Problem Description 

Granular materials are large conglomerations of discrete particles, which may slide against one another but not penetrate. Like a liquid, granular materials can flow to assume the shape of their container. Like a solid, they can support weight, but unlike a solid cannot support a tensile stress. On account of the interesting combination of solid and liquid behavior, it has been suggested that granular material be considered another state of matter entirely. Common examples include sand, sugar and grain.

We are interested in using numerical simulations to better understand granular materials. Simulation of granular material is challenging, requiring the inclusion of many grains and the accurate modeling of contact forces and grain deformation. Relative motion of the grains may bring a grain into contact with many others, only some of which are initially neighbors. Without an efficient algorithm, the number of grains that can be investigated in a simulation is quickly limited. The simulations detailed here involve hundreds of grains, allow for the isolation of parameters and measurement of quantities not accessible experimentally. The ultimate goals of these simulations are to understand under what circumstances homogenized constitutive theories of granular materials are valid, and to suggest new theories based on observed behavior. In the process, fluctuations that may preclude application of such theories can be identified and studied.

An example of the kind of problem that can be investigated is the shearing of granular material. The simulation uses 369 cylindrical grains, and models large material distortion developed by an average shear strain in excess of 80%, with frictional contact using a Coulomb friction model. The calculation required approximately 30 hours on a single processor of a Cray YMP, to run 25,124 computational cycles.