CiteULike: kdesmond's granular

Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials

Jacques Duran — 2007-06-04T21:53:35-00:00

(2000)

Anomalous density dependence of static friction in sand

Viktor Horváth — 2008-05-03T00:04:28-00:00

Physical Review E, Vol. 54, No. 2. (1996), 2005.

Overshoot effect in the Janssen granular column: A crucial test for granular mechanics

G Ovarlez — 2008-04-29T13:43:46-00:00

Physical Review E, Vol. 67, No. 6. (30 June 2003), 060302.

On the Brink of Jamming: Granular Convection in Densely Filled Containers

Frank Rietz — 2008-02-23T22:06:54-00:00

Physical Review Letters, Vol. 100, No. 7. (2008)

Granulates are ubiquitous in nature and technology, but, despite their great importance, their dynamics are by far less well understood than those of liquids. We demonstrate in an almost compactly filled flat (Hele-Shaw) cell, where slow horizontal rotation simulates a variable gravitational force, that unexpected dynamic structures may arise under geometrical restrictions. The cell motion drives regular flow in the compact interior, and convection rolls combine with segregation. The container fill level is crucial for the dynamic regime. A transition from chute flow at lower fill levels to convection in densely packed containers is found. These observations suggest the existence of comparable phenomena in situations where so far no systematic search for dynamic patterns has been performed.

Flow, Ordering, and Jamming of Sheared Granular Suspensions

Denis Grebenkov — 2008-02-23T22:06:19-00:00

Physical Review Letters, Vol. 100, No. 7. (2008)

We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system “flow diagram” in the volume fraction or stress plane (, F): at low the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small F and diverging as the jamming point is approached; if the shear stress is strong enough, at higher an ordered flow regime is found, the order-disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy with the glassy region of thermal systems, slow dynamics followed by kinetic arrest occurs when the ordering transition is prevented.

Granular physics: Creating a dry variety of quicksand

Detlef Lohse — 2008-02-21T23:10:01-00:00

Nature, Vol. 432, No. 7018. (December 2004), pp. 689-690.

Seismicity and stress rotation in a granular model of the brittle crust

David Scott — 2008-02-15T02:54:29-00:00

Nature, Vol. 381 (June 1996), pp. 592-595.

THE basic mechanical process responsible for earthquakes and faulting is not known. The intuitive notion of frictional slip on faults between elastic crustal blocks cannot be reconciled with laboratory measurements of the strength of rocks1, field observations of heat flow2,3 and stress orientation4 around the San Andreas fault in California, and seismological estimates of the energy radiated by earthquakes5. The weakening of large faults by elevated pore-fluid pressure6 has been suggested as one solution to this paradox, but places severe constraints on the hydrological conditions of the faults concerned. Here I propose an alternative model for earthquake mechanics, in which the crust is treated as a system of many interlocking blocks divided by many faults7. The model combines this random granular structure with simple, deterministic mechanical interactions. Numerical simulations of the deformation of an aggregate of rough grains under compressive stress show earthquake-like elastodynamic failures without frictional heat production, and substantial rotation of stresses across shear zones, which mimics field observations. There remain problems of scale in comparing these simulations with nature, but a seismological test of the model may be possible.

Signatures of granular microstructure in dense shear flows

Daniel Mueth — 2008-02-15T02:49:13-00:00

Nature, Vol. 406 (27 July 2000), pp. 385-389.

Granular materials and ordinary fluids react differently to shear stresses. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands1, 2, 3, 4, 5—narrow zones of large relative particle motion, with essentially rigid adjacent regions. Because shear bands mark areas of flow, material failure and energy dissipation, they are important in many industrial, civil engineering and geophysical processes6. They are also relevant to lubricating fluids confined to ultrathin molecular layers7. However, detailed three-dimensional information on motion within a shear band, including the degree of particle rotation and interparticle slip, is lacking. Similarly, very little is known about how the microstructure of individual grains affects movement in densely packed material5. Here we combine magnetic resonance imaging, X-ray tomography and high-speed-video particle tracking to obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.

A Theoretical Study of the Liquid Bridge Forces between Two Rigid Spherical Bodies

Guoping Lian — 2008-01-27T03:34:34-00:00

Journal of Colloid and Interface Science, Vol. 161, No. 1. (November 1993), pp. 138-147.

