t-PiNet: A thermodynamics-informed hierarchical learning for discovering constitutive relations of geomaterials

More attention has been paid to integrating existing knowledge with data to understand the complex mechanical behaviour of geomaterials, but it incurs scepticism and criticism on its generalizability and robustness. Moreover, a common mistake in current data-driven modelling frameworks is that history internal state variables and stress are known upfront and taken as inputs, which violates reality, overestimates model accuracy and cannot be applied to modelling experimental data. To bypass these limitations, thermodynamically consistent hierarchical learning (t-PiNet) with iterative computation is tailored for identifying constitutive relations with applications to geomaterials. This hierarchical structure includes a recurrent neural network to identify internal state variables, followed by using a feedforward neural network to predict Helmholtz free energy, which can further derive dissipated energy and stress. The thermodynamic consistency of t-PiNet is comprehensively validated on the synthetic data generated by von Mises and modified Cam-clay models. Subsequently, the potential of t-PiNet in practice is confirmed by applying it to experiments on kaolin clay. The results indicate neural networks embedded by thermodynamics perform better on the loading space beyond the training data compared with the conventional pure neural network-based modelling method. t-PiNet not only offers a way to identify the mechanical behaviour of materials from experiments but also ensures it is further integrated with numerical methods for simulating engineering-scale problems.