Lawrence Berkeley National Laboratory

Continuum mechanics relies on the fundamental notion of a mesoscopic volume "element" in which properties averaged over discrete particles obey deterministic relationships. Recent work on granular materials suggests a continuum law may be inapplicable, revealing inhomogeneities at the particle level, such as force chains and slow cage breaking. Here, we analyze large-scale Discrete-Element Method (DEM) simulations of different granular flows and show that a "granular element" can indeed be defined at the scale of dynamical correlations, roughly three to five particle diameters. Its rheology is rather subtle, combining liquid-like dependence on deformation rate and solid-like dependence on strain. Our results confirm some aspects of classical plasticity theory (e.g., coaxiality of stress and deformation rate), while contradicting others (i.e., incipient yield), and can guide the development of more realistic continuum models.