Summary
We consider simple shearing flow of a granular material in which the stress is governed by the Coulomb-Mohr yield condition, and which deforms according to the ‘double-shearing’ model of granular material behaviour for incompressible material. We also investigate deformations of a dilatant material in which this shearing deformation is accompanied by an expansion in the direction normal to the shear plane, in this case using the dilatant double-shearing model proposed by Mehrabadi and Cowin. In both cases it is found that in addition to the expected steady stress solution, the equations admit time-dependent stress solutions. For suitable initial conditions these solutions satisfy the positive energy dissipation requirements up to some finite shear. In the unsteady solutions the rotation of the principal stress axes is always away from the steady solution, and in no case is the steady solution approached as a limit of the unsteady solution; this indicates that the steady flow solutions are unstable.
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Spencer, A.J.M. Instability of steady shear flow of granular materials. Acta Mechanica 64, 77–87 (1986). https://doi.org/10.1007/BF01180099
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DOI: https://doi.org/10.1007/BF01180099