Stress transmission and incipient yield flow in dense granular materials

Jammed granular matter transmits stresses non-uniformly like no conventional solid, especially when it is on the verge of failure. Jamming is caused by self-organization of granular matter under external loads, often giving rise to networks of force chains that support the loads non-uniformly. An ongoing debate in the literature concerns the correct way to model the static stress field in such media: good old elasticity theory or newcomer isostaticity theory. The two differ significantly and, in particular in 2D, isostaticity theory leads naturally to force chain solutions. More recently, it has been proposed that real granular materials are made of mixtures of regions, some behaving elastically and some isostatically. The theory to describe these systems has been named stato-elasticity. In this paper, I first present the rationale for stato-elasticity theory. An important step towards the construction of this theory is a good understanding of stress transmission in the regions of pure isostatic states. A brief description is given of recently derived general solutions for 2D isostatic regions with nonuniform structures, which go well beyond the over-simplistic picture of force chains. I then show how the static stress equations are related directly to incipient yield flow and derive the equations that govern yield and creep rheology of dense granular matter at the initial stages of failure. These equations are general and describe strains in granular materials of both rigid and compliant particles.