This paper investigates the steady plane shear flow of dense granular materials using discrete simulations. The authors study the behavior of frictional, inelastic disks under prescribed pressure and shear rate, focusing on the transition between quasi-static and collisional regimes. They introduce a dimensionless number, the inertial number \( I \), which characterizes the ratio of inertial to pressure forces. Small values of \( I \) correspond to the quasi-static regime, while large values indicate the collisional regime. In the intermediate regime, the solid fraction decreases linearly from its maximum value, and the effective friction coefficient increases linearly from its minimum value. These laws are used to deduce a constitutive law for dense granular flows, incorporating both plastic and viscous terms. The study also examines the influence of grain mechanical properties on the dilatancy and friction laws, finding that the local friction coefficient significantly affects the solid fraction but has a minor impact on the friction law. The paper concludes with a discussion on the heterogeneity of stress distribution and shear localization under gravity.This paper investigates the steady plane shear flow of dense granular materials using discrete simulations. The authors study the behavior of frictional, inelastic disks under prescribed pressure and shear rate, focusing on the transition between quasi-static and collisional regimes. They introduce a dimensionless number, the inertial number \( I \), which characterizes the ratio of inertial to pressure forces. Small values of \( I \) correspond to the quasi-static regime, while large values indicate the collisional regime. In the intermediate regime, the solid fraction decreases linearly from its maximum value, and the effective friction coefficient increases linearly from its minimum value. These laws are used to deduce a constitutive law for dense granular flows, incorporating both plastic and viscous terms. The study also examines the influence of grain mechanical properties on the dilatancy and friction laws, finding that the local friction coefficient significantly affects the solid fraction but has a minor impact on the friction law. The paper concludes with a discussion on the heterogeneity of stress distribution and shear localization under gravity.