Continuum-discrete multiscale strategies for simulating granular materials aim to combine the computational efficiency of a continuous method at the macroscale with the accuracy of a discrete method at the micro level. However, oftentimes this approach still falls short in terms of efficiency as the discrete response needs to be solved continuously at several RVEs. Therefore, surrogate models based on machine learning have recently been employed to predict the discrete response. In this presentation, we introduce a data-driven continuum-discrete multiscale methodology for thermomechanical analysis of packed granular media. In particular, we employ the Finite Volume Method to solve the macroscale problem and the DEM to compute the microscale response in RVEs. Therefore, several RVE simulations are performed offline, whose discrete solutions are homogenized. A database of microscale solutions is then created to relate microstructure properties with the variables required in the continuous method at the macroscale. This database is used to train an Artificial Neural Network, which serves as a surrogate model for the continuous method to predict the homogenized microscale response without resorting to online DEM simulations. The focus of this presentation is on thermal effects, including heat conduction and thermal expansion. To simulate these phenomena, we built surrogate models that relate the effective thermal conductivity of granular materials with their local porosity and fabric, as well as the change in these last two properties with the deformation of the particles due to temperature change. In addition, we show the effects of bulk motions within granular media during thermal expansion, which is a phenomenon that cannot be captured by periodic RVEs. Therefore, we simulate this behavior at the macroscale, with a simplistic model based on the mass transport equation. The presented examples, even restricted to two-dimensional analyses, confirm the potential of the methodology as a rapid and accurate predictive tool.

The shear-transformation-zone (STZ) theory is a mesoscale-based approach that attributes the macroscopic plastic deformation of materials to the flipping, creation, and annihilation of mesoscopic structures known as STZs. The theory has been highly successful in capturing the viscoplastic shear behaviors of metallic glasses. In this study, the potential of the STZ theory in constitutive modeling of both fine-grained and coarse-grained granular soils is demonstrated, considering essential soil properties such as dilatancy, pressure sensitivity, and critical state. The study provides a fresh perspective for understanding the yielding mechanism and hardening of soils through the lens of mesostructural evolution.

Granular materials exhibit complex behaviors influenced by particle interactions, contact forces, and temporal dynamics. In this work, we propose a novel Temporal Graph Neural Network (TGN)-based simulator for accurately modeling granular material dynamics. Our approach represents granular systems as temporal graphs, capturing evolving particle interactions over time. The TGN architecture learns temporal dependencies and non-linear relationships among granular particles, enabling accurate simulation of phenomena like granular flows. Specifically, the discrete numerical simulations of column collapse by using hiearchical multiscale modeling are conducted as training and test data for the TGN-based simulatior. The hiearachical multiscale modeling approach couples the material point method (MPM) with the discrete element method (DEM), where the mechanical response of a representative volume element (RVE) simulated by DEM offers constitutive relations to MPM bypassing any continuum-based constitutive models. The TGN-based simulator learns the interactions among material points simulated in MPM at discrete time instants such that it is capable of simulating granular flows under given initial and boundary conditions. In conclusion, our work presents a versatile TGN-based simulator for granular materials, providing a powerful tool for efficiently simulating granular flows. It can be further integrated into digital twin systems for real time simulations.

Acknowledgments

This work was supported by Research Grants Council of Hong Kong (by GRF Project No. 16206322), and the Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone (Grant No. HZQBKCZYB-2020083).

Data-driven methods offer a promising framework for constitutive modeling of materials. However, traditional data-driven models suffer from insufficient generalization capabilities and may produce predictions that contradict established physical laws due to scarce training data. To address these challenges, this study introduces a thermodynamics-informed neural network (TINN) for the elastoplastic constitutive modeling of granular materials. Based on thermodynamic elastoplastic theory, the TINN model integrates elastic free energy, stored plastic work, and dissipation. By incorporating a path-dependent recurrent neural network (RNN) and three sub-fully connected neural networks, the TINN model effectively captures the mechanical response and energy evolution of sheared granular materials. The total loss function of TINN combines data-driven and physics-informed components. The TINN's effectiveness and generalization capabilities are evaluated by testing it on diverse datasets, including both simulated and experimental data. The simulated virtual data are derived from existing elastoplastic models or discrete element method (DEM) simulations employing stress probing techniques. By modifying the loss function, TINN can be easily applied to the prediction of drained and undrained shear tests of sand. It accurately captures the mechanical response of sand and implicitly satisfies the thermodynamic laws. The results demonstrate that the TINN model excels in both generalization and robustness, outperforming pure data-driven methods in terms of performance and reliability.