We derive a general dimensionless form for granular locomotion, which is validated in experiments and Discrete Element Method (DEM) simulations. The form instructs how to scale size, mass, and driving parameters in order to relate dynamic behaviors of different locomotors in the same granular media. The scaling can be derived by assuming intrusion forces arise from Resistive Force Theory (RFT) or equivalently by assuming the granular material behaves as a continuum obeying a frictional yield criterion. The scalings are experimentally confirmed using pairs of wheels of various shapes and sizes under many driving conditions in a common sand bed. We discuss why the two models provide such a robust set of scaling laws even though they neglect a number of the complexities of granular rheology. Motivated by potential extra-planetary applications, the dimensionless form also implies a way to predict wheel performance in one ambient gravity based on tests in a different ambient gravity. We confirm this using DEM simulations, which show that scaling relations are satisfied over an array of driving modes even when gravity differs between scaled tests.
The physical mechanisms that bring about the propulsion of a rotating helix in a granular medium are considered. A propulsive motion along the axis of the rotating helix is induced by both symmetry breaking due to the helical shape, and the anisotropic frictional forces undergone by all segments of the helix in the medium. Helix dynamics is studied as a function of helix rotation speed and its geometrical parameters. The effect of the granular pressure and the applied external load were also investigated. A theoretical model is developed based on the anisotropic frictional force experienced by…
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 runnin…
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 …
Compared to agile legged animals, wheeled and tracked vehicles often suffer large performance loss on granular surfaces like sand and gravel. Understanding the mechanics of legged locomotion on granular media can aid the development of legged robots with improved mobility on granular surfaces; however, no general force model yet exists for granular media to predict ground reaction forces during complex limb intrusions. Inspired by a recent study of sand-swimming, we develop a resistive force model in the vertical plane for legged locomotion on granular media. We divide an intruder of complex m…
Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs, and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to describe the complex interactions of locomotors with GM. In this paper, we use experimental, computational, and theoretical approaches to develop a terramechanics for bio-inspired locomotion in granular environments. We use a fluidized bed to prepare GM with a desired gl…
Mechanisms of locomotion in microscopic systems are of great interest not only for technological applications, but also for the sake of understanding, and potentially harnessing, processes far from thermal equilibrium. Down-scaling is a particular challenge, and has led to a number of interesting concepts including thermal ratchet systems and asymmetric swimmers. Here we present a system which is particularly intriguing, as it is self-assembling and uses a robust mechanism which can be implemented in various settings. It consists of small spheres of different size which adhere to each other, a…
A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. Derived employing the hydrodynamic approach, GSH is such a theory, though as yet a qualitative one. The behavior being accounted for includes static stress distribution, elastic wave, elasto-plastic motion, the critical state and rapid dense flow. The equations and application to a few typical experiments are presented here.
Reciprocal swimming in viscoelastic granular hydrogels
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）；University of Michigan（密歇根大学）；Otto von Guericke University Magdeburg（马格德堡奥托·冯·格里克大学）；Brandenburg University of Applied Sciences（勃兰登堡应用科技大学）
We investigate the sliding of objects on an inclined granular surface close to the avalanche threshold. Our experiments show that the stability is driven by the surface deformations. Heavy objects generate footprint-like deformations which stabilize the objects on the slopes. Light objects do not disturb the sandy surfaces and are also stable. For intermediate weights, the deformations of the surface destabilize the objects and generate sliding. A characteristic pressure for which the solid friction is minimal is evidenced. Applications to the locomotion of devices and animals on sandy slopes …
Granular media are considered "athermal", because the grains are too large to display Brownian type thermal fluctuations. Yet being macroscopic, every grain undergoes thermal expansion, possesses a temperature that may be measured with a thermometer, and consists of many, many internal degrees of freedom that in their sum do affect granular dynamics. Therefore, including them in a comprehensive approach to account for granular behavior entails crucial advantages. The pros and cons of thermal versus athermal descriptions are considered.
Combining high-speed photography with laser profilometry, we study the dynamics and the morphology of liquid-drop impact cratering in wet granular media---a ubiquitous phenomenon relevant to many important geological, agricultural, and industrial processes. By systematically investigating important variables such as impact energy, the size of impinging drops and the degree of liquid saturation in granular beds, we uncover a novel scaling for the size of impact craters. We show that this scaling can be explained by considering the balance between the inertia of impinging drops and the strength …
Scattering methods are widespread used to characterize the structure and constituents of matter on small length scales. This motivates this introductory text on identifying prospective approaches to scattering-based methods for granular media. A survey to light scattering by particles and particle ensembles is given. It is elaborated why the established scattering methods using X-rays and visible light cannot in general be transferred to granular media. Spectroscopic measurements using Terahertz radiation are highlighted as they to probe the scattering properties of granular media, which are s…
We establish that the rheological curve of dry granular media is non-monotonic, both in the presence and absence of external mechanical agitations. In the presence of weak vibrations, the non-monotonic flow curves govern a hysteretic transition between slow but steady and fast, inertial flows. In the absence of vibrations, the non-monotonic flow curve governs the yielding behavior of granular media. Finally, we show that non-monotonic flow curves can be seen in at least two different flow geometries and for several granular materials.
