Radial hopper flow prediction using a constitutive model with   microstructure evolution
  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. 
Jin Sun and Sankaran Sundaresan
cond-mat.soft