Calculus of Variations and Geometric Measure Theory
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E. Davoli - A. Molchanova - U. Stefanelli

Equilibria of charged hyperelastic solids

created by davoli on 16 Apr 2021

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Submitted Paper

Inserted: 16 apr 2021
Last Updated: 16 apr 2021

Year: 2021

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.

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


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