Investigation of dynamics in dense granular media is challenging. Here we present a setup that facilitates gas fluidization of dense granular media in microgravity. The dynamics is characterized using diffusing wave spectroscopy. We demonstrate that agitated granular media reach a steady state within fractions of a second in drop tower flights. The intensity autocorrelation functions obtained in microgravity show a remarkable dependence on sample volume fraction and driving strength. A plateau in correlation merges at low volume fractions and strong driving, while correlation decays only very …
We experimentally probe nonlinear wave propagation in weakly compressed granular media, and observe a crossover from quasi-linear sound waves at low impact, to shock waves at high impact. We show that this crossover grows with the confining pressure $P_0$, whereas the shock wave speed is independent of $P_0$ --- two hallmarks of granular shocks predicted recently. The shocks exhibit powerlaw attenuation, which we model with a logarithmic law implying that local dissipation is weak. We show that elastic and potential energy balance in the leading part of the shocks.
Impact dynamics is measured for spherical and cylindrical projectiles of many different densities dropped onto a variety non-cohesive granular media. The results are analyzed in terms of the material-dependent scaling of the inertial and frictional drag contributions to the total stopping force. The inertial drag force scales similar to that in fluids, except that it depends on the internal friction coefficient. The frictional drag force scales as the square-root of the density of granular medium and projectile, and hence cannot be explained by the combination of granular hydrostatic pressure …
Structural characteristics are considered to be the dominant factors in determining the effective properties of granular media, particularly in the scope of transport phenomena. Towards improved heat management, thermal transport in granular media requires an improved fundamental understanding. In this study, the effects of packing structure on heat transfer in granular media are evaluated at macro- and grain-scales. At the grain-scale, a gas-solid coupling heat transfer model is adapted into a discrete-element-method to simulate this transport phenomenon. The numerical framework is validated …
Density waves are characteristic for fluidized beds and affect measurements on liquid-like dynamics in fluidized granular media. Here, the intensity autocorrelation function as obtainable with diffusing-wave spectroscopy is derived in the presence of density waves. The predictions by the derived form of the IACF match experimental observations from a gas-fluidized bed. The model suggests separability of the contribution from density waves from the contribution by microscopic scatterer displacement to the decay of correlation, thus paves the way for characterizing microscopic particle motions u…
Two approaches exist to account for granular dynamics: The athermal one takes grains as elementary, the thermal one considers the total entropy that includes microscopic degrees of freedom such as phonons and electrons. Discrete element method (DEM), granular kinetic theory and athermal statistical mechanics (ASM) belong to the first, granular solid hydrodynamics (GSH) to the second one. A discussion of the conceptual differences between both is given here, leading, among others, to the following insights: (1) While DEM and granular kinetic theory are well justified to take grains as athermal,…
We discuss the uniform shear flow of a fluidized granular bed composed of monodisperse Hertzian spheres. Considering high densities around the glass transition density of inelastic Hertzian spheres, we report kinetic theory expressions for the Newtonian viscosity as well as the Bagnold coefficient. We discuss the dependence of the transport coefficients on density and coefficient of restitution.
We probe the rheology of weakly vibrated granular flows as function of flow rate, vibration strength and pressure by performing experiments in a vertically vibrated split-bottom shear cell. For slow flows, we establish the existence of a novel vibration dominated granular flow regime, where the driving stresses smoothly vanish as the driving rate is diminished. We distinguish three qualitatively different vibration dominated rheologies, most strikingly a regime where the shear stresses no longer are proportional to the pressure.
When compressed frictional granular media are decompressed, generically a fragile configuration is created at low pressures. Typically this is accompanied by a giant frictional slippage as the fragile state collapses. We show that this instability is understood in terms of a scaling theory with theoretically computable amplitudes and exponents. The amplitude diverges in the thermodynamic limit hinting to the possibility of huge frictional slip events in decompressed granular media. The physics of this slippage is discussed in terms of the probability distribution functions of the tangential an…
Laboratory experiments and numerical simulation reveal that a submerged intruder dragged horizontally at constant velocity within a granular medium experiences a lift force whose sign and magnitude depend on the intruder shape. Comparing the stress on a flat plate at varied inclination angle with the local surface stress on the intruders at regions with the same orientation demonstrates that intruder lift forces are well approximated as the sum of contributions from flat-plate elements. The plate stress is deduced from the force balance on the flowing media near the plate.
The drag force exerted on an object intruding into granular media can depend on the object's velocity as well as the depth penetrated. We report on intrusion experiments at constant speed over four orders in magnitude together with systematic molecular dynamics simulations well beyond the quasi-static regime. We find that velocity dependence crosses over to depth dependence at a characteristic time after initial impact. This crossover time scale, which depends on penetration speed, depth, gravity and intruder geometry, challenges current models that assume additive contributions to the drag.
