Average balance equations, scale dependence, and energy cascade for granular materials

Abstract

A new averaging method linking discrete to continuum variables of granular materials is developed and used to derive average balance equations. Its novelty lies in the choice of the decomposition between mean values and fluctuations of properties which takes into account the effect of gradients. Thanks to a local homogeneity hypothesis, whose validity is discussed, simplified balance equations are obtained. This original approach solves the problem of dependence of some variables on the size of the averaging domain obtained in previous approaches which can lead to huge relative errors (several hundred percentages). It also clearly separates affine and nonaffine fields in the balance equations. The resulting energy cascade picture is discussed, with a particular focus on unidirectional steady and fully developed flows for which it appears that the contact terms are dissipated locally unlike the kinetic terms which contribute to a nonlocal balance. Application of the method is demonstrated in the determination of the macroscopic properties such as volume fraction, velocity, stress, and energy of a simple shear flow, where the discrete results are generated by means of discrete particle simulation.

Accepted forpublication in Physical Review E

References in corpus (8)

• Rheophysics of dense granular materials : Discrete simulation of plane shear flows
• Granular flow down an inclined plane: Bagnold scaling and rheology
• The Jamming Transition in Granular Systems
• A Hydrodynamic model for a dynamical jammed-to-flowing transition in gravity driven granular media
• Diffusion of a granular pulse in a rotating drum
• Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations
• On the relevance of numerical simulations to booming sand
• A model for the onset of oscillations near the stopping angle in an inclined granular flow

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• Flow in an hourglass: particle friction and stiffness matter
• Analysis of granular rheology in a quasi-two-dimensional slow flow by means of discrete element method based simulations
• Self-Diffusion Scalings in Dense Granular Flows
• A new kinetic theory model of granular flows that incorporates particle stiffness
• Velocity scaling in the region of orifice influence in silo draining under gravity
• Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow
• Effect of particle shape on the flow of an hourglass
• Shape matters: Competing mechanisms of particle shape segregation
• Basal layer of granular flow down smooth and rough inclines: kinematics, slip laws and rheology
• Self-diffusion in inhomogeneous granular shearing flows
• Granular surface flows confined between flat, frictional walls. Part 1. Kinematics