New stress and velocity fields for highly frictional granular materials
Author(s)
W. McCue, Scott
Kenneth Johnpillai, I.
M. Hill, James
Griffith University Author(s)
Year published
2005
Metadata
Show full item recordAbstract
The idealized theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit as 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 ...
View more >The idealized theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit as 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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View more >The idealized theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit as 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.
View less >
Journal Title
IMA Journal of Applied Mathematics
Volume
70
Issue
1
Subject
Applied Mathematics
Numerical and Computational Mathematics
Other Mathematical Sciences