Quantitative Rheological Model for Granular Materials: The Importance of Particle Size

Abstract

One of the great puzzles in describing the constitutive behavior of flowing granular media is the role of grain size. Even for relatively simple, stiff, round grains, the length scale of grains themselves is large enough to influence the continuum rheology, causing departures from local model predictions in the presence of flow heterogeneity and thin geometries. Here we present the development of a particular nonlocal model, the nonlocal granular fluidity (NGF) model, which has shown to be quantitatively predictive and able to capture this effect in the various forms it emerges. We show that the model correctly gives steady flow fields of grains over multiple orders of magnitude in many different 2D and 3D geometries without refitting. The same model captures the size-dependent strengthening of thin granular bodies, a phenomenon that may at first glance appear separate from that of predicting steady flow profiles. NGF also correctly captures the so-called secondary rheology of grains, wherein faraway flow alters the apparent yield stress everywhere. The underlying physics of the nonlocal rheology is gradually becoming clearer, as it has recently been shown that the nonlocal fluidity field, which is a key field variable in the model, is a true kinematic state variable. We also discuss the remaining open questions and future directions.