Correlation between compacity distributions in compressed Si powders and in Si sintered pellets

Resistivity measurements have been performed on silicon powder beds with different thicknesses which were submitted to uniaxial pressure (0-640 MPa). For the smallest thicknesses of the Si pellets, the pressure dependence of conductivity may be described using models based on effective medium theory or strongest stresses network. For largest Si thicknesses, it exists an inhomogeneous distribution of pressure in the granular medium as a consequence of arching effects. It is shown that the conductivity variation with Si powder thickness may be understood using a distribution of conductivity induced by the distribution of pressure. Finally, it is shown that the conductivity of the sintered Si pellets is correlated with the uniaxial compression step. Received 14 September 2001 and Received in final form 18 December 2001     

Robust propagation direction of stresses in a minimal granular packing

By employing the adaptive network simulation method, we demonstrate that the ensemble-averaged stress caused by a local force for packings of frictionless rigid beads is concentrated along rays whose slope is consistent with unity: forces propagate along lines at 45 degrees to the horizontal or vertical. This slope is shown to be independent of polydispersity or the degree to which the system is sheared. Further confirmation of this result comes from fitting the components of the stress tensor to the null stress “constitutive equation”. The magnitude of the response is also shown to fall off with the -1/2 power of distance. We argue that our findings are a natural consequence of a system that preserves its volume under small perturbations. Received 30 April 2001 and Received in final form 16 August 2001     

Stress response function of a granular layer: Quantitative comparison between experiments and isotropic elasticity

We measured the vertical pressure response function of a layer of sand submitted to a localized normal force at its surface. We found that this response profile depends on the way the layer has been prepared: all profiles show a single centered peak whose width scales with the thickness of the layer, but a dense packing gives a wider peak than a loose one. We calculate the prediction of isotropic elastic theory in the presence of a bottom boundary and compare it to the data. We found that the theory gives the right scaling and the correct qualitative shape, but fails to really fit the data. Received 3 August 2001     

Directed force chain networks and stress response in static granular materials

A theory of stress fields in two-dimensional granular materials based on directed force chain networks is presented. A general Boltzmann equation for the densities of force chains in different directions is proposed and a complete solution is obtained for a special case in which chains lie along a discrete set of directions. The analysis and results demonstrate the necessity of including nonlinear terms in the Boltzmann equation. A line of nontrivial fixed-point solutions is shown to govern the properties of large systems. In the vicinity of a generic fixed point, the response to a localized load shows a crossover from a single, centered peak at intermediate depths to two propagating peaks at large depths that broaden diffusively. Received 16 January 2002     

Compaction of a granular material under cyclic shear

In this paper we present experimental results concerning the compaction of a granular assembly of spheres under periodic shear deformation. The dynamics of the system is slow and continuous when the amplitude of the shear is constant, but exhibits rapid evolution of the volume fraction when a sudden change in shear amplitude is imposed. This rapid response is shown to be uncorrelated with the slow compaction process. Received 31 March 2000     

The influence of grain shape,friction and cohesion on granular compaction dynamics

This article is a review of our recent and new experimental works on granular compaction. The effects of various microscopic parameters on the compaction dynamics are addressed, in particular the influence of the grain shape, the friction and the cohesion between the grains. Two dimensionnal and three dimensionnal systems are analysed. And the role of dimensionality will be emphasized. Theoretical and numerical investigations provide additional informations about that phenomenon. Indeed numerical models permit us to study the influence of some parameters not easily accessible experimentally. Our results show that the above mentioned parameters have a deep impact on the compaction dynamics. Anisotropic grains lead to two different compaction regimes separated by a “burst" of the packing fraction. Friction is observed to modify how the grains are arranged in the pile. This is confirmed by numerical simulations. Cohesive forces between particles inhibit compaction and lead to extremely low values of the packing fraction.     

On the existence of stationary states during granular compaction

When submitted to gentle mechanical taps a granular packing slowly compacts until it reaches a stationary state that depends on the tap characteristics. The properties of such stationary states are experimentally investigated. The influence of the initial state, taps properties and tapping protocol are studied. The compactivity of the packings is determinated. Our results strongly support the idea that the stationary states are genuine thermodynamic states.     

Experimental compaction of anisotropic granular media

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic and weakly confined granular material, using high-resolution -ray adsorption. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical solicitations evolve to a dense state. We find that the packing fraction evolution is slowed by the grain anisotropy but, as for spherically shaped grains, can be well fitted by a stretched exponential. For a given type of grains, the characteristic times of relaxation and of convection are found to be of the same order of magnitude. On the contrary, compaction mechanisms in the media strongly depend on the grain anisotropy.     

