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. 92118.

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Abstract
The idealised theory for the quasistatic flow of granular materials which satisfy the CoulombMohr 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 twodimensional 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 nondilatant doubleshearing 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 groupinvariant 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 twodimensional wedge hopper is examined as an illustration.
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ID Code:  40051 

Item Type:  Journal Article 
Refereed:  Yes 
Keywords:  granular flow, doubleshearing theory, highly frictional materials, Lie symmetries, exact solutions 
DOI:  10.1093/imamat/hxh054 
ISSN:  14643634 
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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