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A new energy–momentum time integration scheme for non-linear thermo-mechanics

R. Ortigosa, Antonio Gil Orcid Logo, J. Martínez-Frutos, M. Franke, J. Bonet

Computer Methods in Applied Mechanics and Engineering, Volume: 372

Swansea University Author: Antonio Gil Orcid Logo

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Abstract

The aim of this paper is the design a new one-step implicit and thermodynamically consistent Energy–Momentum (EM) preserving time integration scheme for the simulation of thermo-elastic processes undergoing large deformations and temperature fields. Following Bonet et al. (2020), we consider well-po...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa55074
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spelling 2020-12-02T17:01:18.6553963 v2 55074 2020-08-26 A new energy–momentum time integration scheme for non-linear thermo-mechanics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2020-08-26 CIVL The aim of this paper is the design a new one-step implicit and thermodynamically consistent Energy–Momentum (EM) preserving time integration scheme for the simulation of thermo-elastic processes undergoing large deformations and temperature fields. Following Bonet et al. (2020), we consider well-posed constitutive models for the entire range of deformations and temperature. In that regard, the consideration of polyconvexity inspired constitutive models and a new tensor cross product algebra are shown to be crucial in order to derive the so-called discrete derivatives, fundamental for the construction of the algorithmic derived variables, namely the second Piola–Kirchoff stress tensor and the entropy (or the absolute temperature). The proposed scheme inherits the advantages of the EM scheme recently published by Franke et al. (2018), whilst resulting in a simpler scheme from the implementation standpoint. A series of numerical examples will be presented in order to demonstrate the robustness and applicability of the new EM scheme. Although the examples presented will make use of a temperature-based version of the EM scheme (using the Helmholtz free energy as the thermodynamical potential and the temperature as the thermodynamical state variable), we also include in an Appendix an entropy-based analogue EM scheme (using the internal energy as the thermodynamical potential and the entropy as the thermodynamical state variable). Journal Article Computer Methods in Applied Mechanics and Engineering 372 Elsevier BV 0045-7825 Finite element method, Nonlinear thermo-elastodynamics, Energy–momentum scheme, Structure-preserving discretisation 1 12 2020 2020-12-01 10.1016/j.cma.2020.113395 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-12-02T17:01:18.6553963 2020-08-26T13:36:26.7131542 College of Engineering Engineering R. Ortigosa 1 Antonio Gil 0000-0001-7753-1414 2 J. Martínez-Frutos 3 M. Franke 4 J. Bonet 5 55074__18051__b2a34fd4bce044ceb02d8dcdf065e887.pdf 55074.pdf 2020-08-26T13:40:07.5707757 Output 28421403 application/pdf Accepted Manuscript true 2021-09-28T00:00:00.0000000 Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true English
title A new energy–momentum time integration scheme for non-linear thermo-mechanics
spellingShingle A new energy–momentum time integration scheme for non-linear thermo-mechanics
Antonio, Gil
title_short A new energy–momentum time integration scheme for non-linear thermo-mechanics
title_full A new energy–momentum time integration scheme for non-linear thermo-mechanics
title_fullStr A new energy–momentum time integration scheme for non-linear thermo-mechanics
title_full_unstemmed A new energy–momentum time integration scheme for non-linear thermo-mechanics
title_sort A new energy–momentum time integration scheme for non-linear thermo-mechanics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil_***_0000-0001-7753-1414
author Antonio, Gil
author2 R. Ortigosa
Antonio Gil
J. Martínez-Frutos
M. Franke
J. Bonet
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 372
publishDate 2020
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2020.113395
publisher Elsevier BV
college_str College of Engineering
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hierarchy_top_title College of Engineering
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hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description The aim of this paper is the design a new one-step implicit and thermodynamically consistent Energy–Momentum (EM) preserving time integration scheme for the simulation of thermo-elastic processes undergoing large deformations and temperature fields. Following Bonet et al. (2020), we consider well-posed constitutive models for the entire range of deformations and temperature. In that regard, the consideration of polyconvexity inspired constitutive models and a new tensor cross product algebra are shown to be crucial in order to derive the so-called discrete derivatives, fundamental for the construction of the algorithmic derived variables, namely the second Piola–Kirchoff stress tensor and the entropy (or the absolute temperature). The proposed scheme inherits the advantages of the EM scheme recently published by Franke et al. (2018), whilst resulting in a simpler scheme from the implementation standpoint. A series of numerical examples will be presented in order to demonstrate the robustness and applicability of the new EM scheme. Although the examples presented will make use of a temperature-based version of the EM scheme (using the Helmholtz free energy as the thermodynamical potential and the temperature as the thermodynamical state variable), we also include in an Appendix an entropy-based analogue EM scheme (using the internal energy as the thermodynamical potential and the entropy as the thermodynamical state variable).
published_date 2020-12-01T04:23:24Z
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