Distinguish the calibration of conventional and data-driven constitutive model: the role of state boundary surfaces

In conventional constitutive models for granular materials, calibration involves estimating a few parameters within known mathematical expressions. In contrast, data-driven constitutive models couple the model structure and parameters. Addressing this fundamental difference, the development of constitutive models based on Physics-encoded Neural Networks (PeNN) is guided from the perspective of conventional model development, highlighting similarities and differences. The crucial physical information that influences PeNN is explained, and the incorporation of three key state boundary surfaces in pressure–porosity space—critical state, loosest state, and densest state—via physics-informed deep learning is detailed. Physics-informed calibration is performed using the augmented Lagrangian method; then, the calibrated models undergo extensive drained and undrained simulations. Results indicate that using only physical information from state boundary surfaces, without data within these boundaries, fails to calibrate data-driven models; thus, boundary surface information represents partial physical information. While combining partial physical information with reasonably distributed data can improve model development under limited experimental data, adding more partial physical information and data does not necessarily enhance the results. The finding aims to bridge the gap between conventional and data-driven constitutive models, hopefully increasing the reliability and interpretability of data-driven models.