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A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics / Rogelio Ortigosa, Antonio Gil

Computer Methods in Applied Mechanics and Engineering, Volume: 309, Pages: 202 - 242

Swansea University Author: Antonio Gil

Abstract

This work is the third on a series of papers by Gil and Ortigosa (Gil and Ortigosa 2016; Ortigosa and Gil 2016) on the development of a new computational framework for the analysis of Electro Active Polymers, where the concept of polyconvexity (Ball 1976) is extended to the case of electro-magneto-m...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa28513
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spelling 2020-07-20T10:42:47.6507264 v2 28513 2016-06-03 A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2016-06-03 CIVL This work is the third on a series of papers by Gil and Ortigosa (Gil and Ortigosa 2016; Ortigosa and Gil 2016) on the development of a new computational framework for the analysis of Electro Active Polymers, where the concept of polyconvexity (Ball 1976) is extended to the case of electro-magneto-mechanical energy functionals. Specifically, four key novelties are incorporated in this paper. Firstly, a new set of first order hyperbolic equations is presented in the context of nonlinear electro-magneto-elasticity, including conservation laws for all the fields of the extended set of arguments which determine the convex multi-variable nature of the internal energy. Secondly, the one-to-one and invertible relationship between this extended set and its associated entropy conjugate set enables the definition of a generalised convex entropy function, resulting in the symmetrisation of the system when expressed in terms of the entropy variables. Thirdly, this paper shows that, after careful analysis of the eigenvalue structure of the system, the definition of multi-variable convexity in Gil and Ortigosa (2016) leads to positive definiteness of the electro-magneto-acoustic tensor. Therefore, multi-variable convexity ensures the satisfaction of the Legendre–Hadamard condition, hence showing that the speeds of propagation of acoustic and electro-magnetic waves in the neighbourhood of a stationary point are real. Finally, under a characteristic experimental set-up for electrostrictive dielectric elastomers, a study of the material stability of convex and non-convex multi-variable constitutive models is carried out. Journal Article Computer Methods in Applied Mechanics and Engineering 309 202 242 0045-7825 1 9 2016 2016-09-01 10.1016/j.cma.2016.05.019 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-07-20T10:42:47.6507264 2016-06-03T12:15:37.1027674 College of Engineering Engineering Rogelio Ortigosa 1 Antonio Gil 0000-0001-7753-1414 2 0028513-03062016122302.pdf 2016_Ortigosa_Gil_hyperbolicity_electro.pdf 2016-06-03T12:23:02.5800000 Output 11969456 application/pdf Accepted Manuscript true 2017-06-01T00:00:00.0000000 true
title A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics
spellingShingle A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics
Antonio, Gil
title_short A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics
title_full A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics
title_fullStr A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics
title_full_unstemmed A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics
title_sort A new framework for large strain electromechanics based on convex multi-variable strain energies: Conservation laws, hyperbolicity and extension to electro-magneto-mechanics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil
author Antonio, Gil
author2 Rogelio Ortigosa
Antonio Gil
format Journal article
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institution Swansea University
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college_str College of Engineering
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hierarchy_parent_title College of Engineering
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description This work is the third on a series of papers by Gil and Ortigosa (Gil and Ortigosa 2016; Ortigosa and Gil 2016) on the development of a new computational framework for the analysis of Electro Active Polymers, where the concept of polyconvexity (Ball 1976) is extended to the case of electro-magneto-mechanical energy functionals. Specifically, four key novelties are incorporated in this paper. Firstly, a new set of first order hyperbolic equations is presented in the context of nonlinear electro-magneto-elasticity, including conservation laws for all the fields of the extended set of arguments which determine the convex multi-variable nature of the internal energy. Secondly, the one-to-one and invertible relationship between this extended set and its associated entropy conjugate set enables the definition of a generalised convex entropy function, resulting in the symmetrisation of the system when expressed in terms of the entropy variables. Thirdly, this paper shows that, after careful analysis of the eigenvalue structure of the system, the definition of multi-variable convexity in Gil and Ortigosa (2016) leads to positive definiteness of the electro-magneto-acoustic tensor. Therefore, multi-variable convexity ensures the satisfaction of the Legendre–Hadamard condition, hence showing that the speeds of propagation of acoustic and electro-magnetic waves in the neighbourhood of a stationary point are real. Finally, under a characteristic experimental set-up for electrostrictive dielectric elastomers, a study of the material stability of convex and non-convex multi-variable constitutive models is carried out.
published_date 2016-09-01T03:47:28Z
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