Bridging length scales in granular materials using convolutional neural networks

Abstract

Granular materials are complex systems whose macroscopic mechanics are governed by particles at the grain-scale. The need to understand their grain-scale behavior has motivated significant experimental and modeling efforts. Bridging the grain-scale with the continuum scale is important in order to develop constitutive theories based on grain-scale behavior, as well as for interpreting the results of grain-scale models and experiments from a macroscopic context. In this work, we present a new data-driven framework based on convolutional neural networks to bridge the grain-scale and continuum scale in granular materials. We use this framework to obtain a micromechanical model of stress and demonstrate that spatial correlations at the grain-scale are critical for bridging length scales. Our results suggest that it is possible to learn data-driven relationships between the grain-scale and macroscale even if we have limited knowledge about the physical state of a granular system. We also observed that it is possible to train a model to predict macroscopic stress using only a subset of the contact data for each time step. This points to the discovery of a new pattern in granular systems, whereby any spatially correlated subset of contact data is sufficient to model macroscopic stress, regardless of how much force they may be carrying. Finally, we demonstrated that our framework is robust with potential for generalizability in time.