McCue, S.Johnpillai, I.Hill, J.2011-06-222011-06-222005IMA Journal of Applied Mathematics, 2005; 70(1):92-1180272-49601464-3634http://hdl.handle.net/2440/64776The 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.enCopyright Institute of Mathematics and its Applications 2005; all rights reserved.granular materialsexact solutionsLie symmetriesdouble-shearing theoryhighly frictional materialsJournal article002010784910.1093/imamat/hxh0542-s2.0-1404427875730052