This paper is concerned with liquid bridges between two spherical rigid bodies of equal radii under conditions where the effects of gravity are negligible. Previous work on the necessary condition for the stability of such bridges is examined and the minimum free-energy formulation applicable to any contact angle is proven. It is shown that this formulation is a more fundamental criterion for specifying the stable numerical solutions of the Laplace-Young equation, although equivalent to previous conjectures based on the liquid bridge neck diameter and filling angle. At relatively low contact angles, say <40[degree sign], the critical separation for rupture is given by the cube root of the liquid bridge volume to a good approximation. The toroidal approximation provides a simple method of estimating the total liquid bridge force. The "gorge method" of evaluation leads to errors of <10% for all stable separations and a wide range of bridge volumes. The accuracy is independent of contact angle because of geometrical self-similarity. Simple scaling coefficients can be introduced into the toroidal approximation to allow force estimations to be made with relatively high accuracy.

Granular matter: a tentative view

PG de Gennes — 2008-01-27T03:19:26-00:00

Reviews of modern physics, Vol. 71, No. 2. (1999), pp. 374-382.

Granular matter describes large collections of small grains, under conditions in which the Brownian motion of the grains is negligible (sizes d>1 micrometer). The grains can exhibit solidlike behavior and fluidlike behavior, but the description of these states is still controversial. The present discussion is restricted to static problems, for which the main approach is to describe properly the initial state of each volume element, when it was deposited from a fluid flow.

Granular solids, liquids, and gases

Heinrich Jaeger — 2008-01-27T03:16:12-00:00

Reviews of modern physics, Vol. 68, No. 4. (1996), pp. 1259-1273.

Granular materials are ubiquitous in the world around us. They have properties that are different from those commonly associated with either solids, liquids, or gases. In this review the authors select some of the special properties of granular materials and describe recent research developments.

Stationary state volume fluctuations in a granular medium

Matthias Schröter — 2008-01-23T19:30:10-00:00

Physical Review E, Vol. 71 (March 2005), pp. 030301-030305.

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 of postfluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of exhibits, as a function of , 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 temperaturelike state variable introduced in the statistical theory of Edwards and Oakeshott [Physica A 157, 1080 (1989)].

Granular jets

ST Thoroddsen — 2008-01-23T19:03:22-00:00

Physics of Fluids, Vol. 13, No. 1. (2001), pp. 4-6.

Nonlinear elasticity of granular media

DL Johnson — 2008-01-23T18:58:13-00:00

pp. 134-138.

The linear and nonlinear elastic properties of granular media are analyzed within the context of effective medium theories, as well as with numerical molecular dynamic simulations, assuming the validity of the Hertz-Mindlin theory at the single contact level. There is a crucial distinction between force laws which are path independent, leading to a hyper-elastic effective medium theory, and those which are path dependent, for which the deformation history must be followed explicitly. The effective medium theories provide a reasonable description of existing experimental data, considered as a function of applied stress, but there are significant discrepancies. Numerical simulations resolve the question as to whether the problem lies with the treatment of the individual grain-grain contact or with the effective medium approximation (ema). We find that the problem lies principally with the latter: The bulk modulus is well described by the ema but the shear modulus is not, principally because the ema does not correctly allow for the grains to relax from the affine motion assumed by the ema.

Effective temperature and jamming transition in dense, gently sheared granular assemblies

FQ Potiguar — 2008-01-23T18:54:31-00:00

The European Physical Journal E - Soft Matter, Vol. 19, No. 2. (6 February 2006), pp. 171-183.

Abstract. We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation. We find the same temperature for different tracer particles in the system. The temperature becomes independent on the shear rate for slow enough shear suggesting that it is the effective temperature of the jammed packing. However, we also show that the agreement of the effective temperature for different observables is only approximate, for very long times, suggesting that this defintion may not capture the full thermodynamics of the system. On the other hand, we find good agreement between the dynamical effective temperature and a compactivity calculated assuming that all jammed states are equiprobable. Therefore, this definition of temperature may capture an instance of the ergodic hypothesis for granular materials as proposed by theoretical formalisms for jamming. Finally, our simulations indicate that the average shear stress and apparent shear viscosity follow the usual relation with the shear rate for complex fluids. Our results show that the application of shear induces jamming in packings whose particles interact by tangential forces.

