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A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation / Antonio, Gil

Computer Methods in Applied Mechanics and Engineering, Volume: 302, Pages: 293 - 328

Swansea University Author: Antonio, Gil

Abstract

Following the recent work of Bonet et al. (2015), this paper postulates a new convex multi-variable variational framework for the analysis of Electro Active Polymers (EAPs) in the context of reversible nonlinear electro-elasticity. This extends the concept of polyconvexity (Ball, 1976) to strain ene...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 00457825
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa30568
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first_indexed 2016-10-13T18:58:24Z
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spelling 2018-10-01T16:29:24.8815814 v2 30568 2016-10-13 A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2016-10-13 EEN Following the recent work of Bonet et al. (2015), this paper postulates a new convex multi-variable variational framework for the analysis of Electro Active Polymers (EAPs) in the context of reversible nonlinear electro-elasticity. This extends the concept of polyconvexity (Ball, 1976) to strain energies which depend on non-strain based variables introducing other physical measures such as the electric displacement. Six key novelties are incorporated in this work. First, a new definition of the electro-mechanical internal energy is introduced expressed as a convex multi-variable function of a new extended set of electromechanical arguments. Crucially, this new definition of the internal energy enables the most accepted constitutive inequality, namely ellipticity, to be extended to the entire range of deformations and electric fields and, in addition, to incorporate the electro-mechanical energy of the vacuum, and hence that for ideal dielectric elastomers, as a degenerate case. Second, a new extended set of variables, work conjugate to those characterising the new definition of multi-variable convexity, is introduced in this paper. Third, both new sets of variables enable the definition of novel extended Hu–Washizu type of mixed variational principles which are presented in this paper for the first time in the context of nonlinear electro-elasticity. Fourth, some simple strategies to create appropriate convex multi-variable energy functionals (in terms of convex multi-variable invariants) by incorporating minor modifications to a priori non-convex multi-variable functionals are also presented. Fifth, a tensor cross product operation (de Boer, 1982) used in Bonet et al. (2015) to facilitate the algebra associated with the adjoint of the deformation gradient tensor is incorporated in the proposed variational electro-mechanical framework, leading to insightful representations of otherwise complex algebraic expressions. Finally, under a characteristic experimental setup in dielectric elastomers, the behaviour of a convex multi-variable constitutive model capturing some intrinsic nonlinear effects such as electrostriction, is numerically studied. Journal Article Computer Methods in Applied Mechanics and Engineering 302 293 328 00457825 Dielectric elastomers, Nonlinear electro-elasticity, Large strains, Material stability, Mixed variational principles, Polyconvexity 15 4 2016 2016-04-15 10.1016/j.cma.2015.11.036 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2018-10-01T16:29:24.8815814 2016-10-13T15:17:06.7608082 Antonio Gil 0000-0001-7753-1414 1 Rogelio Ortigosa 2 0030568-13102016152526.pdf gil2016.pdf 2016-10-13T15:25:26.0170000 Output 2443511 application/pdf Accepted Manuscript true 2017-01-06T00:00:00.0000000 true
title A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation
spellingShingle A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation
Antonio, Gil
title_short A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation
title_full A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation
title_fullStr A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation
title_full_unstemmed A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation
title_sort A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil
author Antonio, Gil
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 302
container_start_page 293
publishDate 2016
institution Swansea University
issn 00457825
doi_str_mv 10.1016/j.cma.2015.11.036
document_store_str 1
active_str 0
description Following the recent work of Bonet et al. (2015), this paper postulates a new convex multi-variable variational framework for the analysis of Electro Active Polymers (EAPs) in the context of reversible nonlinear electro-elasticity. This extends the concept of polyconvexity (Ball, 1976) to strain energies which depend on non-strain based variables introducing other physical measures such as the electric displacement. Six key novelties are incorporated in this work. First, a new definition of the electro-mechanical internal energy is introduced expressed as a convex multi-variable function of a new extended set of electromechanical arguments. Crucially, this new definition of the internal energy enables the most accepted constitutive inequality, namely ellipticity, to be extended to the entire range of deformations and electric fields and, in addition, to incorporate the electro-mechanical energy of the vacuum, and hence that for ideal dielectric elastomers, as a degenerate case. Second, a new extended set of variables, work conjugate to those characterising the new definition of multi-variable convexity, is introduced in this paper. Third, both new sets of variables enable the definition of novel extended Hu–Washizu type of mixed variational principles which are presented in this paper for the first time in the context of nonlinear electro-elasticity. Fourth, some simple strategies to create appropriate convex multi-variable energy functionals (in terms of convex multi-variable invariants) by incorporating minor modifications to a priori non-convex multi-variable functionals are also presented. Fifth, a tensor cross product operation (de Boer, 1982) used in Bonet et al. (2015) to facilitate the algebra associated with the adjoint of the deformation gradient tensor is incorporated in the proposed variational electro-mechanical framework, leading to insightful representations of otherwise complex algebraic expressions. Finally, under a characteristic experimental setup in dielectric elastomers, the behaviour of a convex multi-variable constitutive model capturing some intrinsic nonlinear effects such as electrostriction, is numerically studied.
published_date 2016-04-15T03:49:34Z
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