Maximum disorder model for dense steady-state flow of granular materials

Abstract

A flow model is developed for dense shear-driven granular flow. As described in the geomechanics literature, a critical state condition is reached after sufficient shearing beyond an initial static packing. During further shearing at the critical state, the stress, fabric, and density remain nearly constant, even as particles are being continually rearranged. The paper proposes a predictive framework for critical state flow, viewing it as a condition of maximum disorder at the micro-scale. The flow model is constructed in a two-dimensional setting from the probability density of the motions, forces, and orientations of inter-particle contacts. Constraints are applied to this probability density: constant mean stress, constant volume, consistency of the contact dissipation rate with the stress work, and the fraction of sliding contacts. The differential form of Shannon entropy, a measure of disorder, is applied to the density, and the Jaynes formalism is used to find the density of maximum disorder in the underlying phase space. The resulting distributions of contact force, movement, and orientation are compared with two-dimensional DEM simulations of biaxial compression. The model favorably predicts anisotropies of the contact orientations, contact forces, contact movements, and the orientations of those contacts undergoing slip. The model also predicts the relationships between contact force magnitude and contact motion. The model is an alternative to affine-field descriptions of granular flow.