A 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 multi-relaxation 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.