A Constitutive Model for Dense Granular Flows Based on Microstructural Descriptors

Abstract

A constitutive model is developed to capture the complex rheological behavior of dense granular flows (solid volume fraction ranging from 0.45 to 0.62) in the quasi-static, intermediate, and inertial regimes. The principal contribution of this work is the development of a contact stress model (CSM) that is a statistical closure for the average contact stress experienced by particles, which is derived from a micromechanical model for the stress. This modeling approach naturally gives rise to the dependence of average contact stress on the average contact force and relevant descriptors of microstructure, which are the average coordination number and the fabric tensor. An expression for the average contact force is obtained from the contact force probability density function that has the same form in many granular flows. Appropriate closures for the coordination number and the fabric tensor are obtained by solving their respective modeled evolution equations proposed by Sun and Sundaresan [J. Fluid Mech. 201...