A Convex Multi-Variable based computational framework for multilayered electro-active polymers

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

doi:10.1016/j.cma.2020.113567

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A Convex Multi-Variable based computational framework for multilayered electro-active polymers

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

Computer Methods in Applied Mechanics and Engineering, Volume: 374, Start page: 113567

Swansea University Authors: Francisco Marin, Antonio Gil

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DOI (Published version): 10.1016/j.cma.2020.113567

Abstract

This paper presents a novel computational framework for the in silico analysis of rank-one multilayered electro-active polymer composites exhibiting complex deformation patterns. The work applies the principles of rank-n homogenisation in the context of extremely deformable dielectric elastomers act...

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Published in:	Computer Methods in Applied Mechanics and Engineering
ISSN:	0045-7825
Published:	Elsevier BV 2021
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URI:	https://cronfa.swan.ac.uk/Record/cronfa55636
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spelling	2022-10-31T18:13:30.7286254 v2 55636 2020-11-10 A Convex Multi-Variable based computational framework for multilayered electro-active polymers 17b7a944b8105f4d35aa96dc252f048f Francisco Marin Francisco Marin true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2020-11-10 FGSEN This paper presents a novel computational framework for the in silico analysis of rank-one multilayered electro-active polymer composites exhibiting complex deformation patterns. The work applies the principles of rank-n homogenisation in the context of extremely deformable dielectric elastomers actuated beyond the onset of geometrical instabilities. Following previous work by the authors (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016; Ortigosa and Gil, 2016) Convex Multi-Variable (CMV) energy density functionals are used to describe the physics of the individual microscopic constituents, which is shown to guarantee ab initio the existence of solutions for the microstructure problem, described in terms of the so-called deformation gradient and electric displacement amplitude vectors. The high nonlinearity of the quasi-static electro-mechanical problem is resolved via a monolithic multi-scale Newton–Raphson scheme, which is enhanced with a tailor-made arc length technique, used to circumvent the onset of geometrical instabilities. 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 possible loss of ellipticity of the homogenised constitutive model is strictly monitored through the minors of the homogenised acoustic tensor. A series of numerical examples is presented in order to demonstrate the effect that the volume fraction, the contrast and the material properties, as well as the level of deformation and electric field, have upon the response of the composites when subjected to large three dimensional stretching, bending and torsion, including the possible development of wrinkling. Journal Article Computer Methods in Applied Mechanics and Engineering 374 113567 Elsevier BV 0045-7825 Finite element method, Nonlinear electro-elasticity, Composite materials, Rank-one laminates 1 2 2021 2021-02-01 10.1016/j.cma.2020.113567 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2022-10-31T18:13:30.7286254 2020-11-10T10:05:20.6523948 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Francisco Marin 1 J. Martínez-Frutos 2 R. Ortigosa 3 Antonio Gil 0000-0001-7753-1414 4 55636__18635__f392b652b88e465d9fc4be161bed83f8.pdf 55636.pdf 2020-11-10T15:26:53.5359574 Output 56720525 application/pdf Accepted Manuscript true 2021-12-04T00:00:00.0000000 ©2020 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 http://creativecommons.org/licenses/by-nc-nd/4.0/
title	A Convex Multi-Variable based computational framework for multilayered electro-active polymers
spellingShingle	A Convex Multi-Variable based computational framework for multilayered electro-active polymers Francisco Marin Antonio Gil
title_short	A Convex Multi-Variable based computational framework for multilayered electro-active polymers
title_full	A Convex Multi-Variable based computational framework for multilayered electro-active polymers
title_fullStr	A Convex Multi-Variable based computational framework for multilayered electro-active polymers
title_full_unstemmed	A Convex Multi-Variable based computational framework for multilayered electro-active polymers
title_sort	A Convex Multi-Variable based computational framework for multilayered 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 J. Martínez-Frutos R. Ortigosa Antonio Gil
format	Journal article
container_title	Computer Methods in Applied Mechanics and Engineering
container_volume	374
container_start_page	113567
publishDate	2021
institution	Swansea University
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doi_str_mv	10.1016/j.cma.2020.113567
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description	This paper presents a novel computational framework for the in silico analysis of rank-one multilayered electro-active polymer composites exhibiting complex deformation patterns. The work applies the principles of rank-n homogenisation in the context of extremely deformable dielectric elastomers actuated beyond the onset of geometrical instabilities. Following previous work by the authors (Gil and Ortigosa, 2016; Ortigosa and Gil, 2016; Ortigosa and Gil, 2016) Convex Multi-Variable (CMV) energy density functionals are used to describe the physics of the individual microscopic constituents, which is shown to guarantee ab initio the existence of solutions for the microstructure problem, described in terms of the so-called deformation gradient and electric displacement amplitude vectors. The high nonlinearity of the quasi-static electro-mechanical problem is resolved via a monolithic multi-scale Newton–Raphson scheme, which is enhanced with a tailor-made arc length technique, used to circumvent the onset of geometrical instabilities. 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 possible loss of ellipticity of the homogenised constitutive model is strictly monitored through the minors of the homogenised acoustic tensor. A series of numerical examples is presented in order to demonstrate the effect that the volume fraction, the contrast and the material properties, as well as the level of deformation and electric field, have upon the response of the composites when subjected to large three dimensional stretching, bending and torsion, including the possible development of wrinkling.
published_date	2021-02-01T04:10:00Z
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A Convex Multi-Variable based computational framework for multilayered electro-active polymers

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