A particle-in-cell solution to the silo discharging problem

The problem of ow of a granular material during the process of discharging a silo is considered in the present paper. The mechanical behaviour of the material is described by the use of the model of the elastic{ plastic solid with the Drucker{Prager yield condition and the non-associative ow rule. The phenomenon of friction between the stored material and the silo walls is taken into account|the Coulomb model of friction is used in the analysis. The problem is analysed by means of the particle-in-cell method|a variant of the nite element method which enables to solve the pertinent equations of motion on an arbitrary computational mesh and trace state variables at points of the body chosen independently of the mesh. The method can be regarded as an arbitrary Lagrangian{Eulerian formulation of the nite element method, and overcomes the main drawback of the updated Lagrangian formulation of FEM related to mesh distortion. The entire process of discharging a silo can be analysed by this approach. The dynamic problem is solved by the use of the explicit time-integration scheme. Several numerical examples are included. The plane strain and axisymmetric problems are solved for silos with at bottoms and conical hoppers. Some results are compared with experimental ones.