Neural networks meet hyperelasticity: A monotonic approach

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 simulations. The findings of our work suggest that monotonicity could be a promising alternative to more constrained PANN models that include both 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.