Green's Function Measurements of Force Transmission in 2D Granular Materials

We describe experiments that probe the response to a point force of 2D granular systems under a variety of conditions. Using photoelastic particles to determine forces at the grain scale, we experimentally show that disorder, packing structure, friction and texture significantly affect the average force response in granular systems. For packings with weak disorder, the mean forces propagate primarily along lattice directions. The width of the response along these preferred directions grows with depth, increasingly so as the disorder of the system grows. Also, as the disorder increases, the two propagation directions of the mean force merge into a single direction. The response function for the mean force in the most strongly disordered system is quantitatively consistent with an elastic description for forces applied nearly normally to a surface. These observations are consistent with recent predictions of Bouchaud et al. and with the anisotropic elasticity models of Goldenberg and Goldhirsch. At this time, it is not possible to distinguish between these two models. The data do not support a diffusive picture, as in the q-model. This system with shear deformation is characterized by stress chains that are strongly oriented along an angle of 45 degrees, corresponding to the compressive direction of the shear deformation. In this case, the spatial correlation function for force has a range of only one particle size in the direction transverse to the chains, and varies as a power law in the direction of the chains, with an exponent of -0.81. The response to forces is strongest along the direction of the force chains, as expected. Forces applied in other directions are effectively refocused towards the strong force chain direction.Comment: 38 pages, 26 figures, added references and content, to appear in Physica

Footprints in Sand: The Response of a Granular Material to Local Perturbations

We experimentally determine ensemble-averaged responses of granular packings to point forces, and we compare these results to recent models for force propagation in a granular material. We used 2D granular arrays consisting of photoelastic particles: either disks or pentagons, thus spanning the range from ordered to disordered packings. A key finding is that spatial ordering of the particles is a key factor in the force response. Ordered packings have a propagative component that does not occur in disordered packings.Comment: 5 pages, 4 eps figures, Phys. Rev. Lett. 87, 035506 (2001

Science in the sandbox: Fluctuations, friction and instabilities

The study of granular materials is a novel and rapidly growing field. These materials are interest for a number of reasons, both practical and theoretical. They exhibit a rich of novel dyanamical states, and they exhibit 'phases'-solid, liquid, and gas-that resemble conventional thermodynamic phases. However, the presence of strong dissipation through friction and inelasticity places these systems well outside the usual class of systems that can be explained by equilibrium thermodynamics. Thus, there are important challenges to create new kinds of statistical physics and new analytical descriptions for the mean and fluctuating behavior of these materials. We explore recent work that focuses on several important issues. These include force propagation and fluctuations in static and driven systems. It is well known that forces propagate through granular structures along networks-force chains, whose structure is a function of history. It is much less clear how to describe this process, and even what kind of structures evolve in physical experiments. After a brief overview of the field, we consider models of force propagation and recent experiments to test these models. Among the latter are experiments that probe force profiles at the base of sandpiles and experiments that determine the Green's function response to point perturbations in granular systems. We also explore the nature of force fluctuations in slowly evolving systems, particulary sheared granular systems. These can be very strong-with rms fluctuations in the force that are as strong as the mean force. Finally, we pursue the analogy between conventional phases of matter, where we particularly focus on the transition between fluid and solid granular states in the presence of sustained horizontal shaking