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Raphael Blumenfeld

Granular piles and marginal rigidity

Abstract: In the first part I will discuss recent experimental results on the build-up of 2D granular piles which show that the density and coordination number of the consolidated piles decrease with increasing of the initial density of falling grains. The coordination number approaches the low value predicted for the theoretical marginal rigidity state as the density approaches a critical value. These results provide an experimental evidence for the existence of the marginal rigidity state of matter. The decrease in the coordination number is traced to the dynamics within an advancing yield front between the consolidating pile and the falling grains. It is shown that the front's size increases with initial density and it appears to diverge as the marginal rigidity state is approached. The relevance of these results to stress transmission in granular assemblies in general are discussed.

In the second part I will describe a first-principles theory for the stress transmission in 2D marginally rigid granular assemblies and show that it has significant effects on the yield and plasticity of 3D such systems. On the basis of the static formalism, a new set of flow equations is proposed for the yield dynamics of granular systems.

Work done in collaboration with Profs Robin C. Ball and Sam F. Edwards.