Testing the Edwards hypothesis in spin systems under tapping dynamics

The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for aaabstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by considering two distinct mechanisms of energy injection: thermal and random tapping. We find that ergodicity depends upon the tapping procedure (i.e. the way the blocked configurations are dynamically accessed): for thermal tapping ergodicity is a good approximation, while it fails to describe the asymptotic stationary state reached by the random tapping dynamics. Received 30 November 2001     

Short-time dynamics of a packing of polyhedral grains under horizontal vibrations

We analyze the dynamics of a 3D granular packing composed of particles of irregular polyhedral shape confined inside a rectangular box with a retaining wall subjected to horizontal harmonic forcing. The simulations are performed by means of the contact dynamics method for a broad set of loading parameters. We explore the vibrational dynamics of the packing, the evolution of solid fraction and the scaling of dynamics with the loading parameters. We show that the motion of the retaining wall is strongly anharmonic as a result of jamming and grain rearrangements. It is found that the mean particle displacement scales with inverse square of frequency, the inverse of the force amplitude and the square of gravity. The short-time compaction rate grows in proportion to frequency up to a characteristic frequency, corresponding to collective particle rearrangements between equilibrium states, and then it declines in inverse proportion to frequency.     

Stability limit of a granular monolayer

A granular monolayer is composed by spherical grains on a horizontal plate. The plate is then tilted until the monolayer breaks down. This critical angle has been measured for different widths and heights of the rectangular monolayer. The highest critical angles are found when one of these two characteristic lengths is less than about 30 bead diameters. When the polydispersity is less than one percent, the monolayer may be stable till angles close to 90^°. Arches induce large critical angles. On the other hand, for a large and high monolayer, the critical angle saturates towards a lower value. This angle is related to the static friction of a grain on the plate. A model based on the block dynamics is proposed to describe the behavior of the avalanche angle as a function of the size of the monolayer and the polydispersity of the beads.-1     

Force chain splitting in granular materials: A mechanism for large-scale pseudo-elastic behaviour

We investigate both numerically and analytically the effect of strong disorder on the large-scale properties of the hyperbolic equations for stresses proposed in J.-P. Bouchaud, M.E. Cates, P. Claudin, J. Phys. I 5, 639 (1995), and J.P. Wittmer, P. Claudin, M.E. Cates, J.-P. Bouchaud, Nature 382, 336 (1996); J.P. Wittmer, P. Claudin, M.E. Cates, J. Phys. I 7, 39 (1997). The physical mechanism that we model is the local splitting of the force chains (the characteristics of the hyperbolic equation) by packing defects. In analogy with the theory of light diffusion in a turbid medium, we propose a Boltzmann-like equation to describe these processes. We show that, for isotropic packings, the resulting large-scale effective equations for the stresses have exactly the same structure as those of an elastic body, despite the fact that no displacement field needs to be introduced at all. Correspondingly, the response function evolves from a two-peak structure at short scales to a broad hump at large scales. We find, however, that the Poisson ratio is anomalously large and incompatible with classical elasticity theory that requires the reference state to be thermodynamically stable. Received 13 November 2000 and Received in final form 3 January 2001     

Correlations and aggregate statistics in granular packs

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Vorono? cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as function of the sample size is discovered and the connection between such anomalous scaling and correlations is explained. It emerges that volume fluctuations might be described by means of a single universal equation for all samples at all cluster sizes.     

About the influence of friction and polydispersity on the jamming behavior of bead assemblies

We study the jamming of bead assemblies placed in a cylindrical container whose bottom is pierced with a circular hole. Their jamming behavior is quantified here by the median jamming diameter, that is the diameter of the hole for which the jamming probability is 0.5. Median jamming diameters of monodisperse assemblies are obtained numerically using the Distinct Element Method and experimentally with steel beads. We obtain good agreement between numerical and experimental results. The influence of friction is then investigated. In particular, the formation of concentric bead rings is observed for low frictions. We identify this phenomenon as a boundary effect and study its influence on jamming. Relying on measures obtained from simulation runs, the median jamming diameter of bidisperse bead assemblies is finally found to depend only on the volume-average diameter of their constituting beads. We formulate this as a tentative law and validate it using bidisperse assemblies of steel beads.     

Elastic medium confined in a column versus the Janssen experiment

We compute the stresses in an elastic medium confined in a vertical column, when the material is at the Coulomb threshold everywhere at the walls. Simulations are performed in 2 dimensions using a spring lattice, and in 3 dimensions, using the Finite Element Method. The results are compared to the Janssen model and to experimental results for a granular material. The necessity to consider elastic anisotropy to render qualitatively the experimental findings is discussed.     

Dynamical diversity and metastability in a hindered granular column near jamming

Granular media jam into a panoply of metastable states. The way in which these states are achieved depends on the nature of local and global constraints on grains; here we investigate this issue by means of a non-equilibrium stochastic model of a hindered granular column near its jamming limit. Grains feel the constraints of grains above and below them differently, depending on their position. A rich phase diagram with four dynamical phases (ballistic, activated, logarithmic and glassy) is revealed. The statistics of the jamming time and of the metastable states reached as attractors of the zero-temperature dynamics is investigated in each of these phases. Of particular interest is the glassy phase, where intermittency and a strong deviation from Edwards' flatness are manifest.     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in