Reflections on the mechanics of granular matter

During recent years, a rather basic conflict has emerged between departments of mechanics/physics concerning the description of granular media. Experts from mechanics measure stress/strain relations, using the so-called triaxial tests, and then use these data to predict the behavior of a sample under given boundary conditions. Some physicists have a different view: they have claimed that it is not possible to define a proper displacement field in a heap of sand, and that the notion of strains is thus ambiguous. In the present text, we conclude that the crucial features are the following: (a) a heap is usually formed from a flowing phase of sand, (b) there is (empirically) a sharp interface between the flowing phase and the frozen heap below, (c) we may define for each grain a displacement, which is measured from the moment when it froze. (This displacement is due, for instance, to a compaction of the heap under its own weight.) We also present some aspects of the dynamics, including dune motions and surface flows of grains. Bouchaud, Cates and coworkers have constructed a very compact description for thin flows. We discuss the practical consequences of this picture, emphasizing some possible extensions for thicker flows. This suggests a number of possible experiments on avalanches.