Calculus of Variations and Geometric Measure Theory

E. Davoli - A. Molchanova - U. Stefanelli

Equilibria of charged hyperelastic solids

created by davoli on 16 Apr 2021
modified on 19 Apr 2022


Accepted Paper

Inserted: 16 apr 2021
Last Updated: 19 apr 2022

Journal: SIAM J. Math. Anal. (SIMA)
Year: 2021


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.

Keywords: capacity, charged materials, mixed Eulerian-Lagrangian formulation, finite distortion