DEM (discrete element method) simulations are used to characterize granular rheology and granular phase transition by studying order parameter (OP) dynamics. These DEM simulations reveal the existence of a third stable granular phase that is neither completely fluid-like nor completely solid-like. Hence, a modified form of the free energy density function is proposed to account for this third stable granular phase observed in DEM simulations. Further, a constitutive model for granular flows is developed based on an objective version [Gao et al., Phys. Rev. E 71(021302), 20051 of the original OP concept proposed by Volfson et al. [Phys. Rev. E 68(021301), 20031, with the intention of capturing the transitional behavior in a continuum description of granular flows. This OP-based model is refined by extracting new model coefficients from 3D DEM simulations of homogeneous shear flow. The proposed linear version of the objective OP model has the advantage that the total granular stress is a linear combination of the solid-like and fluid-like stresses, and it is denoted as the refined order parameter (ROP) model. The performance of this ROP model along with other existing constitutive models is assessed in homogeneous shear flow, and the results are explained by analyzing granular stress data from DEM simulations. (C) 2011 Elsevier Ltd. All rights reserved.