Dissipation, dispersion, and shocks in granular media

An understanding of the propagation of pressure waves in granular bodies is of significant importance to many aspects of industrial handling of bulk materials. In this paper the propagation of longitudinal pressure waves in one-dimensional granular bodies is investigated using a hypoplastic framework. From a one-dimensional simplification of a hypoplastic model, a dynamic version of Janssenʹs equation for the pressure within a silo is constructed. The effect of friction on the propagation of small disturbances in this continuum is studied. Dispersion and dissipation are observed in this system, with the rate of dissipation being related to the Janssen characteristic depth. The paper then addresses the propagation of waves with larger amplitudes and the formation of shock waves is analysed. By examining characteristic solutions to the governing equations, a Hugoniot for shock waves in hypoplastic granular materials is found as well as an expression for the velocity with which shock waves propagate.