New stress and velocity fields for highly frictional granular materials
Data(s) |
2005
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Resumo |
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. |
Formato |
application/pdf |
Identificador | |
Publicador |
Oxford University Press |
Relação |
http://eprints.qut.edu.au/40051/1/c40051.pdf DOI:10.1093/imamat/hxh054 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. |
Direitos |
Copyright 2005 Oxford University Press |
Fonte |
Faculty of Science and Technology; Mathematical Sciences |
Palavras-Chave | #010207 Theoretical and Applied Mechanics #granular flow #double-shearing theory #highly frictional materials #Lie symmetries #exact solutions |
Tipo |
Journal Article |