Ripples and Shear Bands in Plowed Granular Media

Monodisperse packings of dry, air-fluidized granular media typically exist between volume fractions from $\Phi$= 0.585 to 0.64. We demonstrate that the dynamics of granular drag are sensitive to volume fraction $\Phi$ and their exists a transition in the drag force and material deformation from smooth to oscillatory at a critical volume fraction $\Phi_{c}=0.605$. By dragging a submerged steel plate (3.81 cm width, 6.98 cm depth) through $300 \mu m$ glass beads prepared at volume fractions between 0.585 to 0.635 we find that below $\Phi_{c}$ the media deformation is smooth and non-localized while above $\Phi_{c}$ media fails along distinct shear bands. At high $\Phi$ the generation of these shear bands is periodic resulting in the ripples on the surface. Work funded by The Burroughs Wellcome Fund and the Army Research Lab MAST CT

A Terradynamics of Legged Locomotion on Granular Media

The theories of aero- and hydrodynamics predict animal movement and device design in air and water through the computation of lift, drag, and thrust forces. Although models of terrestrial legged locomotion have focused on interactions with solid ground, many animals move on substrates that flow in response to intrusion. However, locomotor-ground interaction models on such flowable ground are often unavailable. We developed a force model for arbitrarily-shaped legs and bodies moving freely in granular media, and used this "terradynamics" to predict a small legged robot's locomotion on granular media using various leg shapes and stride frequencies. Our study reveals a complex but generic dependence of stresses in granular media on intruder depth, orientation, and movement direction and gives insight into the effects of leg morphology and kinematics on movement

Surprising simplicity in the modeling of dynamic granular intrusion

Granular intrusions, such as dynamic impact or wheel locomotion, are complex multiphase phenomena where the grains exhibit solid-like and fluid-like characteristics together with an ejected gas-like phase. Despite decades of modeling efforts, a unified description of the physics in such intrusions is as yet unknown. Here we show that a continuum model based on the simple notions of frictional flow and tension-free separation describes complex granular intrusions near free surfaces. This model captures dynamics in a variety of experiments including wheel locomotion, plate intrusions, and running legged robots. The model reveals that three effects (a static contribution and two dynamic ones) primarily give rise to intrusion forces in such scenarios. Identification of these effects enables the development of a further reduced-order technique (Dynamic Resistive Force Theory) for rapid modeling of granular locomotion of arbitrarily shaped intruders. The continuum-motivated strategy we propose for identifying physical mechanisms and corresponding reduced-order relations has potential use for a variety of other materials.Comment: 41 pages including supplementary document, 10 figures, and 8 vide

Entangled granular media

We study the geometrically induced cohesion of ensembles of granular "u-particles" which mechanically entangle through particle interpenetration. We vary the length-to-width ratio $l/w$ of the u-particles and form them into free-standing vertical columns. In laboratory experiment we monitor the response of the columns to sinusoidal vibration (frequency $f$, peak acceleration $\Gamma$). Column collapse occurs in a characteristic time, $\tau$, which follows the relation $\tau = f^{-1} \exp(\Delta / \Gamma)$. $\Delta$ resembles an activation energy and is maximal at intermediate $l/w$. Simulation reveals that optimal strength results from competition between packing and entanglement.Comment: 4 pages, 5 figure

High hops on sand influenced by added mass effects

Various animals exhibit locomotive behaviors (like sprinting and hopping) involving transient bursts of actuation coupled to the ground through internal elastic elements. The performance of such maneuvers is subject to reaction forces on the feet from the environment. On substrates like dry granular media, the laws that govern these forces are not fully understood and can vary with foot size and shape, material compaction (measured by the volume fraction, f ) and kinematics of intrusion. To gain insight into how such interactions affect jumping on granular media, we study the performance of a self-actuated spring mass robot with a 7.62-cm flat circular foot. We compare performance between two jump strategies: a single-cycle sine-wave actuation (a “single jump”) and a counter-movement pull-up phase proceeded by a single jump (a “stutter jump”); both jump methods perform well on hard ground. We systematically vary F at fixed actuation parameters for both strategies, and find that both of these jumps perform similarly poorly in loose-packed granular media, reaching only 44% of the close-packed jump height. Introducing a delay time between the pull-up phase and the push-off phase of the stutter jump (the delayed stutter jump) results in significantly improved jump heights at low volume fraction, achieving 77% of the close packed height. A 1D simulation of the robot jumping on granular media reveals that the commonly used depth dependent and velocity dependent model of granular intrusion force is insufficient to reproduce experimental jump heights. To gain insight into the behavior of the granular media during these impulsive events, we image a foot through a transparent sidewall, recording high speed videos at different packing states (F = 0.58‑0.63). To monitor grain flow, we adapt particle image velocimetry techniques to perform a 2D particle tracking velocimetry analysis on these images. A region of grains moving with similar downward speed to the intruder emerges. Subsequently, we implement an added-mass model, an effect observed in fluids, to our granular jumping simulation and find agreement with experiment

Stationary state volume fluctuations in a granular medium

A statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles. We periodically fluidize a column of glass beads and find that the sequence of volume fractions phi of post-fluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of phi exhibits, as a function of phi, a minimum corresponding to a maximum in the number of statistically independent regions. Measurements of the fluctuations enable us to determine the compactivity X, a temperature-like state variable introduced in the statistical theory of Edwards and Oakeshott [Physica A {\bf 157}, 1080 (1989)].Comment: published with minor change