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Slow and dense granular flows often exhibit narrow shear bands, making themill-suited for a continuum description. However, smooth granular flows havebeen shown to occur in specific geometries such as linear shear in the absenceof gravity, slow inclined plane flows and, recently, flows in split-bottomCouette geometries. The wide shear regions in these systems should be amenableto a continuum description, and the theoretical challenge lies in findingconstitutive relations between the internal stresses and the flow field. Wepropose a set of testable constitutive assumptions, includingrate-independence, and investigate the additional restrictions on theconstitutive relations imposed by the flow geometries. The wide shear layers inthe highly symmetric linear shear and inclined plane flows are consistent withthe simple constitutive assumption that, in analogy with solid friction, theeffective-friction coefficient (ratio between shear and normal stresses) is aconstant. However, this standard picture of granular flows is shown to beinconsistent with flows in the less symmetric split-bottom geometry - here theeffective friction coefficient must vary throughout the shear zone, or else theshear zone localizes. We suggest that a subtle dependence of theeffective-friction coefficient on the orientation of the sliding layers withrespect to the bulk force is crucial for the understanding of slow granularflows.Comment: 11 pages, 7 figure

Continuum approach to wide shear zones in quasistatic granular matter