Sudden release of energy in explosion creates craters in granular media. In comparison with well-studied impact cratering in granular media, our understanding of explosion cratering is still primitive. Here, we study low-energy lab-scale explosion cratering in 3D granular media using controlled pulses of pressurized air. We identify four regimes of explosion cratering at different burial depths, which are associated with distinct explosion dynamics and result in different crater morphologies. We propose a general relation between the dynamics of granular flows and the surface structures of res…
We develop the concept of frequency dependent effective mass, M(omega), of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of M(omega) provide signatures of the dissipation of acoustic modes, elasticity and aging effects in the granular medium. We perform humidity controlled experiments and interpret the data in terms of a continuum model and a "trap" model of thermally activated capillary bridges at the contact points. The results suggest that attenuation i…
Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, the range of which is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: (i)~static stress distribution, clogging; (ii)~elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; (iii)~rapid dense flow: the $μ$-rheology, Bagnold scaling and the stress minimum; (iv)~elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: she…
Like in liquids, objects moving in granular materials experience a drag force. We investigate here whether and how the object acceleration affect this drag force. The study is based on simulations of a canonical drag test, which involves vertically uplifting a plate through a granular packing with a prescribed acceleration pattern. Depending on the plate size, plate depth and acceleration pattern, results evidence a rate-independent regime and an inertial regime where the object acceleration strongly enhances the drag force. We introduce an elasto-inertial drag force model that captures the me…
We perform numerical simulations to examine particle diffusion at steady shear in a model granular material in two dimensions at the jamming density and zero temperature. We confirm findings by others that the diffusion constant depends on shear rate as $D\sim\dotγ^{q_D}$ with $q_D<1$, and set out to determine a relation between $q_D$ and other exponents that characterize the jamming transition. We then examine the the velocity auto-correlation function, note that it is governed by two processes with different time scales, and identify a new fundamental exponent, $λ$, that characterizes an alg…
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 $Γ$). Column collapse occurs in a characteristic time, $τ$, which follows the relation $τ= f^{-1} \exp(Δ/ Γ)$. $Δ$ resembles an activation energy and is maximal at intermediate $l/w$. Simulation reveals that optimal streng…
Modeling of pores generation in 2-D with granular grains using molecular dynamics method is reported in this work. Grains with certain diameter distribution are let falling due to gravity. Three configurations (larger diameter on top, smaller diameter on top, and mixed) and two kinds of mixture (same grains density and same grains mass) are used in the simulation. Mixture with heterogen density gives higher porosity than the homogen one for higher initial height, but change into opposite condition for lower initial height.
We investigate the evolution of the force network in experimental systems of two-dimensional granular materials under impact. We use the first Betti number, $β_1$, and persistence diagrams, as measures of the topological properties of the force network. We show that the structure of the network has a complex, hysteretic dependence on both the intruder acceleration and the total force response of the granular material. $β_1$ can also distinguish between the nonlinear formation and relaxation of the force network. In addition, using the persistence diagram of the force network, we show that the …
We use a computational model to investigate the emergence of interaction forces between pairs of intruders in a horizontally vibrated granular fluid. The time evolution of a pair of particles shows a maximum of the likelihood to find the pair at contact in the direction of shaking. This relative interaction is further studied by fixing the intruders in the simulation box where we identify effective mechanical forces, and torques between particles and quantify an emergent long range attractive force as a function of the shaking relative angle, amplitude, and the packing density of grains. We de…
Despite the ubiquitousness and technological and scientific importance of granular matter, our understanding is still very poor compared to molecular fluids and solids. Until today, there is no unified description, which indeed seems unreachable. However, it has been proposed that important advances could be attained for noncohesive, hard-sphere like systems, by combining fluid dynamics with phase-field modeling through an appropriate order parameter (Aranson and Tsimring, 2006). Here, we present a review of the dynamics of confined granular matter, for which this systematic approach has prove…
This paper is devoted to the basic question of what factors determine the strain field in a quasi static granular flow. It is shown that using stress - strain rate relations is not the proper way to understand quasi static rheology. An alternative approach is discussed where the local deformation is regarded as the cause of deformation in the vicinity. We suggest a continuum model where the local shear strain is proportional to its Laplacian and the proportionality factor is determined by the local stress. The predicted behavior is tested in a three dimensional shear cell by means of computer …
Characterizing forces on deformable objects intruding into sand and soil requires understanding the solid and fluid-like responses of such substrates and their effect on the state of the object. The most detailed studies of intrusion in dry granular media have revealed that interactions of fixed-shape objects during free impact (e.g. cannonballs) and forced slow penetration can be described by hydrostatic and hydrodynamic-like forces. Here we investigate a new class of granular interactions: rapid intrusions by objects that change shape (self-deform) through passive and active means. Systemati…
We propose a cruiser able to move in a granular medium made of nearly 50-50 bidisperse dissipative particles under gravity. The cruiser has a circular shape with a square indentation on its edge. By shifting and then ejecting granular particles entering its indent-region facing a given direction, the cruiser gains thrust to push itself forward in the same direction, which can be either perpendicular or parallel to gravity. Using molecular dynamics (MD) simulations, we identify three universal phases during one particle-ejection process: 1) acceleration by the ejection thrust, 2) deceleration b…
