Analysis of stresses in two-dimensional isostatic granular systems

We analyze a recently proposed continuous model for stress fields that develop in two-dimensional purely isostatic granular systems. We present a reformulation of the field equations, as a linear first-order hyperbolic system, and show that it is very convenient both for analysis and for numerical computations. Our analysis allows us to predict quantitatively the formation and directions of stress paths and, from these, trajectories and magnitudes of force chains, given the structure in terms of a particular fabric tensor. We further predict quantitatively changes of stresses along the paths, as well as leakage and branching of stress from the main paths into the cones that they make in terms of the fabric tensor. Numerical computations in both Cartesian and cylindrical coordinates verify the analytic results and illustrate the rich behavior discovered. All the phenomena predicted by our solutions have been observed experimentally, suggesting that stresses in isostatic systems can form a base model for a more developed stress theory in granular materials.     

Evolution of percolating force chains in compressed granular media

The evolution of effective force chains percolating through a compressed granular system is investigated. We compressed an ensemble of spherical particles monitoring the macroscopic constitutive behavior and the acoustic signals emitted by microscopic rearrangements of particles. We applied the continuous damage model of fiber bundles to describe the evolution of the array of force chains. The model provides a nonlinear constitutive behavior in good quantitative agreement with the experimental results. The amplitude distribution of acoustic signals was found experimentally to follow a power law of an exponent delta=1.15+/-0.05, which is in good agreement with the analytic solution of the model.     

Stress chain solutions in two-dimensional isostatic granular systems: fabric-dependent paths, leakage, and branching

The stress field equations for two-dimensional disordered isostatic granular materials are reformulated, giving new results beyond the commonly accepted force chains. Localized loads give rise to exactly determinable cones of influence, bounded by stress chains. Disorder couples same-source chains, attenuates stresses along chains, causes stress leakage from chains into the cone, and gives rise to branching. Chains from spatially separate sources do not interact. The formulation is convenient for computation, and several numerical solutions are presented.     

重力作用下颗粒介质应力链的离散元模拟

用离散元的方法模拟了仅有重力作用的二维颗粒系统内部力的分布情况,并根据力的大小得到颗粒之间的应力链.模拟结果与颗粒介质研究中的两个著名模型q模型和α模型作了对比,并与光弹实验的结果作了比较.对比结果表明,模拟结果与实验相似,而与两个概率模型有一定的差异.另外计算结果还表明,颗粒介质中力大小的概率分布极为不均匀,较大的力概率呈指数衰减,应力链的分布具有分形特征. 关键词： 颗粒介质 离散元 应力链 光弹实验     

颗粒链在振动条件下的行为研究

采用实验方法研究打结颗粒链在外部激振下解结过程与激振源以及颗粒链长度的关系.实验结果表明颗粒链结解开所需的时间与振动频率有关,颗粒链解结存在截止频率和最佳振动频率;颗粒链解结时间与链长之间呈非线性关系.同时采用Monte Carlo时步模拟的方法,对珠链解结的动力学模型进行仿真.     

Knots and random walks in vibrated granular chains

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with theoretical values.     

Compaction and force propagation in granular packings

Motivated by experimental results in granular media, and some recently proposed scalar force models for these materials, some aspects of packing properties and their force distributions are studied in a frustrated Ising lattice gas.     

Nonlinear waves in dry and wet Hertzian granular chains

A one-dimensional dry granular medium, a chain of beads which interact via the nonlinear Hertz potential, exhibits strongly nonlinear behaviors. When such an alignment further contains some fluid in the interstices between grains, it may exhibit new interesting features. We report some recent experiments, analysis and numerical simulations concerning nonlinear wave propagation in dry and wet chains of spheres. We consider first a monodisperse chain as a reference case. We then analyze how the pulse characteristics are modified in the presence of an interstitial viscous fluid. The fluid not only induces dissipation but also strongly affect the intergrain stiffness: in a wet chain, wave speed is enhanced and pulses are shorter. Simple experiments performed with a single sphere colliding a wall covered by a thin film of fluid confirm these observations. We demonstrate that even a very small amount of fluid can overcome the Hertzian potential and is responsible for a large increase of contact stiffness. Possible mechanisms for wet contact hardening are related to large fluid shear rate during fast elastohydrodynamic collision between grains.     

Modeling force transmission in granular materials

The probability density function of contact forces in granular materials has been extensively studied and modeled as an outstanding signature of granular microstructure. Arguing that particle environments play a fundamental role in force transmission, we analyze the effects of steric constraints with respect to force balance condition and show that each force may be considered as resulting from a balance between lower and larger forces in proportions that mainly depend on steric effects. This idea leads to a general model that predicts an analytical expression of force density with a single free parameter. This expression fits well our simulation data and generically predicts the exponential fall-off of strong forces, a small peak below the mean force and the non-zero probability of vanishingly small forces.     

