Dense granular flow at the critical state: maximum entropy and topological disorder

Matthew R. Kuhn, University of Portland

Granular Matter, 2014, Volume 16, Issue 4, 499-508.

© Springer-Verlag Berlin Heidelberg 2014

Linked version is final published version.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10035-014-0496-2

Abstract

After extensive quasi-static shearing, dense dry granular flows attain a steady-state condition of porosity and deviatoric stress, even as particles are continually rearranged. The paper considers two-dimensional flow and derives the probability distributions of two topological measures of particle arrangement—coordination number and void valence— that maximize topological entropy. By only considering topological dispersion, the method closely predicts the distribution of void valences, as measured in discrete element (DEM) simulations. Distributions of coordination number are also derived by considering packings that are geometrically and kinetically consistent with the particle sizes and friction coef- ficient. A cross-entropy principle results in a distribution of coordination numbers that closely fits DEM simulations.