New stress and velocity fields for highly frictional granular materials
| dc.contributor.author | McCue, S. | |
| dc.contributor.author | Johnpillai, I. | |
| dc.contributor.author | Hill, J. | |
| dc.date.issued | 2005 | |
| dc.description.abstract | 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 π/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. | |
| dc.description.statementofresponsibility | Scott W. Mccue, I. Kenneth Johnpillai and James M. Hill | |
| dc.identifier.citation | IMA Journal of Applied Mathematics, 2005; 70(1):92-118 | |
| dc.identifier.doi | 10.1093/imamat/hxh054 | |
| dc.identifier.issn | 0272-4960 | |
| dc.identifier.issn | 1464-3634 | |
| dc.identifier.uri | http://hdl.handle.net/2440/64776 | |
| dc.language.iso | en | |
| dc.publisher | Oxford Univ Press | |
| dc.rights | Copyright Institute of Mathematics and its Applications 2005; all rights reserved. | |
| dc.source.uri | https://doi.org/10.1093/imamat/hxh054 | |
| dc.subject | granular materials | |
| dc.subject | exact solutions | |
| dc.subject | Lie symmetries | |
| dc.subject | double-shearing theory | |
| dc.subject | highly frictional materials | |
| dc.title | New stress and velocity fields for highly frictional granular materials | |
| dc.type | Journal article | |
| pubs.publication-status | Published |