electrostatics by means of a capacitary term, which is naturally defined in Eulerian coordinates. The ensuing electroelastic energy is then of mixed Lagrangian-Eulerian type. We prove that minimizers exist by investigating the continuity properties of the capacitary terms under convergence of the deformations