Daniel Wyatt Howell

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 use 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.

Predictability and granular materials

Abstract Granular materials present a number of challenges to predictability. The classical description of a dense granular material is based on Coulomb friction. For a static array of grains, the Coulomb friction forces are typically underdetermined. If we are to make useful statements about such arrays, we must develop new approaches, including the development of statistical descriptions. Granular materials also show large fluctuations in the local forces. These fluctuations are quite sensitive to small perturbations in the packing geometry of the grains. In the past, they have typically been ignored. However, recent experiments and models are beginning to shed new light on their characteristics. This article briefly reviews some of this new work, and in particular presents experimental results characterizing fluctuations and the role of friction in granular materials.

Comparing simulation and experiment of a 2D granular Couette shear device.

Abstract.We present experiments along with molecular-dynamics (MD) simulations of a two-dimensional (2D) granular material in a Couette cell undergoing slow shearing. The grains are disks confined between an inner, rotating wheel and a fixed outer ring. The simulation results are compared to experimental studies and quantitative agreement is found. Tracking the positions and orientations of individual particles allows us to obtain density distributions, velocity and particle rotation rates for the system. The key issue of this paper is to show the extent to which quantitative agreement between an experiment and MD simulations is possible. Besides many differences in model details and the experiment, the qualitative features are nicely reproduced. We discuss the quantitative agreement/disagreement, give possible reasons, and outline further research perspectives.

Fluctuations and Flow for Granular Shearing

We present results from both simulation and experiment on a 2D granular shear-cell. The experiments determine the position of disks and their orientations over time, as well as the force on individual disks. We use computerized particle tracking techniques to achieve the former and photoelasticity to achieve the latter. The simulations use MD force laws and efficient algorithms to simulate as closely as possible the experimental system. We measure the radial dependence of velocities and their distributions. In particular we find that the azimuthal velocity decays exponentially to some background level within a distance of about 7 disk diameters from the shearing wheel. Experimentally the distribution of azimuthal velocities is found to have a complex, roughly bimodal distribution close the the shearing wheel which is indicative of a complex combination of slip, no-slip, and rolling processes at the boundary, and a more exponential distribution away from the shearing surface. The distribution of stresses shows a falloff which is approximately exponential at large forces, although it is probably not possible to determine which among competing models for force distributions best fits these results. The model can capture most but not all of the features seen in the experiment. The mean velocity profile, the qualitative nature of force chains and the distribution of velocities far from the shearing surface are well captured in the simulations. The velocity distribution near the shearing surface and the force distributions differ considerably between theory and experiment.

Statistical Properties of Dense Granular Matter

We review recent work characterizing force fluctuations and transmission in dense granular materials. These forces are carried preferentially on filimentary structures known as force chains. When a system is deformed, these chains tend to resist further deformation; with continued deformation, chains break and rearrange, leading to large spatio-temporal fluctuations. We first consider experiments on force fluctuations, diffusion and mobility under steady-state shear. We then turn to force transmission in static systems as determined by the response to a small point force. These experiments show that the packing structure and friction play important roles in determining the force transmission. Disordered highly frictional packings have responses that are similar to that of an elastic solid. Ordered packings show responses that may be described either by anisotropic elasticity or by a wave-like description.