We report on a numerical study of the shear flow of a simple two-dimensionalmodel of a granular material under controlled normal stress between twoparallel smooth, frictional walls, moving with opposite velocities $\pm$V .Discrete simulations, which are carried out with the contact dynamics method indense assemblies of disks, reveal that, unlike rough walls made of strands ofparticles, smooth ones can lead to shear strain localization in the boundarylayer. Specifically, we observe, for decreasing V, first a fluid-like regime(A), in which the whole granular layer is sheared, with a homogeneous strainrate except near the walls; then (B) a symmetric velocity profile with a solidblock in the middle and strain localized near the walls and finally (C) a statewith broken symmetry in which the shear rate is confined to one boundary layer,while the bulk of the material moves together with the opposite wall. Bothtransitions are independent of system size and occur for specific values of V .Transient times are discussed. We show that the first transition, betweenregimes A and B, can be deduced from constitutive laws identified for the bulkmaterial and the boundary layer, while the second one could be associated withan instability in the behavior of the boundary layer. The boundary zoneconstitutive law, however, is observed to depend on the state of the bulkmaterial nearby.
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