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We discuss two athermal types of dynamics suitable for spin-models designed to model repeated tapping of a granular assembly. These dynamics are applied to a range of models characterized by a 3-spin Hamiltonian aiming to capture the geometric frustration in packings of granular matter.

We briefly describe how mean-field glass models can be extended to the case where the bath and friction are non-thermal. Solving their dynamics, one discovers a temperature with a thermodynamic meaning associated with the slow rearrangements, even though there is no thermodynamic temperature at the level of fast dynamics. This temperature can be shown to match the one defined on the basis of a flat measure over blocked (jammed) configurations. Numerical checks on realistic systems suggest that these features may be valid in general.

The initiation and steady-state dynamics of granular shear flow are investigated experimentally in a Couette geometry with independently moveable outer and inner cylinders. The motion of particles on the top surface is analyzed using fast imaging. During steady state rotation of both cylinders at different rates, a shear band develops close to the inner cylinder for all combinations of speeds of each cylinder we investigated. Experiments on flow initiation were carried out with one of the cylinders fixed. When the inner cylinder is stopped and restarted after a lag time of seconds to minutes in the same direction, a shear band develops immediately. When the inner cylinder is restarted in the opposite direction, shear initially spans the whole material, i.e. particles far from the shear surface are moving significantly more than in steady state.

We discuss the application of synchrotron X-ray microtomography (XMT) to granular matter, foams, crumpled membranes, and paper. XMT provides rapid, high-resolution, fully three-dimensional characterization of each of these classes of material. In some cases, subsequent three-dimensional image processing allows the virtual reconstruction of the disordered material as a specified assemblage of idealized basic structural units. This allows measurement of otherwise inaccessible correlation functions and can also be used as the starting point for data-initiated simulations.

The elastic properties of granular materials can be enormously nonlinear as compared with the properties of non-porous materials. Experiments on isotropic compression of a granular assembly of spheres show that the shear μ, and bulk k, moduli vary with the confining pressure faster than the 1/3 power law predicted by Hertz–Mindlin elasticity theory. Moreover, the ratio between the experimental bulk and shear moduli is found to be constant but with a value larger than the theoretical prediction. Numerical simulations resolve the question as to whether the problem lies with the treatment of the grain-grain contact or with the elastic framework. We find that the problem lies principally with the latter; the affine assumption (which underlies the elastic formulation) is found to be valid for k but to breakdown seriously for μ. This explains why the experimental and numerical values of μ(p) are much smaller than the elastic predictions. In this paper we review recent progress on the understanding of this problem based on microscopic simulations, elasticity theory and more innovative ideas such as jamming, fragility and thermodynamics of granular materials.

The contact network of a frictionless polydisperse granular packing is isostatic in the limit of low applied pressure. It is argued here that, on disordered isostatic networks, displacement–displacement and stress–stress static Green functions are described by random multiplicative processes and have a truncated power-law distribution, with a cut-off that grows exponentially with distance. If the external pressure is increased sufficiently, excess contacts are created, the packing becomes hyperstatic, and the abovementioned anomalous properties disappear because Green functions now have a bounded distribution. Thus, the low-pressure, isostatic, limit is a critical point.