Radial hopper flow prediction using a constitutive model with microstructure evolution

TL;DR

This paper develops a continuum model with microstructure evolution to predict granular flow in a conical hopper, capturing variable stress ratios and effects of particle properties, validated against discrete element simulations.

Contribution

It introduces a novel constitutive model incorporating microstructure evolution for strain rate-independent granular flows in hoppers.

Findings

Variable stress ratio along the flow, contrasting with constant assumptions.

Particle friction increases stress ratio but decreases flow rate.

Normal-stress differences influence stress distribution and discharge rate.

Abstract

We present theoretical predictions of granular flow in a conical hopper based on a continuum theory employing a recently-developed constitutive model with microstructure evolution by Sun and Sundaresan [1]. The model is developed for strain rate-independent granular flows. The closures for the pressure and the macroscopic friction coefficient are linked to microstructure through evolution equations for the coordination number and fabric. The material constants in the model are functions of particle-level properties. A salient prediction is the variable stress ratio along the flow direction, in contrast to the constant ratio employed in some widely-used plasticity theories, but supported by results obtained from discrete element simulations. The model permits direct interrogation of the influence of particle-particle friction as well as normal-stress differences on the stress distribution and discharge rate. Increasing particle friction leads to higher stress ratios, but lower normal stress and flow rates, while considering normal-stress differences results in the opposite effects.