Applied Mathematics Seminar

Granular materials occur in many industrial situations throughout the world. Due to the variety of possible behaviourof granular materials, determining a mathematical model to predict the flow of such materials is difficult. In this talk, we utilise the proper mechanical continuum theory of granular materials to examine three industrial granular problems, namely gravity flow from hoppers, determining the stress distribution beneath a stock-pile, and examining the formation of rat-holes. We derive the only known exact solution to the governing equations that has two arbitrary constants of integration. This exact parametric solution corresponds to the special case of an angle of internal friction equal to ninety degrees. Although this is non-physical, there exist materials as Silica and Alumina cake that exhibit large angles of internal friction. Moreover, the solution presented might provide bounds for physically meaningful cases.