A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics

Ortigosa, R.; Martínez-Frutos, J.; Pérez-Escolar, A.; Castañar, I.; Hellmer, Niklas; Gil, Antonio

doi:10.1016/j.cma.2025.117741

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A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics

R. Ortigosa

, J. Martínez-Frutos

, A. Pérez-Escolar, I. Castañar

, Niklas Hellmer, Antonio Gil

Computer Methods in Applied Mechanics and Engineering, Volume: 437, Start page: 117741

Swansea University Authors: Niklas Hellmer, Antonio Gil

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DOI (Published version): 10.1016/j.cma.2025.117741

Abstract

This manuscript introduces a novel neural network-based computational framework for constistutive modelling of thermo-electro-mechanically coupled materials at finite strains, with four key innovations: (i) It supports calibration of neural network models with various input forms, such as Ψnn(F, E0,...

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Published in:	Computer Methods in Applied Mechanics and Engineering
ISSN:	0045-7825
Published:	Elsevier BV 2025
Online Access:	Check full text
URI:	https://cronfa.swan.ac.uk/Record/cronfa68679

first_indexed	2025-01-13T20:35:09Z
last_indexed	2025-03-12T05:34:57Z
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These models comply with physical laws and material symmetries by utilizing isotropic or anisotropic invariants corresponding to the material’s symmetry group. (ii) A calibration approach is developed for the case of experimental data, where entropy η is typically unmeasurable. (iii) The framework accommodates models like enn(F, D0, η), specially convenient for the imposition of polyconvexity across the three physics involved. A detailed calibration study is conducted evaluating various neural network architectures and considering a large variety of ground truth thermo-electro-mechanical constitutive models. The results demonstrate excellent predictive performance on larger datasets, validated through complex finite element simulations using both ground truth and neural network-based models. 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Martínez-Frutos and I. Castañar acknowledge the support of grant PID2022-141957OA-C22 funded by MICIU/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. R. Ortigosa and J. Martínez-Frutos also acknowledge the support provided by the Autonomous Community of the Region of Murcia, Spain through the programme for the development of scientific and technical research by competitive groups (21996/PI/22), included in the Regional Program for the Promotion of Scientific and Technical Research of Fundacion Seneca - Agencia de Ciencia Tecnologia de la Region de Murcia. N. Ellmer and A. J. Gil acknowledge the support provided by the defence, science and technology laboratory (Dstl), United Kingdom. A. J. 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spelling	2025-03-11T14:08:03.4582997 v2 68679 2025-01-13 A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics a4ee2ab85ef1dbcd71b56b2dab40f6bb Niklas Hellmer Niklas Hellmer true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2025-01-13 MACS This manuscript introduces a novel neural network-based computational framework for constistutive modelling of thermo-electro-mechanically coupled materials at finite strains, with four key innovations: (i) It supports calibration of neural network models with various input forms, such as Ψnn(F, E0, θ), enn(F, D0, η), Υnn(F, E0, η), or Γnn(F, D0, θ), with F representing the deformation gradient tensor, E0 and D0 the electric field and electric displacement field, respectively and finally, θ and η, the temperature and entropy fields. These models comply with physical laws and material symmetries by utilizing isotropic or anisotropic invariants corresponding to the material’s symmetry group. (ii) A calibration approach is developed for the case of experimental data, where entropy η is typically unmeasurable. (iii) The framework accommodates models like enn(F, D0, η), specially convenient for the imposition of polyconvexity across the three physics involved. A detailed calibration study is conducted evaluating various neural network architectures and considering a large variety of ground truth thermo-electro-mechanical constitutive models. The results demonstrate excellent predictive performance on larger datasets, validated through complex finite element simulations using both ground truth and neural network-based models. Crucially, the framework can be straightforwardly extended to scenarios involving other physics. Journal Article