Denisty variation in pseudo-steady plastic flow of granular media

In the Paper two pseudo-steady problems of plane plastic flow of dilatant material are considered, and the distributions of densities within the deforming regions determined. The kinematic solutions discussed are characterized by dilation occurring exclusively across velocity discontinuity lines, that are treated in the analysis as shocks. The first problem is that of flow of granular material through a hopper, and the kinematic solution suggested by Drescher, Cousens & Bransby (1978) is used. It is shown that in the radial flow zone the density distribution is non-uniform. As a second problem, the indentation of a wedge into a ponderable half-space is considered, and a kinematic solution similar to that proposed by Hodge (1950) is adopted. It is found that regions with different density exist. An upper limit load for the process of wedge indentation is determined, and the solution for weightless material is compared with that given by Shield (1953). A comparison with some of the experimental results obta...