Physics-Informed Neural Network Engines to Predict Viscoelastic Behavior of Elastomers/Hydrogels

Abstract This study presents a physics-informed neural network (PINN) framework to model the nonlinear viscoelastic behavior of polymers and soft materials. By integrating principles from polymer science, statistical physics, and continuum mechanics, the model captures key inelastic features such as permanent set, strain rate dependence, and multirelaxation behavior. The formulation is based on an eight-chain network representation, with a rheological model composed of a rate-independent hyperelastic spring and a rate-dependent Maxwell element. To improve generalizability and reduce computational cost, the model employs machine-learned (ML) surrogate free energy functions trained with minimal experimental data. These surrogate models embed physical constraints, such as thermodynamic consistency and polyconvexity, directly into the learning architecture. As a result, the proposed framework outperforms conventional constitutive models in predictive accuracy and training efficiency. The approach is validated against experimental data for elastomers, hydrogels, and biological tissues across varying strain rates. Despite its complex formulation, the numerical implementation remains accessible and efficient, making it suitable for a wide range of soft material applications. The model can be easily integrated in elastomer aging-prediction software such as K-Load 2. The viscoelastic model developed here is intended for open-source incorporation into broader digital-twin frameworks for simulating the nonlinear viscoelastic response of soft materials, see Github for source codes. This ensures future reproducibility and facilitates industrial deployment while maintaining full scientific independence of the present study.