A general, three-dimensional law to predict dry granular flow in arbitrary geometries has remained an elusive challenge in engineering. To address this challenge we begin by deriving an elasto-plastic continuum model for granular flow.  The model merges a nonlinear granular elasticity law based on a mean-field generalization of Hertzian contact, with a recently proposed rate-sensitive plasticity law for flowing grains that gives the flow rate when stresses exceed a Drucker-Prager yield criterion.  We test the model's ability to predict steady flow and stress profiles in multiple inhomogeneous flow environments using finite-element analysis and comparing the results against experiments and discrete particle simulations.  While overall effective, this local model does not capture some phenomena observed in the slow, creeping flow regime.  As flow-rate decreases, granular stresses are observed to become largely rate-independent and a dominating length-scale emerges in the mechanics.  We account for these effects using the notion of nonlocal fluidity, which has proven successful in treating nonlocal effects in emulsions.  In a similar spirit, we recast the local granular flow model in terms of granular fluidity and then add a diffusive second-order term scaled by the particle size, which spreads flowing zones accordingly.  Below the yield stress, the local contribution vanishes and the fluidity becomes rate-independent, as we require.  We implement the modified law in multiple geometries and validate its predictions for velocity, shear-rate, and stress against discrete particle simulations over several order of magnitude in flow rate.

WEDNESDAY, FEBRUARY 29, 2012
3:00 PM
MARYLAND HALL 110
hmao@jhu.edu