SAMSI Meeting, September 10, 2006 Title: Stochastic plasticity: A multiscale model for granular flow Speaker: Martin Z. Bazant (MIT) Abstract: There has been much recent interest in modeling granular materials. Fast, dilute granular flows are well described by kinetic theory and hydrodynamics of inelastic gases, but there has not yet emerged any general theory -- statistical or continuum -- for dense granular flows. For example, no existing model can describe both draining silos and Coette cell, even qualitatively. Here, we present a cooperative mechanism for random packing dynamics based on diffusing "spots" of free volume. The Spot Model can produce very realistic silo drainage, in close agreement with discrete-element simulations of 400,000 spherical, viscoelectric spheres with frictional contacts. For general dense flows, we drive the dynamics via a "stochastic flow rule" for Mohr-Coulolmb plasticity, where stresses are at incipient yield, on average. Spots act as carriers of plastic deformation, analogous to dislocations in a crystal, and perform random walks along slip lines, biased by a local fluidization force. In the contiuum limit, this simple model can accurately describe many granular flows in silos, Coette cells, plate-dragging, and heaps, with no adjustable parameters, other than the friction angle and the spot size (set by velocity correlations).