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November  2008, 7(6): 1361-1374. doi: 10.3934/cpaa.2008.7.1361

Nonuniformity of deformation preceding shear band formation in a two-dimensional model for Granular flow

Scott Gordon 1,

1. 

Department of Mathematics, University of West Georgia, Carrollton, GA 30118, United States

Received  August 2007 Revised  April 2008 Published  August 2008

The onset of shear band formation in granular materials has been linked to the governing partial differential equations becoming ill-posed which has in turn been linked to nonassociativity of the flow rule. If uniform material properties and uniform deformation are assumed, ill-posedness occurs simultaneously at all points in the sample. This work derives a one-dimensional model from a two-dimensional model for granular flow with a nonassociative flow rule and shows that, shortly before the onset of ill-posedness, deformation can become highly non-uniform at a point where the material is slightly weakened.
Keywords: granular material, nonassociative flow rule, Shear band, non-uniform deformation..
Mathematics Subject Classification: Primary: 74C99; Secondary: 35B2.
Citation: Scott Gordon. Nonuniformity of deformation preceding shear band formation in a two-dimensional model for Granular flow. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1361-1374. doi: 10.3934/cpaa.2008.7.1361
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