Continuum Dynamics of Dense Granular Materials

Recent developments in the continuum modeling of granular materials address the long-standing problem of ill-posedness in the evolution equations. The μ(I)-rheology, in which the friction coefficient μ depends on shear rate through the dimensionless inertial number I, introduced more than a decade ago by Pouliquen and co-authors, is a crucial step in establishing regimes in which equations for incompressible 2-D granular flow are well-posed, leaving specific thresholds for the onset of ill-posedness. The introduction of compressibility, a physically relevant property captured by a variable packing fraction φ, is introduced first by prescribing φ as a decreasing function Φ(I) of inertial number. However, the resulting dynamic equations are shown to be ill-posed. A more sophisticated approach, via constitutive laws derived from Critical State Soil Mechanics, results in a set of conditions under which granular flow is well posed. This significant breakthrough in the continuum modeling of granular materials is being further explored through detailed simulation of prototypical flows.