Granular Flows

The epigrammatic quote by a French Nobel laureate is familiar to many in the field of granular mechanics and reflects a long-standing scientific fascination and practical interest. This is acknowledged by many others and summarized in the articles listed under Further Reading. As a general definition, we understand by granular medium a particle assembly dominated by pairwise nearest-neighbor interactions and usually limited to particles larger than 1 micrometer in diameter, for which the direct mechanical effects of Van der Waals and ordinary thermal (“Brownian”) forces are negligible. This includes a large class of materials, such as cereal grains, pharmaceutical tablets and capsules, geomaterials such as sand, and the masses of rock and ice in planetary rings. Most of the present article is concerned with dry granular materials in which there are negligible effects of air or other gases in the interstitial space, or else with granular materials completely saturated by an interstitial liquid. In this case, liquid surface-tension at “capillary necks” between grains, as in the wet sand of sand castles, or related forms of cohesion are largely negligible. There are several important and interrelated aspects of granular mechanics: (i) experiment and industrial or geotechnical applications, (ii) analytical and computational micromechanics (grainlevel dynamics), (iii) homogenization (“upscaling” or “coarse graining”) to obtain smoothed continuum models from the Newtonian mechanics of discrete grains, (iv) mathematical classification and solution of the continuum field equations for granular flow, and (v) development of continuum models (“constitutive equations”) for stress-deformation behavior. The present article focuses on (v), since the study of most of the preceding items either depends on it, or is strongly motivated by it. The following discussion of (iv) sets the stage for the subsequent coverage of (v).