Equilibria of charged hyperelastic solids

Elisa Davoli; Anastasia Molchanova; Ulisse Stefanelli

doi:10.1137/21M1413286

Equilibria of charged hyperelastic solids

Elisa Davoli, Anastasia Molchanova, Ulisse Stefanelli

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This involves 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.

Original language	English
Pages (from-to)	1470–1487
Number of pages	18
Journal	SIAM Journal on Mathematical Analysis
Volume	54
Issue number	2
DOIs	https://doi.org/10.1137/21M1413286
Publication status	Published - 2022

Austrian Fields of Science 2012

101002 Analysis

Keywords

capacity
charged materials
finite distortion
mixed Eulerian-Lagrangian formulation

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10.1137/21M1413286

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abstract = "We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This involves 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.",

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AB - We investigate equilibria of charged deformable materials via the minimization of an electroelastic energy. This involves 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.

KW - capacity

KW - charged materials

KW - finite distortion

KW - mixed Eulerian-Lagrangian formulation

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DO - 10.1137/21M1413286

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

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Equilibria of charged hyperelastic solids

Abstract

Austrian Fields of Science 2012

Keywords

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