Numerical study of the stress response of two-dimensional dense granular packings

N Gland — 2008-01-23T18:52:29-00:00

The European Physical Journal E - Soft Matter, Vol. 20, No. 2. (4 June 2006), pp. 179-184.

Abstract. We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.

Signatures of Glass Formation in a Fluidized Bed of Hard Spheres

Daniel Goldman — 2008-01-23T18:42:00-00:00

Physical Review Letters, Vol. 96, No. 14. (2006)

We demonstrate that a fluidized bed of hard spheres during defluidization displays properties associated with formation of a glass. The final state is rate dependent, and as this state is approached, the bed exhibits heterogeneity with increasing time and length scales. The formation of a glass results in the arrest of macroscopic particle motion and thus the loss of fluidization. Microscopic motion persists in this state, but the bed can be jammed by application of a small increase in flow rate. Thus a fluidized bed can serve as a test system for studies of glass formation and jamming.

Understanding the Frequency Distribution of Mechanically Stable Disk Packings

Guo-Jie Gao — 2008-01-01T22:19:51-00:00

(8 Jun 2006)

Relative frequencies of mechanically stable (MS) packings of frictionless bidisperse disks are studied numerically in small systems. The packings are created by successively compressing or decompressing a system of soft purely repulsive disks, followed by energy minimization, until only infinitesimal particle overlaps remain. For systems of up to 14 particles most of the MS packings were generated. We find that the packings are not equally probable as has been assumed in recent thermodynamic descriptions of granular systems. Instead, the frequency distribution, averaged over each packing-fraction interval $Δ φ$, grows exponentially with increasing $φ$. Moreover, within each packing-fraction interval MS packings occur with frequencies $f_k$ that differ by many orders of magnitude. Also, key features of the frequency distribution do not change when we significantly alter the packing-generation algorithm--for example frequent packings remain frequent and rare ones remain rare. These results indicate that the frequency distribution of MS packings is strongly influenced by geometrical properties of the multidimensional configuration space. By adding thermal fluctuations to a set of the MS packings, we were able to examine a number of local features of configuration space near each packing including the time required for a given packing to break to a distinct one, which enabled us to estimate the energy barriers that separate one packing from another. We found a positive correlation between the packing frequencies and the heights of the lowest energy barriers $ε_0$. We also examined displacement fluctuations away from the MS packings to correlate the size and shape of the local basins near each packing to the packing frequencies.

Random close packing revisited: Ways to pack frictionless disks

Ning Xu — 2008-01-01T22:16:32-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 71, No. 6. (2005)

We create collectively jammed (CJ) packings of 50-50 bidisperse mixtures of smooth disks in two dimensions (2D) using an algorithm in which we successively compress or expand soft particles and minimize the total energy at each step until the particles are just at contact. We focus on small systems in 2D and thus are able to find nearly all of the collectively jammed states at each system size. We decompose the probability P() for obtaining a collectively jammed state at a particular packing fraction into two composite functions: (1) the density of CJ packing fractions (), which only depends on geometry, and (2) the frequency distribution (), which depends on the particular algorithm used to create them. We find that the function () is sharply peaked and that () depends exponentially on . We predict that in the infinite-system-size limit the behavior of P() in these systems is controlled by the density of CJ packing fractions—not the frequency distribution. These results suggest that the location of the peak in P() when N can be used as a protocol-independent definition of random close packing.

Jamming at zero temperature and zero applied stress: The epitome of disorder

Corey O’hern — 2007-09-21T04:00:05-00:00

Physical Review E, Vol. 68, No. 1. (25 July 2003), 011306.

We have studied how two- and three-dimensional systems made up of particles interacting with finite range; repulsive potentials jam (i.e.; develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions φ; the system is not jammed and each particle can move without impediment from its neighbors. For each configuration; there is a unique jamming threshold φ c at which particles can no longer avoid each other; and the bulk and shear moduli simultaneously become nonzero. The distribution of φ c values becomes narrower as the system size increases; so that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close packing. In fact; our results provide a well-defined meaning for “random close packing” in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold; point J ; occurring at zero temperature and applied stress and at the random-close-packing density; has properties reminiscent of an ordinary critical point. As point J is approached from higher packing fractions; power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure; shear modulus; and excess number of overlapping neighbors. Moreover; near point J ; certain quantities no longer self-average; suggesting the existence of a length scale that diverges at J . However; point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally; as point J is approached from high packing fractions; the density of vibrational states develops a large excess of low-frequency modes. Indeed; at point J ; the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity—perhaps even at the glass transition.

