Neural Networks as Physics-Consistent Surrogates: An \textit{Explainable AI} Validation Framework for Learning Constitutive Relations

Abstract: This paper presents a Physics-\textit{Explainable AI} (XAI) framework to validate and interpret neural networks for the constitutive modeling of solid materials. The study bridges the gap between data-driven models and continuum mechanics by applying a suite of explainability methods to neural networks trained on three distinct material behaviors: hyperelasticity (\textit{Mooney-Rivlin}), elastoplasticity (\textit{Chaboche}), and viscoelasticity (\textit{Fractional Zener}). First, high-fidelity surrogate models, including dense feed-forward networks, LSTMs, and GRUs, are trained on synthetically generated data to accurately capture complex material responses. The core of the work then employs XAI techniques to "open the black box" and confirm that the networks learn physically meaningful principles. For hyperelasticity, gradient-based attributions (\textit{Grad Input} (GI)) successfully match the analytical tangent modulus, proving the network learned material stiffness. For elastoplasticity, \textit{SHapley Additive exPlanations} (SHAP) and \textit{Principal Component Analysis} (PCA) demonstrate the \textit{Recurrent Neural Network} (RNN) internalizes path-dependent memory, with SHAP identifying \textit{plastic strain} as the dominant feature governing the stress prediction. For viscoelasticity, latent-space and wavelet analyses of the \textit{Gated Recurrent Unit. } GRU layers reveal a clear temporal hierarchy, with different layers encoding instantaneous elastic response, intermediate relaxation, and long-term fractional memory. Ultimately, the study demonstrates that the XAI framework can verify that the neural networks are not merely curve-fitting but are, in fact, learning the underlying physical mechanisms of stiffness, history-dependence, and temporal damping.