Neural networks meet hyperelasticity: A monotonic approach

作者：Dominik K. Klein, Mokarram Hossain, Konstantin Kikinov, Maximilian Kannapinn, Stephan Rudykh, Antonio J. Gil · 发表于：European Journal of Mechanics - A/Solids · 年份：2025 · DOI：10.1016/j.euromechsol.2025.105900 · 被引用次数：7 · 研究领域：Elasticity and Material Modeling、Model Reduction and Neural Networks、Elasticity and Wave Propagation

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 synthesized 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 right Cauchy–Green tensor. In incompressible hyperelasticity, this is a relaxed version of the ellipticity (or rank-one 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 simul...