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A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation / Rogelio Ortigosa; Antonio Gil

Computer Methods in Applied Mechanics and Engineering, Volume: 302, Pages: 329 - 360

Swansea University Author: Antonio, Gil

Abstract

In Gil and Ortigosa (2016), Gil and Ortigosa introduced a new convex multi-variable framework for the numerical simulation of Electro Active Polymers (EAPs) in the presence of extreme deformations and electric fields. This extends the concept of polyconvexity to strain energies which depend on non-s...

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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/cronfa26099
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spelling 2016-10-13T15:53:40.6270709 v2 26099 2016-02-05 A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2016-02-05 EEN In Gil and Ortigosa (2016), Gil and Ortigosa introduced a new convex multi-variable framework for the numerical simulation of Electro Active Polymers (EAPs) in the presence of extreme deformations and electric fields. This extends the concept of polyconvexity to strain energies which depend on non-strain based variables. The consideration of the new concept of multi-variable convexity guarantees the well posedness of generalised Gibbs’ energy density functionals and, hence, opens up the possibility of a new family of mixed variational principles. The aim of this paper is to present, as an example, the Finite Element implementation of two of these mixed variational principles. These types of enhanced methodologies are known to be necessary in scenarios in which the simpler displacement-potential based formulation yields non-physical results, such as volumetric locking, bending and shear locking, pressure oscillations and electro-mechanical locking, to name but a few. Crucially, the use of interpolation spaces in which some of the unknown fields are described as piecewise discontinuous across elements can be used in order to efficiently condense these fields out. This results in mixed formulations with a computational cost comparable to that of the displacement-potential based approach, yet far more accurate. Finally, a series of very challenging numerical examples are presented in order to demonstrate the accuracy, robustness and efficiency of the proposed methodology. Journal Article Computer Methods in Applied Mechanics and Engineering 302 329 360 0045-7825 15 4 2016 2016-04-15 10.1016/j.cma.2015.12.007 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2016-10-13T15:53:40.6270709 2016-02-05T16:55:12.4877732 College of Engineering Engineering Rogelio Ortigosa 1 Antonio Gil 0000-0001-7753-1414 2 0026099-13102016155307.pdf ortigosa2016(2).pdf 2016-10-13T15:53:07.4600000 Output 8536122 application/pdf Accepted Manuscript true 2016-12-30T00:00:00.0000000 false
title A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation
spellingShingle A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation
Antonio, Gil
title_short A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation
title_full A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation
title_fullStr A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation
title_full_unstemmed A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation
title_sort A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil
author Antonio, Gil
author2 Rogelio Ortigosa
Antonio Gil
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 302
container_start_page 329
publishDate 2016
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2015.12.007
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description In Gil and Ortigosa (2016), Gil and Ortigosa introduced a new convex multi-variable framework for the numerical simulation of Electro Active Polymers (EAPs) in the presence of extreme deformations and electric fields. This extends the concept of polyconvexity to strain energies which depend on non-strain based variables. The consideration of the new concept of multi-variable convexity guarantees the well posedness of generalised Gibbs’ energy density functionals and, hence, opens up the possibility of a new family of mixed variational principles. The aim of this paper is to present, as an example, the Finite Element implementation of two of these mixed variational principles. These types of enhanced methodologies are known to be necessary in scenarios in which the simpler displacement-potential based formulation yields non-physical results, such as volumetric locking, bending and shear locking, pressure oscillations and electro-mechanical locking, to name but a few. Crucially, the use of interpolation spaces in which some of the unknown fields are described as piecewise discontinuous across elements can be used in order to efficiently condense these fields out. This results in mixed formulations with a computational cost comparable to that of the displacement-potential based approach, yet far more accurate. Finally, a series of very challenging numerical examples are presented in order to demonstrate the accuracy, robustness and efficiency of the proposed methodology.
published_date 2016-04-15T03:41:18Z
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