Two-state model to describe the rheological behavior of vibrated granular matter.

In this paper, we present a model aimed at predicting the rheological response of a 3D dry granular system to nonstationary mechanical solicitations, subjected or not to vibrations. This model is based on a phenomenological two-state approach related to the inherent bimodal behavior of chain forces in granular packing. It is set up from a kinetic equation describing the dynamics of the contact network. To allow experimental assessment, the kinetic equation is transformed into a differential constitutive equation, relating stress to strain, from which rheological properties can be derived. Its integration allows predicting and describing several rheological behaviors, in stationary and nonstationary conditions, including viscous (Newtonian) and frictional (Coulombian) regimes, as well as elastic linear (Hookean and Maxwellian) and nonlinear behaviors. Despite its simplicity, since it involves only three independent parameters, the model is in very close agreement with experiments. Moreover, within experimental errors, the values of these parameters are independent of the type of test used to determine them, evidence of the self-consistency of the model.