© 1993 by Oxford University Press
THE RIGID-PLASTIC BOUNDARY IN STATICALLY INDETERMINATE PROBLEMS IN THE MECHANICS OF GRANULAR MATERIALS
( University of Manchester Institute of Science and Technology PO Box 88, Manchester M60 1QD )
A complete formulation for general statically indeterminate boundary-value problems is presented for a continuum, rigid-plastic, model of granular materials satisfying the stress-equilibrium conditions, the Coulomb yield criterion and the double-shearing kinematic equations. Equations for the velocity field in the neighbourhood of a finite stress discontinuity are derived. The calculus of variations is used to formulate a method for obtaining the characteristic curves which separate the rigid and deforming regions and which are subject to a mixed boundary condition containing both stress and velocity variables. The criterion is applied to the region in the vicinity of the exit of a wedge shaped channel under conditions of converging flow. On the assumptions of radial flow sufficiently far inside the channel, rigid flow on exit and a transitional region which includes a curvilinear fan of characteristic curves it turns out that velocity and stress fields can be found satisfying all the required boundary conditions but that the necessary condition that the work-rate be everywhere non-negative fails to be satisfied.