Computer Methods in Applied Mechanics and Engineering 437 117741 Elsevier BV 0045-7825 Neural networks; Machine learning; Thermo-electro-mechanics; Dielectric elastomers; Finite elements 15 3 2025 2025-03-15 10.1016/j.cma.2025.117741 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University R. Ortigosa, J. Martínez-Frutos and I. Castañar acknowledge the support of grant PID2022-141957OA-C22 funded by MICIU/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. R. Ortigosa and J. Martínez-Frutos also acknowledge the support provided by the Autonomous Community of the Region of Murcia, Spain through the programme for the development of scientific and technical research by competitive groups (21996/PI/22), included in the Regional Program for the Promotion of Scientific and Technical Research of Fundacion Seneca - Agencia de Ciencia Tecnologia de la Region de Murcia. N. Ellmer and A. J. Gil acknowledge the support provided by the defence, science and technology laboratory (Dstl), United Kingdom. A. J. Gil acknowledges the financial support provided by the Leverhulme Trust, United Kingdom . 2025-03-11T14:08:03.4582997 2025-01-13T12:32:52.5765638 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering R. Ortigosa 0000-0002-4542-2237 1 J. Martínez-Frutos 0000-0002-7112-3345 2 A. Pérez-Escolar 3 I. Castañar 0000-0003-4139-9380 4 Niklas Hellmer 5 Antonio Gil 0000-0001-7753-1414 6 68679__33289__b55935d79c6841dca7563c9c29c24b32.pdf 68679.pdf 2025-01-13T12:38:40.3650444 Output 38261862 application/pdf Accepted Manuscript true Author accepted manuscript document released under the terms of a Creative Commons CC-BY licence using the Swansea University Research Publications Policy (rights retention). true eng https://doi.org/10.1016/j.cma.2025.117741
title	A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics
spellingShingle	A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics Niklas Hellmer Antonio Gil
title_short	A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics
title_full	A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics
title_fullStr	A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics
title_full_unstemmed	A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics
title_sort	A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics
author_id_str_mv	a4ee2ab85ef1dbcd71b56b2dab40f6bb 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv	a4ee2ab85ef1dbcd71b56b2dab40f6bb_*_Niklas Hellmer 1f5666865d1c6de9469f8b7d0d6d30e2_*_Antonio Gil
author	Niklas Hellmer Antonio Gil
author2	R. Ortigosa J. Martínez-Frutos A. Pérez-Escolar I. Castañar Niklas Hellmer Antonio Gil
format	Journal article
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container_volume	437
container_start_page	117741
publishDate	2025
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issn	0045-7825
doi_str_mv	10.1016/j.cma.2025.117741
publisher	Elsevier BV
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description	This manuscript introduces a novel neural network-based computational framework for constistutive modelling of thermo-electro-mechanically coupled materials at finite strains, with four key innovations: (i) It supports calibration of neural network models with various input forms, such as Ψnn(F, E0, θ), enn(F, D0, η), Υnn(F, E0, η), or Γnn(F, D0, θ), with F representing the deformation gradient tensor, E0 and D0 the electric field and electric displacement field, respectively and finally, θ and η, the temperature and entropy fields. These models comply with physical laws and material symmetries by utilizing isotropic or anisotropic invariants corresponding to the material’s symmetry group. (ii) A calibration approach is developed for the case of experimental data, where entropy η is typically unmeasurable. (iii) The framework accommodates models like enn(F, D0, η), specially convenient for the imposition of polyconvexity across the three physics involved. A detailed calibration study is conducted evaluating various neural network architectures and considering a large variety of ground truth thermo-electro-mechanical constitutive models. The results demonstrate excellent predictive performance on larger datasets, validated through complex finite element simulations using both ground truth and neural network-based models. Crucially, the framework can be straightforwardly extended to scenarios involving other physics.
published_date	2025-03-15T08:13:07Z
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A generalized theory for physics-augmented neural networks in finite strain thermo-electro-mechanics

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