A physics-informed evolutionary regression framework for constitutive modelling of sand

Several constitutive models are designed to capture the complex behaviour of soil under various conditions. Traditionally, the theoretical frameworks of the models are empirically derived from limited experimental data and specific soil types and stress paths. However, these models are limited by soil complexity behaviour and the difficulty of measuring parameters experimentally, which is time-consuming and costly. Machine learning (ML)-based approaches can develop constitutive models, offering solutions to complex geomaterial behaviours. However, insufficient integration of relevant physics and thermodynamic laws into ML-based material models leads to poor extrapolation and physical inconsistency. The lack of thermodynamic consistency may affect the models’ robustness and predictive reliability when applied beyond the training domain. Accordingly, this study presents a novel thermodynamically consistent constitutive model for predicting the plastic behaviour of sand, formulated within a Hypoplasticity framework and developed using a physics-informed evolutionary regression (PIER) approach. Main features are I) enforcing a non-negative dissipation rate to guarantee thermodynamical consistency, II) enhancing extrapolation capability outside of the training range, and III) improving computational efficiency and interpretability via explicit stress–strain equations compared to black-box neural network models. The PIER model is validated against experimental data from monotonic drained triaxial compression tests on sand samples across a wide range of densities and stress states. They demonstrate the broad applicability of the PIER for predicting contractive and dilative behaviours without the additional state variables or material parameters. Relative to the Hypoplasticity constitutive model, the proposed approach demonstrates comparable predictive performance while maintaining consistency with thermodynamic principles.