Statistics of the contact network in frictional and frictionless granular packings

Leonardo Silbert — 2008-01-01T22:14:34-00:00

Physical Review E, Vol. 66, No. 6. (10 December 2002), 061303.

Simulated granular packings with different particle friction coefficient μ are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces P ( f ) are computed and compared with existing experimental data. Here f ≡ F / F ̅ is the contact force F normalized by the average value F ̅ . P ( f ) exhibits exponential-like decay at large forces; a plateau/peak near f =1; with additional features at forces smaller than the average that depend on μ. Additional information beyond the one-point force distribution functions is provided in the form of the force-force spatial distribution function and the contact point radial distribution function. These quantities indicate that correlations between forces are only weakly dependent on friction and decay rapidly beyond approximately three particle diameters. Distributions of particle-particle contact angles show that the contact network is not isotropic and only weakly dependent on friction. High force-bearing structures; or force chains; do not play a dominant role in these three-dimensional; unloaded packings.

Force Chains, Microelasticity, and Macroelasticity

C Goldenberg — 2008-01-01T22:13:49-00:00

Physical Review Letters, Vol. 89, No. 8. (2002), 084302.

It has been claimed that quasistatic granular materials; as well as nanoscale materials; exhibit departures from elasticity even at small loadings. It is demonstrated; using 2D and 3D models with interparticle harmonic interactions; that such departures are expected at small scales [below O (100) particle diameters]; at which continuum elasticity is invalid; and vanish at large scales. The models exhibit force chains on small scales; and force and stress distributions which agree with experimental findings. Effects of anisotropy; disorder; and boundary conditions are discussed as well.

Friction enhances elasticity in granular solids

C Goldenberg — 2005-05-13T07:43:38-00:00

Nature, Vol. 435, No. 7039., pp. 188-191.

Granular solids, liquids, and gases

Heinrich Jaeger — 2005-11-15T05:15:04-00:00

Rev. Mod. Phys., Vol. 68, No. 4. (October 1996), pp. 1259-1273.

Granular materials are ubiquitous in the world around us. They have properties that are different from those commonly associated with either solids, liquids, or gases. In this review the authors select some of the special properties of granular materials and describe recent research developments.

Shock wave structure in a strongly nonlinear lattice with viscous dissipation

EB Herbold — 2008-01-01T17:37:07-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 75, No. 2. (2007)

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (Fn) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient pc, defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3/2). The expression for pc in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

Elastic wave propagation in confined granular systems

E Somfai — 2008-01-01T17:12:24-00:00

Phys. Rev. E, Vol. 72, No. 2. (August 2005), 021301.

We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wave front followed by random oscillations made of multiply scattered waves. We find that the coherent wave front is insensitive to details of the packing: force chains do not play an important role in determining this wave front. The coherent wave propagates linearly in time, and its amplitude and width depend as a power law on distance, while its velocity is roughly compatible with the predictions of macroscopic elasticity. As there is at present no theory for the broadening and decay of the coherent wave, we numerically and analytically study pulse propagation in a one-dimensional chain of identical elastic balls. The results for the broadening and decay exponents of this system differ significantly from those of the random packings. In all our simulations, the speed of the coherent wave front scales with pressure as p<SUP>1/6</SUP> ; we compare this result with experimental data on various granular systems where deviations from the p<SUP>1/6</SUP> behavior are seen. We briefly discuss the eigenmodes of the system and effects of damping are investigated as well.

Surface elastic waves in granular media under gravity and their relation to booming avalanches

L Bonneau — 2008-01-01T17:11:47-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 75, No. 1. (2007)

Due to the nonlinearity of Hertzian contacts, the speed of sound c in granular matter is expected to increase with pressure as P1/6. A static layer of grains under gravity is thus stratified so that the bulk waves are refracted toward the surface. The reflection at the surface being total, there is a discrete number of modes (both in the sagittal plane and transverse to it) localized close to the free surface. The shape of these modes and the corresponding dispersion relation are investigated in the framework of an elastic description taking into account the main features of granular matter: Nonlinearity between stress and strain and the existence of a yield transition. We show in this context that the surface modes localized at the free surface exhibit a waveguide effect related to the nonlinear Hertz contact. Recent results about the song of dunes are reinterpreted in light of the theoretical results. The predicted propagation speed is compared with measurements performed in the field. Taking into account the finite depth effects, we show that the booming instability threshold can be explained quantitatively by a waveguide cutoff frequency below which no sound can propagate. Therefore, we propose another look at a recent controversy, confirming that the song of dunes can well originate from a coupling between avalanching grains and surface elastic waves once the specificity of surface waves (we baptized Rayleigh-Hertz) is correctly taken into account.

