Normal Stresses in Steady-State and Transient Frictional Granular Flows

Steady flow of sheared frictional granular matter is well-described by a plastic yield criterion along with a rate-dependent viscoplastic rheology. However, existing constitutive formulations focus exclusively on steady-state simple shear rheology. Using stress-controlled discrete element simulations, we highlight that normal stresses are crucial in the rheology of granular matter, both in steady flow above yield stress and transient creep flow below yield stress. The evolution of shear and normal stress components with strain rate is described in terms of friction-dependent viscometric flow functions, and the effect of friction on the directionality of stress and strain rate tensors is assessed. Additionally, correlations between the evolution of bulk stress tensor and granular fabric—both in transient and steady-state flows—are also described. These results provide important inputs toward formulating rheological constitutive equations that predict stresses during arbitrary deformations of frictional granular matter.