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).