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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 ofgranular 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 theoryor newcomer isostaticity theory. The two differ significantly and, in particular in 2D, isostaticity theory leads naturally toforce 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 firstpresent the rationale for stato-elasticity theory. An important step towards the construction of this theory is a good understanding of stress transmission in the region so f pure isostatic states. Ab rief description is given of recently derived general solutions for 2D isostaticregions with nonuniform structures, which go well beyond the over-simplisticpicture of force chains. It hen 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.

Stress transmission and incipient yield flow in dense granular materials