New stress and velocity fields for highly frictional granular materials

McCue, Scott W., Johnpillai, I. Kenneth, & Hill, James M. (2005) New stress and velocity fields for highly frictional granular materials. IMA Journal of Applied Mathematics, 70(1), pp. 92-118.

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The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

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3 citations in Scopus
2 citations in Web of Science®
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ID Code: 40051
Item Type: Journal Article
Refereed: Yes
Keywords: granular flow, double-shearing theory, highly frictional materials, Lie symmetries, exact solutions
DOI: 10.1093/imamat/hxh054
ISSN: 1464-3634
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Theoretical and Applied Mechanics (010207)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2005 Oxford University Press
Deposited On: 15 Feb 2011 00:04
Last Modified: 10 Aug 2011 14:58

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