Enforcing Physics in Hyperelasticity Modeling Using Kolmogorov-Arnold Networks

Rubber-like materials exhibit complex mechanical behavior due to their chain-like macromolecular structure. Accurate modeling of their hyperelastic properties is crucial for predictive analysis and design of elastomeric products. Traditional phenomenological models are physically well-posed but often sacrifice accuracy, while data-driven methods fit complex behaviors well but lack physics constraints. In this paper, we develop a framework using the recently proposed Kolmogorov-Arnold Networks (KANs) to combine data-driven flexibility with physical consistency and interpretability in hyperelasticity modeling. We demonstrate the effectiveness of our approach by modeling Treloar’s experimental data and show that our KAN-based model can capture the material behavior accurately while ensuring physical soundness.