Title: A Stochastic Flow Rule for Dense Granular Plasticity

Author (Talk): Ken Kamrin, MIT Mathematics

Abstract:

There have been many continuum models proposed for dense granular flow, but a general theory is still lacking--- able to simultaneously describe a wide assortment of flows such as gravity driven drainage and forced shear cells. Here, we begin with a firm mechanical rooting by employing classical Mohr-Coulomb plasticity to calculate quasi-2D stresses. We then propose the "Stochastic Flow Rule" (SFR) to convert these stresses into a flow field. The SFR takes into account two crucial aspects of granular material motion: flow correlation at a distinct length-scale and randomness in the material composition. These notions are upheld in a manner similar to the Spot Model (Bazant 2000) in which diffusing ``spots'' cause chain-like cooperative particle displacements. By applying stick-slip fluidization along slip-lines, the SFR systematically determines the spot drift which can then be used to determine a full flow field. SFR predictions match experiment and simulation well for a diverse variety of flow geometries and with essentially no fit parameters.