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A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers

Roman Poya, Antonio Gil Orcid Logo, Rogelio Ortigosa, Rubén Sevilla Orcid Logo, Javier Bonet, Wolfgang A. Wall

Computer Methods in Applied Mechanics and Engineering

Swansea University Authors: Antonio Gil Orcid Logo, Rubén Sevilla Orcid Logo

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DOI (Published version): 10.1016/j.cma.2017.09.020

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This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme. With an emphasis on accurate geometrical representat...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa35289
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With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation. The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016, 2016). Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models. In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings. For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime. In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches. Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications.</abstract><type>Journal Article</type><journal>Computer Methods in Applied Mechanics and Engineering</journal><publisher/><issnPrint>0045-7825</issnPrint><keywords>Monolithic &amp;amp; staggered electro-elasticity; High order curvilinear meshes; Dielectric elastomers; Material instability; Wrinkling</keywords><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2017</publishedYear><publishedDate>2017-12-31</publishedDate><doi>10.1016/j.cma.2017.09.020</doi><url/><notes/><college>COLLEGE NANME</college><department>Civil Engineering</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>CIVL</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2020-06-01T17:00:29.4817468</lastEdited><Created>2017-09-15T10:19:37.8912513</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering</level></path><authors><author><firstname>Roman</firstname><surname>Poya</surname><order>1</order></author><author><firstname>Antonio</firstname><surname>Gil</surname><orcid>0000-0001-7753-1414</orcid><order>2</order></author><author><firstname>Rogelio</firstname><surname>Ortigosa</surname><order>3</order></author><author><firstname>Rub&#xE9;n</firstname><surname>Sevilla</surname><orcid>0000-0002-0061-6214</orcid><order>4</order></author><author><firstname>Javier</firstname><surname>Bonet</surname><order>5</order></author><author><firstname>Wolfgang A.</firstname><surname>Wall</surname><order>6</order></author></authors><documents><document><filename>0035289-15092017102022.pdf</filename><originalFilename>poya2017(2).pdf</originalFilename><uploaded>2017-09-15T10:20:22.2100000</uploaded><type>Output</type><contentLength>19746626</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2018-09-28T00:00:00.0000000</embargoDate><copyrightCorrect>false</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling 2020-06-01T17:00:29.4817468 v2 35289 2017-09-15 A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false b542c87f1b891262844e95a682f045b6 0000-0002-0061-6214 Rubén Sevilla Rubén Sevilla true false 2017-09-15 CIVL This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme. With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation. The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016, 2016). Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models. In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings. For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime. In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches. Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications. Journal Article Computer Methods in Applied Mechanics and Engineering 0045-7825 Monolithic &amp; staggered electro-elasticity; High order curvilinear meshes; Dielectric elastomers; Material instability; Wrinkling 31 12 2017 2017-12-31 10.1016/j.cma.2017.09.020 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-06-01T17:00:29.4817468 2017-09-15T10:19:37.8912513 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Roman Poya 1 Antonio Gil 0000-0001-7753-1414 2 Rogelio Ortigosa 3 Rubén Sevilla 0000-0002-0061-6214 4 Javier Bonet 5 Wolfgang A. Wall 6 0035289-15092017102022.pdf poya2017(2).pdf 2017-09-15T10:20:22.2100000 Output 19746626 application/pdf Accepted Manuscript true 2018-09-28T00:00:00.0000000 false eng
title A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers
spellingShingle A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers
Antonio Gil
Rubén Sevilla
title_short A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers
title_full A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers
title_fullStr A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers
title_full_unstemmed A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers
title_sort A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
b542c87f1b891262844e95a682f045b6
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
b542c87f1b891262844e95a682f045b6_***_Rubén Sevilla
author Antonio Gil
Rubén Sevilla
author2 Roman Poya
Antonio Gil
Rogelio Ortigosa
Rubén Sevilla
Javier Bonet
Wolfgang A. Wall
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
publishDate 2017
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2017.09.020
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
active_str 0
description This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme. With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation. The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016, 2016). Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models. In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings. For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime. In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches. Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications.
published_date 2017-12-31T03:43:52Z
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