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A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics

Marlon Franke Orcid Logo, Felix Zähringer, Moritz Hille, Rogelio Ortigosa, Peter Betsch Orcid Logo, Antonio Gil Orcid Logo

International Journal for Numerical Methods in Engineering, Volume: 124, Issue: 10, Pages: 2135 - 2170

Swansea University Author: Antonio Gil Orcid Logo

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DOI (Published version): 10.1002/nme.7209

Abstract

A novel mixed framework and energy-momentum consistent integration scheme in the field of coupled nonlinear thermo-electro-elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of poly-convex strain energy functions. For this elastodynamic...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa62464
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spelling v2 62464 2023-01-27 A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2023-01-27 CIVL A novel mixed framework and energy-momentum consistent integration scheme in the field of coupled nonlinear thermo-electro-elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of poly-convex strain energy functions. For this elastodynamic framework, the properties of the so-called tensor cross product are exploited to derive a mixed formulation via a Hu-Washizu type extension of the strain energy function. Afterwards, a general path to incorporate non-potential problems for mixed formulations is demonstrated. To this end, the strong form of the mixed framework is derived and supplemented with the energy balance as well as Maxwell’s equations neglecting magnetic and time dependent effects. By additionally choosing an appropriate energy function, this procedure leads to a fully coupled thermo-electro-elastodynamic formulation which benefits from the properties of the underlying mixed framework. In addition, the proposed mixed framework facilitates the design of a new energy-momentum consistent time integration scheme by employing discrete derivatives in the sense of Gonzalez. A one-step integration scheme of second-order accuracy is obtained which is shown to be stable even for large time steps. Eventually, the performance of the novel formulation is demonstrated in several numerical examples. Journal Article International Journal for Numerical Methods in Engineering 124 10 2135 2170 Wiley 0029-5981 1097-0207 Nonlinear thermo-electro-elastodynamics, polyconvexity, tensor cross product, non-potential mixed formulation, energy-momentum scheme 30 5 2023 2023-05-30 10.1002/nme.7209 http://dx.doi.org/10.1002/nme.7209 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University Other DFG, German Research Foundation, project number 443238377 21132/SF/19, Fundación Séneca, Región de Murcia Fundación Séneca, grant 20911/PI/18, and PID2021-125687OA-I00 2023-06-02T15:52:33.9433951 2023-01-27T13:25:14.0714433 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Marlon Franke 0000-0002-6695-6289 1 Felix Zähringer 2 Moritz Hille 3 Rogelio Ortigosa 4 Peter Betsch 0000-0002-0596-2503 5 Antonio Gil 0000-0001-7753-1414 6 Under embargo Under embargo 2023-01-27T13:41:28.2939107 Output 13760864 application/pdf Accepted Manuscript true 2024-01-27T00:00:00.0000000 true eng 62464__27674__46a9d4b6775248b18c3f9ac5dff7c518.pdf 62464.pdf 2023-06-01T15:27:50.7903871 Output 3968503 application/pdf Version of Record true This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. true eng http://creativecommons.org/licenses/by/4.0/
title A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics
spellingShingle A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics
Antonio Gil
title_short A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics
title_full A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics
title_fullStr A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics
title_full_unstemmed A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics
title_sort A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Antonio Gil
author2 Marlon Franke
Felix Zähringer
Moritz Hille
Rogelio Ortigosa
Peter Betsch
Antonio Gil
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 124
container_issue 10
container_start_page 2135
publishDate 2023
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.7209
publisher Wiley
college_str Faculty of Science and Engineering
hierarchytype
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
url http://dx.doi.org/10.1002/nme.7209
document_store_str 1
active_str 0
description A novel mixed framework and energy-momentum consistent integration scheme in the field of coupled nonlinear thermo-electro-elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of poly-convex strain energy functions. For this elastodynamic framework, the properties of the so-called tensor cross product are exploited to derive a mixed formulation via a Hu-Washizu type extension of the strain energy function. Afterwards, a general path to incorporate non-potential problems for mixed formulations is demonstrated. To this end, the strong form of the mixed framework is derived and supplemented with the energy balance as well as Maxwell’s equations neglecting magnetic and time dependent effects. By additionally choosing an appropriate energy function, this procedure leads to a fully coupled thermo-electro-elastodynamic formulation which benefits from the properties of the underlying mixed framework. In addition, the proposed mixed framework facilitates the design of a new energy-momentum consistent time integration scheme by employing discrete derivatives in the sense of Gonzalez. A one-step integration scheme of second-order accuracy is obtained which is shown to be stable even for large time steps. Eventually, the performance of the novel formulation is demonstrated in several numerical examples.
published_date 2023-05-30T15:52:32Z
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score 11.013148

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