Characteristic relations for a model for the flow of granular materials

Harris, D. (2001) Characteristic relations for a model for the flow of granular materials. Mathematical, Physical and Engineering Sciences, 457 (2006). pp. 347-370. ISSN 1471-2946

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Abstract

A model for the flow of granular materials is considered which is based upon the physical and kinematic concepts of yield on a slip surface, a shearing motion across the slip surface, dilatation or contraction normal to the slip surface and rotation of the slip surface. The equations governing the model are presented in both tensorial and Cartesian equation form. For planar deformations a full analysis of the characteristic directions is carried out. The characteristic equation is a sextic polynomial with five distinct real roots defining a pair of velocity characteristic directions, a pair of stress characteristic directions and a direction associated with both the continuity equation and the slip rotation. Using the characteristic directions to define characteristic coordinates, the equations governing the model relative to these characteristic coordinates are presented. An application of the model to chute flow is considered.

Item Type: Article
Uncontrolled Keywords: Granular Materials Plasticity Models Hyperbolic Partial Differential Equations Characteristic Directions And Relations Fabric
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
MSC 2010, the AMS's Mathematics Subject Classification > 74 Mechanics of deformable solids
Depositing User: Ms Lucy van Russelt
Date Deposited: 12 Jul 2006
Last Modified: 20 Oct 2017 14:12
URI: http://eprints.maths.manchester.ac.uk/id/eprint/373

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