Isostaticity in granular matter

Recent work (PRL V81, 1998, p. 1634) has proven that cohesionless granular packings are isostatic in the limit of low applied pressure, and suggested that this property is responsible for the peculiar static behavior of granular materials. On disordered isostatic systems, stress-stress response functions are power-law distributed, with a cutoff that grows exponentially with distance. If the external pressure is increased sufficiently, excess contacts are created, the packing becomes hyperstatic, and the medium behaves as a normal elastic continuum. I discuss here these ideas briefly, and also report on numerical results (mainly stress distributions) from a simple two-dimensional model of packings which captures the essential physics of stress transmission in granulates under varying load conditions.