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Neural networks meet hyperelasticity: A monotonic approach

Dominik K. Klein Orcid Logo, Mokarram Hossain Orcid Logo, Konstantin Kikinov, Maximilian Kannapinn Orcid Logo, Stephan Rudykh Orcid Logo, Antonio Gil Orcid Logo

European Journal of Mechanics - A/Solids, Volume: 116, Start page: 105900

Swansea University Authors: Mokarram Hossain Orcid Logo, Antonio Gil Orcid Logo

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DOI (Published version): 10.1016/j.euromechsol.2025.105900

Abstract

We propose and apply a novel parametrized physics-augmented neural network (PANN) constitutive model to experimental data of rubber-like materials whose behavior depends on manufacturing parameters. For this, we conduct experimental investigations on a 3D printed digital material at different mix ra...

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Published in: European Journal of Mechanics - A/Solids
ISSN: 0997-7538
Published: Elsevier BV 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa70540
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Using this relaxed ellipticity condition, the monotonic PANN model provides more flexibility than comparable approaches from literature that are elliptic by construction by formulating the PANN model to be both monotonic and convex. The monotonic PANN yields excellent results for a variety of different materials with largely varying qualitative and quantitative stress behavior. Although calibrated on uniaxial tensile data only, it leads to a stable numerical behavior of 3D finite element simulations. The findings of our work suggest that monotonicity could be a promising alternative to more constrained PANN models that includeboth convexity and monotonicity, in particular, when considering highly nonlinear and parametrized materials. This paper has three key novelties: (1) We propose a novel parametrized hyperelastic PANN model that is monotonic in both strain invariants and additional parameters. 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spelling 2025-10-30T15:34:11.2946784 v2 70540 2025-09-30 Neural networks meet hyperelasticity: A monotonic approach 140f4aa5c5ec18ec173c8542a7fddafd 0000-0002-4616-1104 Mokarram Hossain Mokarram Hossain true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2025-09-30 ACEM We propose and apply a novel parametrized physics-augmented neural network (PANN) constitutive model to experimental data of rubber-like materials whose behavior depends on manufacturing parameters. For this, we conduct experimental investigations on a 3D printed digital material at different mix ratios and consider several datasets from literature, including Ecoflex at different Shore hardness, a photocured 3D printing material at different grayscale values, and a EPDM rubber synthesised with different amounts of curatives. We introduce a parametrized hyperelastic PANN model which can represent material behavior at different manufacturing parameters. The proposed model fulfills common mechanical conditions of hyperelasticity. In addition, the hyperelastic potential of the proposed model is monotonic in isotropic isochoric strain invariants of the rightCauchy-Green tensor. In incompressible hyperelasticity, this is a relaxed version of the ellipticity (or rankone convexity) condition. Using this relaxed ellipticity condition, the monotonic PANN model provides more flexibility than comparable approaches from literature that are elliptic by construction by formulating the PANN model to be both monotonic and convex. The monotonic PANN yields excellent results for a variety of different materials with largely varying qualitative and quantitative stress behavior. Although calibrated on uniaxial tensile data only, it leads to a stable numerical behavior of 3D finite element simulations. The findings of our work suggest that monotonicity could be a promising alternative to more constrained PANN models that includeboth convexity and monotonicity, in particular, when considering highly nonlinear and parametrized materials. This paper has three key novelties: (1) We propose a novel parametrized hyperelastic PANN model that is monotonic in both strain invariants and additional parameters. (2) We apply parametrized hyperelastic PANN models to experimental data of rubber-like materials whose behavior depends on manufacturing parameters. (3) With these highly nonlinear datasets, we benchmark the monotonic PANN model against existing PANN model formulations from literature. Furthermore, we compare the performance of different PANN models in terms of material stability and performance in finite element simulations. Journal Article European Journal of Mechanics - A/Solids 116 105900 Elsevier BV 0997-7538 1 3 2026 2026-03-01 10.1016/j.euromechsol.2025.105900 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University Another institution paid the OA fee D.K. Klein acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Germany, project number 492770117) and support by a fellowship of the German Academic Exchange Service (DAAD). D.K. Klein and M. Kannapinn acknowledge support by the Graduate School of Computational Engineering at TU Darmstadt. M. Hossain acknowledges the support of the EPSRC, United Kingdom (EP/Z535710/1) and the Royal Society (UK) through the International Exchange Grant (IEC/NSFC/211316). S. Rudykh and K. Kikinov acknowledge support of the European Research Council (ERC) through Grant No. 852281 – MAGIC. A.J. Gil acknowledges the financial support provided by UK Defence, Science and Technology Laboratory through grant DSTLX 10000157545 and The Leverhulme Trust, United Kingdom. 