Quasistatic to inertial transition in granular materials and the role of fluctuations
Transition quasi-statique inertielle dans les matériaux granulaires et rôle des fluctuations
Résumé
On the base of discrete element numerical simulations of a Couette cell, we revisit the rheology of granular materials in the quasi-static and inertial regimes, and discuss the origin of the transition between these two regimes. We show that quasi-static zones are the seat of a creep process whose rate is directly related to the existence and magnitude of velocity fluctuations. The mechanical behaviour in quasi-static regime is characterized by a novel, three-variable constitutive law relating the friction coefficient (normalized stress), the inertial number (normalized shear rate), and the normalized velocity fluctuations. Importantly, this constitutive law appears to remain also valid in the inertial regime, where it can account for the one-to-one relationship observed between the friction coefficient and the inertial number. The abrupt transition between the quasi-static and inertial regimes is then related to the mode of production of the fluctuations within the material, from non-local and artificially sustained by the boundary conditions in the quasi-static regime, to purely local and self-sustained in the inertial regime. This quasi-static to inertial transition occurs at a critical inertial number or, equivalently, at a critical level of fluctuations.