An Automata Model of Granular Materials

A new modeling technique (the Lattice Grain Model) is presented for the simulation of two-dimensional granular systems involving large numbers (lo4 to 10‘) of grains. These granular systems (e.g., rock slides, planetary rings, industrial powders, etc.) may include both high shear rate regions as well as static plugs of grains and cannot easily be handled within the framework of existing continuum theories such as soil mechanics. The Lattice Grain Model (LGrM) is similar to the Lattice Gas Model (LGM), which was introduced as a discrete model of fluids, in that the computation is carried out by means of cellular automata which evolve according to a simple set of rules based on local interactions. This allows large simulations to be programmed onto a hypercube concurrent processor in a straightforward manner. However, it differs from LGM in that it includes the inelastic collisions and volume-filling properties of macroscopic grains. Examples to be presented will include Couette flow, flow through an hourglass, and gravity-driven flows around obstacles.