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A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

Rogelio Ortigosa, Antonio Gil Orcid Logo, Chun Hean Lee, Chun Hean Lee Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 310, Pages: 297 - 334

Swansea University Authors: Antonio Gil Orcid Logo, Chun Hean Lee Orcid Logo

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DOI (Published version): 10.1016/j.cma.2016.06.025

Abstract

The series of papers published by Gil and Ortigosa (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016, 0000) introduced a new convex multi-variable variational and computational framework for the numerical simulation of Electro Active Polymers (EAPs) in scenarios characterised by extreme deformations a...

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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/cronfa29251
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Building upon this body of work, five key novelties are incorporated in this paper. First, a generalisation of the concept of multi-variable convexity to energy functionals additively decomposed into isochoric and volumetric components. This decomposition is typical of nearly and truly incompressible materials, group which represents the majority of the most relevant EAPs. Second, convexification or regularisation strategies are applied to a priori non-convex multi-variable isochoric functionals to yield physically meaningful convex multi-variable functionals. Third, based on the mixed variational principles introduced in Gil and Ortigosa (2016) in the context of compressible electro-elasticity, a novel extended Hu&#x2013;Washizu mixed variational principle for nearly and truly incompressible scenarios is presented. From the computational standpoint, a static condensation procedure is applied in order to condense out the element-wise extra fields, the resulting formulation having a comparable cost to the more standard three-field displacement-potential-pressure mixed formulation. Fourth, the computational framework for the three-field mixed variational principle in nearly and truly incompressible scenarios is also presented. In this case, the novelty resides in the consideration of convex multi-variable energy functionals. Ultimately, this leads to the definition of new tangent operators for the Helmholtz&#x2019;s energy functional in the specific context of incompressible electro-elasticity. Fifth, a Petrov&#x2013;Galerkin stabilisation technique is applied on the three-field formulation for the circumvention of the Ladyz&#x2D8;enskaja&#x2013;Babus&#x2D8;ka&#x2013;Brezzi (LBB) condition, enabling the use of linear tetrahedral finite elements for the interpolation of the unknowns of the problem. 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spelling 2016-10-07T09:52:01.3436796 v2 29251 2016-07-20 A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false e3024bdeee2dee48376c2a76b7147f2f 0000-0003-1102-3729 Chun Hean Lee Chun Hean Lee true false 2016-07-20 CIVL The series of papers published by Gil and Ortigosa (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016, 0000) introduced a new convex multi-variable variational and computational framework for the numerical simulation of Electro Active Polymers (EAPs) in scenarios characterised by extreme deformations and/or extreme electric fields. Building upon this body of work, five key novelties are incorporated in this paper. First, a generalisation of the concept of multi-variable convexity to energy functionals additively decomposed into isochoric and volumetric components. This decomposition is typical of nearly and truly incompressible materials, group which represents the majority of the most relevant EAPs. Second, convexification or regularisation strategies are applied to a priori non-convex multi-variable isochoric functionals to yield physically meaningful convex multi-variable functionals. Third, based on the mixed variational principles introduced in Gil and Ortigosa (2016) in the context of compressible electro-elasticity, a novel extended Hu–Washizu mixed variational principle for nearly and truly incompressible scenarios is presented. From the computational standpoint, a static condensation procedure is applied in order to condense out the element-wise extra fields, the resulting formulation having a comparable cost to the more standard three-field displacement-potential-pressure mixed formulation. Fourth, the computational framework for the three-field mixed variational principle in nearly and truly incompressible scenarios is also presented. In this case, the novelty resides in the consideration of convex multi-variable energy functionals. Ultimately, this leads to the definition of new tangent operators for the Helmholtz’s energy functional in the specific context of incompressible electro-elasticity. Fifth, a Petrov–Galerkin stabilisation technique is applied on the three-field formulation for the circumvention of the Ladyz˘enskaja–Babus˘ka–Brezzi (LBB) condition, enabling the use of linear tetrahedral finite elements for the interpolation of the unknowns of the problem. Finally, a series of challenging numerical examples is presented in order to provide an exhaustive comparison of the different variational formulations presented in this paper. Journal Article Computer Methods in Applied Mechanics and Engineering 310 297 334 0045-7825 1 10 2016 2016-10-01 10.1016/j.cma.2016.06.025 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2016-10-07T09:52:01.3436796 2016-07-20T15:41:33.6831818 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Rogelio Ortigosa 1 Antonio Gil 0000-0001-7753-1414 2 Chun Hean Lee 3 Chun Hean Lee 0000-0003-1102-3729 4 0029251-29072016111617.pdf ortigosa2016.pdf 2016-07-29T11:16:17.3870000 Output 16861033 application/pdf Accepted Manuscript true 2017-07-16T00:00:00.0000000 false
title A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies
spellingShingle A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies
Antonio Gil
Chun Hean Lee
title_short A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies
title_full A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies
title_fullStr A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies
title_full_unstemmed A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies
title_sort A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
e3024bdeee2dee48376c2a76b7147f2f
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
e3024bdeee2dee48376c2a76b7147f2f_***_Chun Hean Lee
author Antonio Gil
Chun Hean Lee
author2 Rogelio Ortigosa
Antonio Gil
Chun Hean Lee
Chun Hean Lee
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 310
container_start_page 297
publishDate 2016
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2016.06.025
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
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description The series of papers published by Gil and Ortigosa (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016, 0000) introduced a new convex multi-variable variational and computational framework for the numerical simulation of Electro Active Polymers (EAPs) in scenarios characterised by extreme deformations and/or extreme electric fields. Building upon this body of work, five key novelties are incorporated in this paper. First, a generalisation of the concept of multi-variable convexity to energy functionals additively decomposed into isochoric and volumetric components. This decomposition is typical of nearly and truly incompressible materials, group which represents the majority of the most relevant EAPs. Second, convexification or regularisation strategies are applied to a priori non-convex multi-variable isochoric functionals to yield physically meaningful convex multi-variable functionals. Third, based on the mixed variational principles introduced in Gil and Ortigosa (2016) in the context of compressible electro-elasticity, a novel extended Hu–Washizu mixed variational principle for nearly and truly incompressible scenarios is presented. From the computational standpoint, a static condensation procedure is applied in order to condense out the element-wise extra fields, the resulting formulation having a comparable cost to the more standard three-field displacement-potential-pressure mixed formulation. Fourth, the computational framework for the three-field mixed variational principle in nearly and truly incompressible scenarios is also presented. In this case, the novelty resides in the consideration of convex multi-variable energy functionals. Ultimately, this leads to the definition of new tangent operators for the Helmholtz’s energy functional in the specific context of incompressible electro-elasticity. Fifth, a Petrov–Galerkin stabilisation technique is applied on the three-field formulation for the circumvention of the Ladyz˘enskaja–Babus˘ka–Brezzi (LBB) condition, enabling the use of linear tetrahedral finite elements for the interpolation of the unknowns of the problem. Finally, a series of challenging numerical examples is presented in order to provide an exhaustive comparison of the different variational formulations presented in this paper.
published_date 2016-10-01T03:35:37Z
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score 11.012678

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