2005/10/19 by Martin Depken, Martin van Hecke, Wim van Saarloos · 1 citation
Engineering · Environmental Science · Physics and Astronomy · #Classical mechanics #Composite material #Constitutive equation #Continuum hypothesis #Couette flow #Flow (mathematics) #Geology #Geotechnical engineering #Granular flow and fluidized beds #Granular material #Landslides and related hazards #Materials science #Mechanics #Physics #Quasistatic process #Rheology #Shear (geology) #Shear flow #Shear rate #Shear stress #Simple shear #Sports Dynamics and Biomechanics #Thermodynamics #cond-mat.soft
paper · pdf · doi:10.1103/physreve.73.031302
11 pages, 7 figures
arxiv created 2005/10/19 · openalex publication_date 2006/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Slow and dense granular flows often exhibit narrow shear bands, making them ill suited for a continuum description. However, smooth granular flows have been shown to occur in specific geometries such as linear shear in the absence of gravity, slow inclined plane flows and, recently, flows in split-bottom Couette geometries. The wide shear regions in these systems should be amenable to a continuum description, and the theoretical challenge lies in finding constitutive relations between the internal stresses and the flow field. We propose a set of testable constitutive assumptions, including rate independence, and investigate the additional restrictions on the constitutive relations imposed by the flow geometries. The wide shear layers in the highly symmetric linear shear and inclined plane flows are consistent with the simple constitutive assumption that, in analogy with solid friction, the effective-friction coefficient (ratio between shear and normal stresses) is a constant. However, this standard picture of granular flows is shown to be inconsistent with flows in the less symmetric split-bottom geometry--here the effective friction coefficient must vary throughout the shear zone, or else the shear zone localizes. We suggest that a subtle dependence of the effective-friction coefficient on the orientation of the sliding layers with respect to the bulk force is crucial for the understanding of slow granular flows.