12 Pages

Jamming and static stress transmission in granular materials

In this paper we consider assemblies of cohesionless rough particles, whose rigidity is sufficient that individual particle deformations remain always small. Such assemblies are sometimes argued to be governed by the continuum me-

chanics of a Hookean elastic solid (perhaps with a very high modulus). But this implicitly assumes that each granular con­ tact is capable equally of supporting tensile as compressive loads. For a cohesionless medium this is certainly untrue: Cohesionless granular assemblies are therefore not elastic.1 The question is not one of principle, but of degree-how important is the prohibition of tensile forces? This is not completely clear; some would argue2 that it represents a neg­ ligible effect and that an elastic model remains basically sound, so long as the mean stresses in the material remain compressive everywhere. However, a fully elastic granular assembly would be one in which grains were, effectively, glued permanently to their neighbors on first contact. Be­ cause the packing is microscopically disordered, it is pos­ sible that, during subsequent loading a significant fraction of such contacts would become tensile, even if the load being applied remains everywhere compressive on average. If so, the absence of tensile forces is a major, even dominant, fac­ tor.