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Shearing flows in a Goodman-Cowin type granular material - theory and numerical results

Wang, Yongqi and Hutter, Kolumban (1999):
Shearing flows in a Goodman-Cowin type granular material - theory and numerical results.
In: Particulate Science and Technology, Taylor and Francis Group, pp. 97-124, 17, (1-2), ISSN 0272-6351,
DOI: 10.1080/02726359908906807,
[Online-Edition: http://www.tandfonline.com/doi/abs/10.1080/02726359908906807],
[Article]

Abstract

Goodman and Cowin (1972) proposed a continuum theory of a dry cohesionless granular material in which the solid volume fraction v is treated as an independent kinematic field for which an additional balance law of equilibrated forces is postulated. By adopting the Müller-Liu approach to the exploitation of the entropy inequality we show that in a constitutive model containing v1, v and grad v as independent variables results agree with the classical Coleman-Noll approach only provided the Helmholtz free energy does not depend on v, for which the Goodman-Cowin equations are reproduced. This reduced theory is then applied to analyses of steady fully-developed horizontal shearing flow and gravity flows of granular materials down an inclined plane and between vertical parallel plates. It is demonstrated that the equations and numerical results, presented by Passman et al. (1980) are false, and they are corrected. The results show that the dynamical behaviour of these materials is quite different from that of a viscous fluid. In some cases the dilatant shearing layers exist only in the narrow zones near the boundaries.

Item Type: Article
Erschienen: 1999
Creators: Wang, Yongqi and Hutter, Kolumban
Title: Shearing flows in a Goodman-Cowin type granular material - theory and numerical results
Language: English
Abstract:

Goodman and Cowin (1972) proposed a continuum theory of a dry cohesionless granular material in which the solid volume fraction v is treated as an independent kinematic field for which an additional balance law of equilibrated forces is postulated. By adopting the Müller-Liu approach to the exploitation of the entropy inequality we show that in a constitutive model containing v1, v and grad v as independent variables results agree with the classical Coleman-Noll approach only provided the Helmholtz free energy does not depend on v, for which the Goodman-Cowin equations are reproduced. This reduced theory is then applied to analyses of steady fully-developed horizontal shearing flow and gravity flows of granular materials down an inclined plane and between vertical parallel plates. It is demonstrated that the equations and numerical results, presented by Passman et al. (1980) are false, and they are corrected. The results show that the dynamical behaviour of these materials is quite different from that of a viscous fluid. In some cases the dilatant shearing layers exist only in the narrow zones near the boundaries.

Journal or Publication Title: Particulate Science and Technology
Volume: 17
Number: 1-2
Publisher: Taylor and Francis Group
Uncontrolled Keywords: granular materials; constitutive equations; iteration method; granular shearing flow
Divisions: Study Areas
16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Study Areas > Study Area Mechanic
Date Deposited: 30 Aug 2011 14:35
DOI: 10.1080/02726359908906807
Official URL: http://www.tandfonline.com/doi/abs/10.1080/02726359908906807
Additional Information:

DOI: 10.1080/02726359908906807

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