# 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.

## Abstract

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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ID Code: | 40051 |
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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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