A Mathematical Model for Localization in Granular Flow

The phrase ‘localization of flow’ refers to a phenomenon in plasticity in which deformation becomes concentrated in thin bands of intense shearing. This paper proposes a two-dimensional continuum model which isolates some mathematical issues relevant to such shear banding. The challenge is to follow...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical and physical sciences Mathematical and physical sciences, 1992-02, Vol.436 (1897), p.217-250
Main Author: Schaeffer, David G.
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Classical and quantum physics: mechanics and fields
Classical mechanics of continuous media: general mathematical aspects
Eigenvalues
Exact sciences and technology
Granular materials
Mathematical constants
Mathematical discontinuity
Mathematical functions
Mathematical models
Physics
Plane waves
Trajectories
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Summary:The phrase ‘localization of flow’ refers to a phenomenon in plasticity in which deformation becomes concentrated in thin bands of intense shearing. This paper proposes a two-dimensional continuum model which isolates some mathematical issues relevant to such shear banding. The challenge is to follow the solution after ill- posedness appears in the equations. A particular solution in this régime is constructed in the quasi-static approximation. The paper also lists several open problems suggested by the model. Besides addressing research questions, the paper is partly intended as an expository paper for mathematicians interested in shear bands.
ISSN:1364-5021
0962-8444
1471-2946
2053-9177
DOI:10.1098/rspa.1992.0016