2025-10-30T15:34:11.2946784 2025-09-30T08:49:57.4678746 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Dominik K. Klein 0000-0002-1722-8330 1 Mokarram Hossain 0000-0002-4616-1104 2 Konstantin Kikinov 3 Maximilian Kannapinn 0000-0001-9342-0802 4 Stephan Rudykh 0000-0002-4568-8326 5 Antonio Gil 0000-0001-7753-1414 6 70540__35513__347efb1acf1a448b8e63938b7fab3caf.pdf 70540.VoR.pdf 2025-10-30T15:31:44.7958117 Output 4684235 application/pdf Version of Record true © 2025 The Authors. This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/
title Neural networks meet hyperelasticity: A monotonic approach
spellingShingle Neural networks meet hyperelasticity: A monotonic approach
Mokarram Hossain
Antonio Gil
title_short Neural networks meet hyperelasticity: A monotonic approach
title_full Neural networks meet hyperelasticity: A monotonic approach
title_fullStr Neural networks meet hyperelasticity: A monotonic approach
title_full_unstemmed Neural networks meet hyperelasticity: A monotonic approach
title_sort Neural networks meet hyperelasticity: A monotonic approach
author_id_str_mv 140f4aa5c5ec18ec173c8542a7fddafd
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 140f4aa5c5ec18ec173c8542a7fddafd_***_Mokarram Hossain
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Mokarram Hossain
Antonio Gil
author2 Dominik K. Klein
Mokarram Hossain
Konstantin Kikinov
Maximilian Kannapinn
Stephan Rudykh
Antonio Gil
format Journal article
container_title European Journal of Mechanics - A/Solids
container_volume 116
container_start_page 105900
publishDate 2026
institution Swansea University
issn 0997-7538
doi_str_mv 10.1016/j.euromechsol.2025.105900
publisher Elsevier BV
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
document_store_str 1
active_str 0
description We propose and apply a novel parametrized physics-augmented neural network (PANN) constitutive model to experimental data of rubber-like materials whose behavior depends on manufacturing parameters. For this, we conduct experimental investigations on a 3D printed digital material at different mix ratios and consider several datasets from literature, including Ecoflex at different Shore hardness, a photocured 3D printing material at different grayscale values, and a EPDM rubber synthesised with different amounts of curatives. We introduce a parametrized hyperelastic PANN model which can represent material behavior at different manufacturing parameters. The proposed model fulfills common mechanical conditions of hyperelasticity. In addition, the hyperelastic potential of the proposed model is monotonic in isotropic isochoric strain invariants of the rightCauchy-Green tensor. In incompressible hyperelasticity, this is a relaxed version of the ellipticity (or rankone convexity) condition. Using this relaxed ellipticity condition, the monotonic PANN model provides more flexibility than comparable approaches from literature that are elliptic by construction by formulating the PANN model to be both monotonic and convex. The monotonic PANN yields excellent results for a variety of different materials with largely varying qualitative and quantitative stress behavior. Although calibrated on uniaxial tensile data only, it leads to a stable numerical behavior of 3D finite element simulations. The findings of our work suggest that monotonicity could be a promising alternative to more constrained PANN models that includeboth convexity and monotonicity, in particular, when considering highly nonlinear and parametrized materials. This paper has three key novelties: (1) We propose a novel parametrized hyperelastic PANN model that is monotonic in both strain invariants and additional parameters. (2) We apply parametrized hyperelastic PANN models to experimental data of rubber-like materials whose behavior depends on manufacturing parameters. (3) With these highly nonlinear datasets, we benchmark the monotonic PANN model against existing PANN model formulations from literature. Furthermore, we compare the performance of different PANN models in terms of material stability and performance in finite element simulations.
published_date 2026-03-01T05:31:05Z
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score 11.089386

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