Modelling of silo discharge and filling problems by the material point method

The problems of flow of a granular material is the processes of silo discharge and filling are considered. Dynamic, two-dimensional problems are analyzed, both the plane and axisymmetric ones. The material point method is applied as an analytical tool, a variant of the finite element method capable of solving pertinent equations of motion on an arbitrary computational element mesh and tracing state variables at material points chosen independently of the mesh. The mechanical behaviour of a granular material is described with non-associative elastic-perfectly plastic and elastic-viscoplastic material models with the Drucker-Prager yield condition. The influence of friction between the flowing granular body and silo walls is taken into account. The material point method enables one to analyze silos of arbitrary shapes, including silos with inserts controlling the flow of the stored material. The mass and funnel types of flows are analyzed