Structural signature of jamming in granular media

Eric Corwin — 2005-06-23T02:21:24-00:00

Nature, Vol. 435, No. 7045., pp. 1075-1078.

Experimental and computational studies of jamming

Chaoming Song — 2007-12-31T22:09:31-00:00

Journal of Physics: Condensed Matter, Vol. 17, No. 24. (2005), pp. S2755-S2770.

Jamming is a common feature of out-of-equilibrium systems showing slow relaxation dynamics. Here we review our efforts in understanding jamming in granular materials using experiments and computer simulations. We first obtain an estimation of an effective temperature for a slowly sheared granular material very close to jamming. The measurement of the effective temperature is realized in the laboratory by slowly shearing a closely packed ensemble of spherical beads confined by an external pressure in a Couette geometry. All the probe particles, independent of their characteristic features, equilibrate at the same temperature, given by the packing density of the system. This suggests that the effective temperature is a state variable for the nearly jammed system. Then we investigate numerically whether the effective temperature can be obtained from a flat average over the jammed configuration at a given energy in the granular packing, as postulated by the thermodynamic approach to grains.

Experimental investigation of granular dynamics close to the jamming transition

G Caballero — 2007-12-31T22:08:00-00:00

Journal of Physics: Condensed Matter, Vol. 17, No. 24. (2005), pp. S2503-S2516.

We present different experiments on dense granular assemblies with the aim of clarifying the notion of 'jamming transition' for these assemblies of non-Brownian particles. The experimental set-ups differ in the way in which external perturbations are applied in order to unjam the systems. The first experiment monitors the response to a locally applied deformation of a model packing at rest. The two other experiments study local and collective dynamics in a granular assembly weakly excited by vibration.

Jamming transition in emulsions and granular materials

HP Zhang — 2007-12-31T22:05:10-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 72, No. 1. (2005)

We investigate the jamming transition in packings of emulsions and granular materials via molecular dynamics simulations. The emulsion model is composed of frictionless droplets interacting via nonlinear normal forces obtained using experimental data acquired by confocal microscopy of compressed emulsions systems. Granular materials are modeled by Hertz-Mindlin deformable spherical grains with Coulomb friction. In both cases, we find power-law scaling for the vanishing of pressure and excess number of contacts as the system approaches the jamming transition from high volume fractions. We find that the construction history parametrized by the compression rate during the preparation protocol has a strong effect on the micromechanical properties of granular materials but not on emulsions. This leads the granular system to jam at different volume fractions depending on the histories. Isostaticity is found in the packings close to the jamming transition in emulsions and in granular materials at slow compression rates and infinite friction. Heterogeneity of interparticle forces increases as the packings approach the jamming transition which is demonstrated by the exponential tail in force distributions and the small values of the participation number measuring spatial localization of the forces. However, no signatures of the jamming transition are observed in structural properties, like the radial distribution functions and the distributions of contacts.

Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material

Aaron Keys — 2007-12-31T22:01:32-00:00

Nat Phys, Vol. 3, No. 4. (April 2007), pp. 260-264.

Jamming Transition in Granular Systems

TS Majmudar — 2007-12-31T21:59:04-00:00

Physical Review Letters, Vol. 98, No. 5. (2007)

Recent simulations have predicted that near jamming for collections of spherical particles, there will be a discontinuous increase in the mean contact number Z at a critical volume fraction c. Above c, Z and the pressure P are predicted to increase as power laws in -c. In experiments using photoelastic disks we corroborate a rapid increase in Z at c and power-law behavior above c for Z and P. Specifically we find a power-law increase as a function of -c for Z-Zc with an exponent around 0.5, and for P with an exponent around 1.1. These exponents are in good agreement with simulations. We also find reasonable agreement with a recent mean-field theory for frictionless particles.

