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Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers

Francisco Marin, R. Ortigosa, J. Martínez-Frutos, Antonio Gil Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 389, Start page: 114358

Swansea University Authors: Francisco Marin, Antonio Gil Orcid Logo

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DOI (Published version): 10.1016/j.cma.2021.114358

Abstract

This paper analyses the viscoelastic up-scaling effects in electro-active polymers endowed with amicro-structure architecture in the form of a rank-one laminate. The principles of rank-n homogeneisation and thermodynamical consistency are combined in the context of extremely deformable dielectric el...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa58637
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The principles of rank-n homogeneisation and thermodynamical consistency are combined in the context of extremely deformable dielectric elastomers actuated well beyond the onset of geometrical instabilities. To ensure the robustness of the resulting methodology, Convex Multi-Variable (CMV) energy density functionals enriched with a nonlinear continuum viscoelastic description are used to describe the physics of the individual microscopic constituents. The high nonlinearity of the visco-electro-mechanical problem is resolved via a monolithic multi-scale Newton-Raphson scheme with a Backward-Euler (implicit) time integration scheme. A tensor cross product operation between vectors and tensors and an additive decomposition of the micro-scale deformation gradient (in terms of macro-scale and fluctuation components) are used to considerably reduce the complexity of the algebra. The resulting computational framework permits to explore the time-dependent in-silico analysis of rank-one electro-active polymer composites exhibiting extremely complex deformation patterns, paying particular attention to viscoelastic up-scaling effects. A comprehensive series of numerical examples is presented, where specially revealing conclusions about the rate-dependency of the composite electro-active polymer are observed as a function of its microstructure orientation and viscoelastic content. In a rectangular film subjected to extreme bending deformation, two different deformation modes are observed with one prevailing mode depending on the laminate composition. For the case of a square membrane where extreme deformation induces buckling, it is shown that the viscoelastic contribution leads to larger values of (stable) deformation, due to the regularisation that viscoelasticity inherently provides.</abstract><type>Journal Article</type><journal>Computer Methods in Applied Mechanics and Engineering</journal><volume>389</volume><journalNumber/><paginationStart>114358</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0045-7825</issnPrint><issnElectronic/><keywords>viscoelasticity, finite element method, nonlinear electro-elasticity, rank-one laminates, electro-active polymer</keywords><publishedDay>1</publishedDay><publishedMonth>2</publishedMonth><publishedYear>2022</publishedYear><publishedDate>2022-02-01</publishedDate><doi>10.1016/j.cma.2021.114358</doi><url/><notes/><college>COLLEGE NANME</college><department>Science and Engineering - Faculty</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>FGSEN</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2021-12-17T17:24:19.0949663</lastEdited><Created>2021-11-12T15:50:25.2935826</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>Francisco</firstname><surname>Marin</surname><order>1</order></author><author><firstname>R.</firstname><surname>Ortigosa</surname><order>2</order></author><author><firstname>J.</firstname><surname>Mart&#xED;nez-Frutos</surname><order>3</order></author><author><firstname>Antonio</firstname><surname>Gil</surname><orcid>0000-0001-7753-1414</orcid><order>4</order></author></authors><documents><document><filename>58637__21519__9c71d6d7f7ad40d383ec0a393ed15b3a.pdf</filename><originalFilename>58637.pdf</originalFilename><uploaded>2021-11-12T15:59:10.0329488</uploaded><type>Output</type><contentLength>12872590</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2022-12-13T00:00:00.0000000</embargoDate><documentNotes>&#xA9;2021 All rights reserved. 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spelling 2021-12-17T17:24:19.0949663 v2 58637 2021-11-12 Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers 17b7a944b8105f4d35aa96dc252f048f Francisco Marin Francisco Marin true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2021-11-12 FGSEN This paper analyses the viscoelastic up-scaling effects in electro-active polymers endowed with amicro-structure architecture in the form of a rank-one laminate. The principles of rank-n homogeneisation and thermodynamical consistency are combined in the context of extremely deformable dielectric elastomers actuated well beyond the onset of geometrical instabilities. To ensure the robustness of the resulting methodology, Convex Multi-Variable (CMV) energy density functionals enriched with a nonlinear continuum viscoelastic description are used to describe the physics of the individual microscopic constituents. The high nonlinearity of the visco-electro-mechanical problem is resolved via a monolithic multi-scale Newton-Raphson scheme with a Backward-Euler (implicit) time integration scheme. A tensor cross product operation between vectors and tensors and an additive decomposition of the micro-scale deformation gradient (in terms of macro-scale and fluctuation components) are used to considerably reduce the complexity of the algebra. The resulting computational framework permits to explore the time-dependent in-silico analysis of rank-one electro-active polymer composites exhibiting extremely complex deformation patterns, paying particular attention to viscoelastic up-scaling effects. A comprehensive series of numerical examples is presented, where specially revealing conclusions about the rate-dependency of the composite electro-active polymer are observed as a function of its microstructure orientation and viscoelastic content. In a rectangular film subjected to extreme bending deformation, two different deformation modes are observed with one prevailing mode depending on the laminate composition. For the case of a square membrane where extreme deformation induces buckling, it is shown that the viscoelastic contribution leads to larger values of (stable) deformation, due to the regularisation that viscoelasticity inherently provides. Journal Article Computer Methods in Applied Mechanics and Engineering 389 114358 Elsevier BV 0045-7825 viscoelasticity, finite element method, nonlinear electro-elasticity, rank-one laminates, electro-active polymer 1 2 2022 2022-02-01 10.1016/j.cma.2021.114358 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-12-17T17:24:19.0949663 2021-11-12T15:50:25.2935826 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Francisco Marin 1 R. Ortigosa 2 J. Martínez-Frutos 3 Antonio Gil 0000-0001-7753-1414 4 58637__21519__9c71d6d7f7ad40d383ec0a393ed15b3a.pdf 58637.pdf 2021-11-12T15:59:10.0329488 Output 12872590 application/pdf Accepted Manuscript true 2022-12-13T00:00:00.0000000 ©2021 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers
spellingShingle Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers
Francisco Marin
Antonio Gil
title_short Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers
title_full Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers
title_fullStr Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers
title_full_unstemmed Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers
title_sort Viscoelastic up-scaling rank-one effects in in-silico modelling of electro-active polymers
author_id_str_mv 17b7a944b8105f4d35aa96dc252f048f
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 17b7a944b8105f4d35aa96dc252f048f_***_Francisco Marin
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Francisco Marin
Antonio Gil
author2 Francisco Marin
R. Ortigosa
J. Martínez-Frutos
Antonio Gil
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container_title Computer Methods in Applied Mechanics and Engineering
container_volume 389
container_start_page 114358
publishDate 2022
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doi_str_mv 10.1016/j.cma.2021.114358
publisher Elsevier BV
college_str Faculty of Science and Engineering
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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
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description This paper analyses the viscoelastic up-scaling effects in electro-active polymers endowed with amicro-structure architecture in the form of a rank-one laminate. The principles of rank-n homogeneisation and thermodynamical consistency are combined in the context of extremely deformable dielectric elastomers actuated well beyond the onset of geometrical instabilities. To ensure the robustness of the resulting methodology, Convex Multi-Variable (CMV) energy density functionals enriched with a nonlinear continuum viscoelastic description are used to describe the physics of the individual microscopic constituents. The high nonlinearity of the visco-electro-mechanical problem is resolved via a monolithic multi-scale Newton-Raphson scheme with a Backward-Euler (implicit) time integration scheme. A tensor cross product operation between vectors and tensors and an additive decomposition of the micro-scale deformation gradient (in terms of macro-scale and fluctuation components) are used to considerably reduce the complexity of the algebra. The resulting computational framework permits to explore the time-dependent in-silico analysis of rank-one electro-active polymer composites exhibiting extremely complex deformation patterns, paying particular attention to viscoelastic up-scaling effects. A comprehensive series of numerical examples is presented, where specially revealing conclusions about the rate-dependency of the composite electro-active polymer are observed as a function of its microstructure orientation and viscoelastic content. In a rectangular film subjected to extreme bending deformation, two different deformation modes are observed with one prevailing mode depending on the laminate composition. For the case of a square membrane where extreme deformation induces buckling, it is shown that the viscoelastic contribution leads to larger values of (stable) deformation, due to the regularisation that viscoelasticity inherently provides.
published_date 2022-02-01T04:15:19Z
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score 11.014224

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