Publisher's Note: Relaxation-type nonlocal inertial-number rheology for dry granular flows [Phys. Rev. E 96 , 062909 (2017)]

Abstract

This corrects the article DOI: 10.1103/PhysRevE.96.062909.

Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials

“…We now discuss the inclusion of non-monotonicity of the local rheological response into the NGF model. Taking inspiration from previous hysteretic nonlocal models 41,42 , we add a new term to the right-hand side of the fluidity equation (2b). The constitutive equations (2) becomė…”

Analytical nonlocal model for shear localization in wall-bounded dense granular flow

“…Indeed, the rateindependence characterizes quasistatic granular rheology and suggests that the finite shear zones in the three regimes are generated by nonlocal processes driven by wall shearing along grain contact network. While several nonlocal approaches have been put forward to account for similar long-range transport phenomenon [6][7][8][9][10][11]15], here we adopt a simple yet effective Landau-Ginzburg approach which introduces a diffusion-reaction equation describing shear-induced fluidization processes, which has been shown to well capture the nonlocal rheology of 2D free-surface inclined flows and confined sheared flows [6,10,11]. [12]).…”

“…where μc denotes a critical friction coefficient at which the material yields, and α and β are positive exponents with β>α>0. Note that different forms of Floc have been proposed in literature [6,10,11]. For a steady, quasistatic flow considered here, the unsteady term and the higher-order source terms in Eq.…”

“…(3) hence extends the classical Mohr-Coulomb plasticity theory which indicates zero thickness for shear zone. Note that in order to predict flow profiles the OP has been linked to a variety of rheological parameters such as the fraction of fluid stress contribution [6], a granular fluidity, the inverse of viscosity scaled by pressure [8,10], and the inertial number I, a scaled shear rate by pressure indicating the quasistatic and the inertial regimes [9,11]. Also note that the form of Eq.…”

“…However, many studies have shown that solid boundary can have a strong influence on shear localization [2,4,5,12,13]. It is interpreted as nonlocal effects that wall disturbances can fluidize regions below yield through long-range transport along grain-scale contact network [5][6][7][8][9][10][11]. Several nonlocal models with diffusion order parameter have been proposed to capture wall shear localization in 2D confined flows [6][7][8][9][10][11].…”