Synchronization and emergence in complex systems

We show how novel behaviour can emerge in complex systems at the global level through synchronization of the activities of their constituent units. Two mechanisms are suggested for the emergence, namely non-diffusive coupling and time delays. In this way, simple units can synchronize to display complex dynamics, or conversely, simple dynamics may arise from complex constituents.     

Coarsening in granular systems

We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular media. Thereafter, dilute systems, the so-called “granular gases”, are discussed: idealized kinetic models, such as the gas of inelastic hard spheres in the cooling regime, are the optimal playground to study the slow growth of correlated structures, e.g., shear patterns, vortices, and clusters. In fluidized experiments, liquid–gas or solid–gas separations have been observed. In the case of monolayers of particles, phase coexistence and coarsening appear in several different setups, with mechanical or electrostatic energy input. Phenomenological models describe, even quantitatively, several experimental measures, both for the coarsening dynamics and for the dynamic transition between different granular phases. The origin of the underlying bistability is in general related to negative compressibility from granular hydrodynamics computations, even if the understanding of the mechanism is far from complete. A relevant problem, with important industrial applications, is related to the demixing or segregation of mixtures, for instance in rotating tumblers or on horizontally vibrated plates. Finally, the problem of compaction of highly dense granular materials, which is relevant in many practical situations, is usually described in terms of coarsening dynamics: there, bubbles of misaligned grains evaporate, allowing the coalescence of optimally arranged islands and a progressive reduction of the total occupied volume.     

Strain stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model system to investigate the contribution of entanglements to strain stiffening. The chain packings are sheared in uniaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds the scale of the confining pressure, similar to granular packings of unconnected particles. In contrast, packings of chains which are long enough to form loops exhibit strain stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.     

Observation of two-wave structure in strongly nonlinear dissipative granular chains

In a strongly nonlinear viscous granular chain impacted by a single grain we observe a wave disturbance that consists of two parts exhibiting two time scales of dissipation. Above a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shocklike attenuating pulse.     

Jamming transition in granular systems

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 phi(c). Above phi(c), Z and the pressure P are predicted to increase as power laws in phi-phi(c). In experiments using photoelastic disks we corroborate a rapid increase in Z at phi(c) and power-law behavior above phi(c) for Z and P. Specifically we find a power-law increase as a function of phi-phi(c) for Z-Z(c) with an exponent beta around 0.5, and for P with an exponent psi 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.     

Hopping conductivity in granular systems

The model of variable-range hopping between microscopic localization centers in disordered semiconductors including Coulomb correlations is transferred to the mesoscopic situation of electron tunneling between small metal particles in granular materials. As a result we obtain for the temperature dependence of the dc conductivity well known formulas (Abeles, Mott) with certain limitations of their applicability. There is good agreement with existing experiments.     

颗粒体系中力分布的标量力网系综模型

建立了便于解析计算的标量力网系综模型研究颗粒体系中的力分布问题.所提出的Laplace变换法有效地解决了复杂约束条件下概率密度函数的积分问题,并给出体系中层数较少时极限分布的表达式.发现一般情况下极限分布为多项式与指数函数的乘积,力分布在接近平均力处取最大值,大于平均力时呈指数减小. 关键词： 静态颗粒体系 力空间 力网系综     

Large force fluctuations in a flowing granular medium

We study fluctuations in the force at the boundary of a 2D granular flow. The forces are mainly impulsive at all flow rates. The probability distribution of impulses decays exponentially at large impulses, as do the forces in a static granular medium. At small impulses, the distribution evolves continuously with flow rate with no indication of the transition from collisional flow to intermittently jamming flows. However, the distribution of the time interval between collisions tends to a power law, P(tau) - tau(-3/2), showing a clear dynamical signature of the approach to jamming.     

Wall-enhanced convection in vibrofluidized granular systems

An event-driven molecular dynamics simulation of inelastic hard spheres contained in a cylinder and subject to strong vibration reproduces accurately experimental results [R. D. Wildman et al., Phys. Rev. Lett. 86, 3304 (2001)] for a system of vibrofluidized glass beads. In particular, we are able to obtain the velocity field and the density and temperature profiles observed experimentally. In addition, we show that the appearance of convection rolls is strongly influenced by the value of the sidewall-particle restitution coefficient. Suggestions for observing more complex convection patterns are proposed.