Granular Plasticity
by
Shaun Hendy
IRL Applied Mathematics

Slow granular flows in hoppers are often modelled as rigid-plastic flows with frictional yield conditions. However, such constituitive relations lead to systems of partial differential equations that are ill-posed: they possess instabilities in the short-wavelength limit. In addition, features of these flows clearly depend on microstructure in a way not modelled by such continuum models. Here we attempt to address both short-comings by splitting velocities and pressures into "fluctuating" plus "average" parts and time-averaging the rigid-plastic flow equations to produce effective equations which depend on the "average" variables and variances of the "fluctuating" variables. Microstructural physics can be introduced by appealing to the kinetic theory of inelastic hard-sphere gases to develop a constituitive relation for the "fluctuating" variables. The equations can then be closed by demanding that this system be stable in the short-wavelength limit.

Date received: October 11, 2001