Instability of steady shear flow of granular materials
type: Item
instance of: scholarly article
title: Instability of steady shear flow of granular materials
zbMATH Open document ID: 0618.73116
DOI: 10.1007/BF01180099
author: A. J. M. Spencer
published in: Acta Mechanica
publication date: 1986-01-01T00:00:00Z
review text: 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 \textit{M. M. Mehrabadi} and \textit{S. C. Cowin} [e.g. J. Mech. Phys. Solids 29, 269-282 (1981)]. 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.
Mathematics Subject Classification ID: 74L10
Mathematics Subject Classification ID: 74H99
zbMATH DE Number: 4003701
zbMATH Keywords: simple shearing flow
zbMATH Keywords: granular material
zbMATH Keywords: Coulomb-Mohr yield condition
zbMATH Keywords: 'double-shearing' model
zbMATH Keywords: incompressible material
zbMATH Keywords: dilatant material
zbMATH Keywords: shearing deformation
zbMATH Keywords: dilatant double-shearing model
zbMATH Keywords: steady stress solution
zbMATH Keywords: time-dependent stress solutions
zbMATH Keywords: initial conditions
zbMATH Keywords: positive energy dissipation requirements
zbMATH Keywords: finite shear
MaRDI profile type: Publication
cites work: Initial planar deformation of dilatant granular materials
cites work: Q3208243
description: scientific article; zbMATH DE number 4003701