Dynamics of Impact Cratering in Shallow Sand Layers

JF Boudet — 2007-12-31T21:43:41-00:00

Physical Review Letters, Vol. 96, No. 15. (2006)

When a solid sphere impacts a shallow layer of sand deposited on a solid surface, a crater can be obtained. The dynamics of the opening of the crater can be followed accurately. During this opening, the radius of the crater can be conveniently modeled by an exponential saturation with a well-defined time constant. The crater then closes up partially once the opening phase is over as the sand avalanches down the slope of the crater. We here present a detailed study of the full dynamics of the crater formation as well as the dynamics of the corrola formed during this process. A simple model accounts for most of our observations.

Voronoi neighbor statistics of homogeneously sheared inelastic hard disks and hard spheres

Senthil Kumar — 2007-12-31T21:41:51-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 73, No. 5. (2006)

In this work we extend our earlier Voronoi neighbor analysis [J. Chem. Phys. 123, 074502 (2005)] to homogeneously sheared inelastic hard-particle structures, the simplest model for rapid granular matter. The pair distribution function is partitioned into the nth neighbor coordination number (Cn), and the nth neighbor position distribution [fn(r)]. The distribution of the number of Voronoi faces (Pn) is also considered since C1 is its mean. We report the Cn and Pn for the homogeneously sheared inelastic hard-disk and hard-sphere structures. These statistics are sensitive to shear ordering transition, the nonequilibrium analogue of the freezing transition. In the near-elastic limit, the sheared fluid statistics approach that of the thermodynamic fluid. On shear ordering, due to the onset of order, the Cn for sheared structures approach that of the thermodynamic solid phase. The suppression of nucleation by the homogeneous shear is evident in these statistics. As inelasticity increases, the shear ordering packing fraction increases. Due to the topological instability of the isotropically perturbed face-centered cubic lattice, polyhedra with faces 12 to 18, with a mean at 14, coexist even in the regular close packed limit for the thermodynamic hard-sphere solid. In shear ordered inelastic hard-sphere structures there is a high incidence of 14-faceted polyhedra and a consequent depletion of polyhedra with faces 12, 13, 15–18, due to the formation of body-centered-tetragonal (bct) structures. These bct structures leave a body-centered-cubic-like signature in the Cn and Pn data. On shear ordering, close-packed layers slide past each other. However, with a velocity-dependent coefficient of restitution, at a critical shear rate these layers get disordered or amorphized. We find that the critical shear rate for amorphization is inversely proportional to the particle diameter, as compared to the inverse square scaling observed in dense colloidal suspensions.

Unified force law for granular impact cratering

Hiroaki Katsuragi — 2007-12-31T21:38:11-00:00

Nat Phys, Vol. 3, No. 6. (June 2007), pp. 420-423.

Penetration of spheres into loose granular media

John de Bruyn — 2007-12-31T21:32:24-00:00

Canadian Journal of Physics, Vol. 82, No. 6. (3 June 2004), pp. 439-446.

Morphology and Scaling of Impact Craters in Granular Media

Amanda Walsh — 2007-12-31T21:24:11-00:00

Physical Review Letters, Vol. 91, No. 10. (2003), 104301.

We present the results of experiments on impact craters formed by dropping a steel ball vertically into a container of small glass beads. As the energy of impact increases; we observe a progression of crater morphologies analogous to that seen in craters on the moon. We find that both the diameter and the depth of the craters are proportional to the 1/4 power of the energy. The ratio of crater diameter to rim-to-floor depth is constant for low-energy impacts; but increases at higher energy; similar to what is observed for lunar craters.

Dynamics of shallow impact cratering

MA Ambroso — 2007-12-31T21:14:27-00:00

Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 72, No. 4. (2005)

We present data for the time dependence of wooden spheres penetrating into a loose noncohesive packing of glass beads. The stopping time is a factor of 3 longer than the time d/v0 needed to travel the total penetration distance d at the impact speed v0. The acceleration decreases monotonically throughout the impact. These kinematics are modeled by a position- and velocity-dependent stopping force that is constrained to reproduce prior observations for the scaling of the penetration depth with the total drop distance.

The jamming route to the glass state in weakly perturbed granular media

G D'Anna — 2007-12-31T21:09:45-00:00

Nature, Vol. 413, No. 6854. (2001), pp. 407-409.