Simulating granular media on the computer

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Granular materials, like sand or powder, can present very intriguing effects. When shaken, sheared or poured they show segregation, convection and spontaneous fluctuations in densities and stresses. I will discuss the modeling of a granular medium on a computer by simulating a packing of elastic spheres via Molecular Dynamics. Dissipation of energy and shear friction at collisions are included. In the physical range the friction coefficient is found to be a linear function of the angle of repose. On a vibrating plate the formation of convection cells due to walls or amplitude modulations can be observed. The onset of fluidization can be determined and is in good agreement with experiments. Segregation of larger particles is found to be always accompanied by convection cells. There is also ample experimental evidence showing the existence of spontaneous density patterns in granular material flowing through pipes or hoppers. The Molecular Dynamics simulations show that these density fluctuations follow a 1/fα spectrum. I compare this behavior to deterministic one-dimensional traffic models. A model with continuous positions and velocities shows self-organized critical jamming behind a slower car. The experimentally observed effects are also reproduced by Lattice Gas and Boltzmann Lattice Models. Density waves are spontaneously generated when the viscosity has a nonlinear dependence on density which characterizes granular flow. We also briefly sketch a thermodynamic formalism for loose granular material. In a dense packing non-linear acoustic phenomena, like the pressure dependence of the sound velocity are studied. Finally the plastic shear bands occurring in large scale deformations of compactified granular media are investigated using an explicit Lagrangian technique.