The modelling of granular flow using the particle-in-cell method
Granular flow occurs in a broad spectrum of industrial applications that range from separation and mixing in the pharmaceutical industry, to grinding and crushing, blasting, stockpile construction, flow in and from hoppers, silos, bins, and conveyer belts, agriculture, mining and earthmoving. Two totally different approaches of modelling granular flow are the Discrete Element Method (DEM) and continuum methods such as Finite Element Methods (FEM). Continuum methods can be divided into nonpolar or classic continuum methods and polar continuum methods. Large displacements are usually present during granular flow which, without remeshing, cannot be solved with standard finite element methods due to severe mesh distortion. The Particle-in-Cell (PIC) method, which is a so-called meshless method, eliminates this problem since all the state variables are traced by material points moving through a fixed mesh. The main goal of this research was to model the flow of noncohesive granular material in front of flat bulldozer blades and into excavator buckets using a continuum method. A PIC code was developed to model these processes under plane strain conditions. A contact model was used to model Coulomb friction between the material and the bucket/blade. Analytical solutions, published numerical and experimental results were used to validate the contact model and to demonstrate the code’s ability to model large displacements and deformations. The ability of both DEM and PIC to predict the forces acting on the blade and bucket and the material flow patterns were demonstrated. Shear bands that develop during the flow of material were investigated. As part of the PIC analyses, a comparison between classic continuum and polar continuum (Cosserat) results were made. This includes mesh size and orientation dependency, flow patterns and the forces acting on the blade and the bucket. It is concluded that the interaction of buckets and blades with granular materials can successfully be modelled with PIC. In the cases conducted here, the nonpolar continuum was more accurate than the polar continuum, but the polar continuum results were less dependent on the mesh size. The next step would be to apply this technology to solve industrial problems.