PROBABILISTIC THREE-DIMENSIONAL MODEL FOR SLOW SHEARING PARTICULATE FLOW: DRY FRICTION

Abstract

Abstract A probabilistic model for the slow shearing motion of spherical particles dominated by dry inter-particle frictional forces is proposed. The particles can move by sliding, rolling, solid body rotation and jumping following the criterion of minimum energy dissipation. The continuous deformation of particle assembly is regarded as a Markov process in discrete time and continuous space. The components of the contact angle between two neighboring particles are taken as the primary random variables. The coefficients of the probabilistic governing equation are determined from the rate of energy dissipation and micromechanical analysis of particle motion. The inter-particle sliding and rolling friction laws are input data. The constitutive relationships, apparent viscosity and internal friction angle of the particulate material as a whole are obtained by integration. The validity of the proposed model is verified by comparing the model predictions to analytical solutions and available experimental results.