# 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.

Impact and interest:

**Citation counts** are sourced monthly from **Scopus** and **Web of Science®** citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the **Google Scholar™** indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

**42**since deposited on 15 Feb 2011

**11**in the past twelve months

**Full-text downloads** displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

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 |

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page