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A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics

M. Franke, Rogelio Ortigosa Martinez Orcid Logo, J. Martínez-Frutos, Antonio Gil Orcid Logo, P. Betsch

Computer Methods in Applied Mechanics and Engineering, Volume: 389, Start page: 114298

Swansea University Authors: Rogelio Ortigosa Martinez Orcid Logo, Antonio Gil Orcid Logo

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DOI (Published version): 10.1016/j.cma.2021.114298

Abstract

The aim of this paper is the design of a new one-step implicit and thermodynamically consistentEnergy-Momentum (EM) preserving time integration scheme for the simulation of thermoelectro-elastic processes undergoing large deformations. The time integration scheme takes advantageof the notion of poly...

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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/cronfa58544
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spelling 2021-12-17T16:04:15.0369861 v2 58544 2021-11-03 A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics f2db4bab004a6f5943408d554159ff99 NULL Rogelio Ortigosa Martinez Rogelio Ortigosa Martinez true true 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2021-11-03 The aim of this paper is the design of a new one-step implicit and thermodynamically consistentEnergy-Momentum (EM) preserving time integration scheme for the simulation of thermoelectro-elastic processes undergoing large deformations. The time integration scheme takes advantageof the notion of polyconvexity and of a new tensor cross product algebra. These twoingredients are shown to be crucial for the design of so-called discrete derivatives fundamental forthe calculation of the second Piola-Kirchhoff stress tensor, the entropy and the electric field. Inparticular, the exploitation of polyconvexity and the tensor cross product, enable the derivationof comparatively simple formulas for the discrete derivatives. This is in sharp contrast to muchmore elaborate discrete derivatives which are one of the main downsides of classical EM timeintegration schemes. The newly proposed scheme inherits the advantages of EM schemes recentlypublished in the context of thermo-elasticity and electro-mechanics, whilst extending to the moregeneric case of nonlinear thermo-electro-mechanics. Furthermore, the manuscript delves intosuitable convexity/concavity restrictions that thermo-electro-mechanical strain energy functionsmust comply with in order to yield physically and mathematically admissible solutions. Finally, aseries of numerical examples will be presented in order to demonstrate robustness and numericalstability properties of the new EM scheme. Journal Article Computer Methods in Applied Mechanics and Engineering 389 114298 Elsevier BV 0045-7825 finite element method, nonlinear thermo-electro-elastodynamics, energy-momentumscheme, tensor cross product, polyconvexity, dielectric elastomers, electro active polymers 1 2 2022 2022-02-01 10.1016/j.cma.2021.114298 COLLEGE NANME College of Engineering COLLEGE CODE Swansea University 2021-12-17T16:04:15.0369861 2021-11-03T14:23:49.5286331 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering M. Franke 1 Rogelio Ortigosa Martinez NULL 2 J. Martínez-Frutos 3 Antonio Gil 0000-0001-7753-1414 4 P. Betsch 5 58544__21424__e8cd47c9a40d4a8db434f989858ff0da.pdf 58544.pdf 2021-11-03T14:31:06.5827941 Output 9671024 application/pdf Accepted Manuscript true 2022-12-11T00:00:00.0000000 ©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 A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics
spellingShingle A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics
Rogelio Ortigosa Martinez
Antonio Gil
title_short A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics
title_full A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics
title_fullStr A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics
title_full_unstemmed A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics
title_sort A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics
author_id_str_mv f2db4bab004a6f5943408d554159ff99
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv f2db4bab004a6f5943408d554159ff99_***_Rogelio Ortigosa Martinez
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Rogelio Ortigosa Martinez
Antonio Gil
author2 M. Franke
Rogelio Ortigosa Martinez
J. Martínez-Frutos
Antonio Gil
P. Betsch
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 389
container_start_page 114298
publishDate 2022
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2021.114298
publisher Elsevier BV
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 aim of this paper is the design of a new one-step implicit and thermodynamically consistentEnergy-Momentum (EM) preserving time integration scheme for the simulation of thermoelectro-elastic processes undergoing large deformations. The time integration scheme takes advantageof the notion of polyconvexity and of a new tensor cross product algebra. These twoingredients are shown to be crucial for the design of so-called discrete derivatives fundamental forthe calculation of the second Piola-Kirchhoff stress tensor, the entropy and the electric field. Inparticular, the exploitation of polyconvexity and the tensor cross product, enable the derivationof comparatively simple formulas for the discrete derivatives. This is in sharp contrast to muchmore elaborate discrete derivatives which are one of the main downsides of classical EM timeintegration schemes. The newly proposed scheme inherits the advantages of EM schemes recentlypublished in the context of thermo-elasticity and electro-mechanics, whilst extending to the moregeneric case of nonlinear thermo-electro-mechanics. Furthermore, the manuscript delves intosuitable convexity/concavity restrictions that thermo-electro-mechanical strain energy functionsmust comply with in order to yield physically and mathematically admissible solutions. Finally, aseries of numerical examples will be presented in order to demonstrate robustness and numericalstability properties of the new EM scheme.
published_date 2022-02-01T04:15:09Z
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