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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
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa70540
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 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.
College: Faculty of Science and Engineering
Funders: 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.
Start Page: 105900

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