Frictional–collisional constitutive relations for granular materials, with application to plane shearing

Abstract

Within a granular material stress is transmitted by forces exerted at points of mutual contact between particles. When the particles are close together and deformation of the assembly is slow, contacts are sustained for long times, and these forces consist of normal reactions and the associated tangential forces due to friction. When the particles are widely spaced and deformation is rapid, on the other hand, contacts are brief and may be regarded as collisions, during which momentum is transferred. While constitutive relations are available which model both these situations, in many cases the average contact times lie between the two extremes. The purpose of the present work is to propose constitutive relations and boundary conditions for this intermediate case and to solve the corresponding equations of motion for plane shear of a cohesionless granular material between infinite horizontal plates. It is shown that, in general, not all the material between the plates participates in shearing, and the solutions for the shearing material are coupled to a yield condition for the non-shearing material to give a complete solution of the problem.

Numerical simulation and validation of dilute turbulent gas–particle flow with inelastic collisions and turbulence modulation

“…Particle linear and rotational velocity prior to collision, particle impact angle, particle shape and wall roughness are among the major parameters which are necessary for a complete characterization of particle-wall collisions [22]. On the other hand, more simplified wall boundary conditions were proposed by Johnson and Jackson [23] and are widely used for gas-solid flow. These are adopted in the present study in order to cope with a reasonable level of closure.…”

Eulerian–Eulerian simulation of dense solid–gas cylindrical fluidized beds: Impact of wall boundary condition and drag model on fluidization

“…Several models have been proposed for the solids slip velocity in the TFM (e.g. [21][22][23]). For the two limiting cases i.e.…”

“…While the expressions in [21] are convenient, conditions in bubbling fluidized beds usually operate between these two limits where interpolation is non-trivial and may yield considerable error in the prediction of the slip velocity [1]. The most widely used approach continues to be the Johnson-Jackson model [23] which evaluates the solids slip velocity at the walls based on simple and physically sound arguments.…”

“…The Johnson-Jackson boundary condition [23] considers the tangential momentum transferred through particle-wall interactions by (a) Coulomb friction characterized by the frictional coefficient µ and (b) collisions characterized by the normal restitution coefficient e w and the specularity coefficient φ. Several analytical and semi-empirical models have been developed to evaluate µ and e w in terms of flow parameters such as the impact velocity, impact angle, particle spin and the particle and wall properties [25][26][27][28][29].…”

Mathematical Model of Solid Flow Behavior in a Real Dimension Blast Furnace

“…Therefore, the surface stress τs in Eq. (3) may be considered to consist of two parts: [38][39][40][41][42] . (4) where, as it is introduced by Zhang et al, 8) τrd is the ratedependent part of the surface stress and τri is the rateindependent part.…”