Construction of force network of static granular systems under constraints

Abstract

A granular system is de ned as a large collection of macroscopic grains (linear dimensions greater than 1 m) of solid matter, with thermal uctuations being irrelevant. Some examples of granular matter are sand, rice, co ee, salt, etc. This kind of matter is very important in industry. The second most manufactured class of materials are in the form of granular matter [2]. Granular materials can ow like a liquid (like sand in an hourglass), resist deformation like a solid (like the sand under feet at the beach), or quickly transition between these states (like pebbles in a rockslide). Granular materials have properties that have no equivalent in regular materials like wood, metal, or rubber. In solids like these a force applied to the surface propagates through the material smoothly and predictably. If a uniform force is applied to the surface of a material, every equally sized cross-section of that material bears the same amount of load. In granular materials, however, the situation is very di erent: in a sand pile under stress (that is, when a force is applied to its surface), the force is distributed unevenly { some individual sand grains bear far more load than others. Surprisingly, this remains true even when the sand grains themselves are identical. Whats more, the load-bearing grains connect to one another to make a fractal, lightning-like pattern inside the material, like that shown in Figure 1.1 [1]. These string-like arrangements of load-bearing grains are called force chains.