Abstract
This work employs a Landau-Ginzburg-type nonlocal rheology model to account for shear localization in a wall-bounded dense granular flow. The configuration is a 3D shear cell in which the bottom bumpy wall moves at a constant speed, while a load pressure is applied at the top bumpy wall, with flat but frictional lateral walls. At a fixed pressure, shear zones transit from the top to the bottom when increasing lateral wall friction coefficient. With a quasi-2D model simplification, asymptotic solutions for fluidization order parameters near the top and bottom boundaries are sought separately. Both solutions are the Airy function in terms of a depth coordinate scaled by a characteristic length which measures the width of the corresponding shear zone. The theoretical predictions for the shear zone widths against lateral wall friction coefficient and load pressure agree well with data extracted from particle-based simulation for the flow.
Highlights
Granular flow is ubiquitous in many industrial applications and geophysical events, yet a unified description remains a challenge
The solutions reveal two decay lengths associated with the shear zone widths at the top and bottom
A key conclusion draw from the present study is that the formation of the shear zones strongly depends on the extent of nonuniformity in the effective friction coefficient μ near the solid boundaries, as shown in Eq (15) and (16)
Summary
Granular flow is ubiquitous in many industrial applications (grain transport and storage) and geophysical events (landslides and debris flows), yet a unified description remains a challenge. The material deforms nonuniformly by means of shear bands near boundaries [1,2,3,4,5,12,13] Such a shear localization phenomenon is often described by a constant yield bulk friction for the flow to occur [1,3]. Artoni and Richard show that shear localization can occur at several locations along the depth in a 3D rectangular parallelepiped periodic cell flow [12] or in a 3D torsional shear cell flow [13]. They found that the location of shear localization strongly depends on lateral wall friction coefficient. The asymptotic method and the width-averaging technique are employed to reduce the model so that analytical solutions are possible to predict the effect of lateral wall friction and other parameters on shear localization and its transition
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