Slow granular flows: The dominant role of tiny fluctuations

What mechanism governs slow flows of granular media? Microscopically, the grains experience enduring frictional contacts in these flows. However, a straightforward translation to a macroscopic frictional rheology, where the shear stresses are proportional to the normal stresses with a rate-independent friction coefficient, fails to capture important aspects of slow granular flows. There is now overwhelming evidence that agitations, tiny fluctuations of the grain positions, associated with large fluctuation of their contact forces, play a central role for slow granular flows. These agitations are generated in flowing regions, but travel deep inside the quiescent zones, and lead to a nonlocal rheology.     

Stationary shear flows of dense granular materials: a tentative continuum modelling

We propose a simple continuum model to interpret the shearing motion of dense, dry and cohesion-less granular media. Compressibility, dilatancy and Coulomb-like friction are the three basic ingredients. The granular stress is split into a rate-dependent part representing the rebound-less impacts between grains and a rate-independent part associated with long-lived contacts. Because we consider stationary flows only, the grain compaction and the grain velocity are the two main variables. The predicted velocity and compaction profiles are in apparent qualitative agreement with most of the experimental or numerical results concerning free-surface shear flows as well as confined shear flows.Received: 24 March 2004, Published online: 29 June 2004PACS: 45.70.Ht Avalanches - 45.70.-n Granular systems - 83.80.Fg Granular solids     

Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow

We investigate the bulk rheology of dense granular flow down a rough slope, where the density profile has been found to show a plateau except for the boundary layers in simulations [Silbert et al., Phys. Rev. E 64, 051302 (2001)]. It is demonstrated that both the Bagnold scaling and the framework of kinetic theory are applicable in the bulk, which allows us to extract the constitutive relations from simulation data. The detailed comparison of our data with the kinetic theory shows quantitative agreement for the normal and shear stresses, but there exists a slight discrepancy in the energy dissipation, which causes a rather large disagreement in the kinetic theory analysis of the flow.     

Rheological properties of dense granular flows

Recent progresses in understanding the behavior of dense granular flows are presented. After presenting a bulk rheology of granular materials, I focus on the new developments to account for non-local effects, and on ongoing research concerning the surface rheology and the evolution of mechanical properties for heterogeneous systems.     

Contact forces in a granular packing

We present the results of a systematic numerical investigation of force distributions in granular packings. We find that all the main features of force transmission previously established for two-dimensional systems of hard particles hold in three-dimensional systems and for soft particles, too. In particular, the probability distribution of normal forces falls off exponentially for forces above the mean force. For forces below the mean, this distribution is either a decreasing power law when the system is far from static equilibrium, or nearly uniform at static equilibrium, in agreement with recent experiments. Moreover, we show that the forces below the mean do not contribute to the shear stress. The subnetwork of the contacts carrying a force below the mean thus plays a role similar to a fluid surrounding the solid backbone composed of the contacts carrying a force above the mean. We address the issue of the computation of contact forces in a packing at static equilibrium. We introduce a model with no local simplifying force rules, that allows for an exact computation of contact forces for given granular texture and boundary conditions. (c) 1999 American Institute of Physics.     

Shear thickening and migration in granular suspensions

We study the emergence of shear thickening in dense suspensions of non-Brownian particles. We combine local velocity and concentration measurements using magnetic resonance imaging with macroscopic rheometry experiments. In steady state, we observe that the material is heterogeneous, and we find that the local rheology presents a continuous transition at low shear rate from a viscous to a shear thickening, Bagnoldian, behavior with shear stresses proportional to the shear rate squared, as predicted by a scaling analysis. We show that the heterogeneity results from an unexpectedly fast migration of grains, which we attribute to the emergence of the Bagnoldian rheology. The migration process is observed to be accompanied by macroscopic transient discontinuous shear thickening, which is consequently not an intrinsic property of granular suspensions.     

基于超二次曲面的颗粒材料缓冲性能离散元分析

自然界或工业中普遍是由非球形颗粒组成的复杂体系,与球形颗粒相比,非球形颗粒间的高离散和咬合互锁可使冲击载荷引起的能量有效衰减实现缓冲作用.基于连续函数包络的超二次曲面单元能准确地描述非球形颗粒的几何形态,并可精确地计算单元间的接触碰撞作用.本文采用离散元方法对冲击载荷作用下非球形颗粒物质的缓冲性能进行数值分析,并与圆柱体冲击的理论结果和球体冲击的实验结果进行对比验证.在此基础之上,进一步研究了筒底作用力在不同颗粒层厚度和形状等因素影响下的变化规律.计算结果表明:不同颗粒形状都存在一个临界厚度H_c.当HH_c时,缓冲率随H的增加而增加;当HH_c时,缓冲率的变化不再显著并趋于稳定值.此外,减小颗粒表面尖锐度和增加或减小圆柱形和长方形颗粒的长宽比都会提高颗粒材料的缓冲效果.     

Computing Particle Surface Areas and Contact Areas from Three‐Dimensional Tomography Data of Particulate Materials

Microtomography is an emerging technique for particle and particulate‐materials characterization. To use this technology effectively, robust and accurate computational algorithms are needed to compute relevant particle properties, including particle surface area and particle‐particle contact area. However, the most accurate algorithms that have been developed for computing the exposed (void/solid) surface area in a microtomography image cannot be used directly for computing surface areas or particle‐particle contact areas for individual particles in a dense packing. This paper presents an algorithm for extracting particle contact areas from a digitized, segmented image of a packed granular material, which in turn can be used to find individual particle surface areas (even if the complete surfaces are not exposed because of contacts in the packing). Results show that small errors in the binary surface‐area computations are magnified in the course of determining particle contact areas; the total error in the computation depends mainly on the size of the contact area in voxel units.     

Kinetic theory for sheared granular flows

Rapid granular flows are far-from-equilibrium-driven dissipative systems where the interaction between the particles dissipates energy, and so a continuous supply of energy is required to agitate the particles and facilitate the rearrangement required for the flow. This is in contrast to flows of molecular fluids, which are usually close to equilibrium, where the molecules are agitated by thermal fluctuations. Sheared granular flows form a class of flows where the energy required for agitating the particles in the flowing state is provided by the mean shear. These flows have been studied using the methods of kinetic theory of gases, where the particles are treated in a manner similar to molecules in a molecular gas, and the interactions between particles are treated as instantaneous energy-dissipating binary collisions. The validity of the assumptions underlying kinetic theory, and their applicability to the idealistic case of dilute sheared granular flows are first discussed. The successes and challenges for applying kinetic theory for realistic dense sheared granular flows are then summarised.     

The Fractal Characteristic of Particles in Granular Material Flows and Its Effect on Effective Thermal Conductivity

According to the fact that many pulverized particles possess fractal characteristic, a fractal model for studying fine particles in granular material flows is first proposed. An expression of particles' fractal distribution is derived to describe the relationship between the particle fractal dimensions and particle velocity distribution function. In accordance with this model, the theoretical particle effective thermal conductivity is derived. The analytical results show that for the small Biot-Fourier number, the effective thermal conductivity increases with the square root of the granular temperature. For very large Biot-Fourier number, the effective thermal conductivity linearly increases with the granular temperature. Numerically calculated results show that the thermal conductivity increases with the particle size fractal dimensions and decreases with the particle surface fractal dimensions.     

Unifying suspension and granular rheology

Using an original pressure-imposed shear cell, we study the rheology of dense suspensions. We show that they exhibit a viscoplastic behavior similarly to granular media successfully described by a frictional rheology and fully characterized by the evolution of the friction coefficient μ and the volume fraction ? with a dimensionless viscous number I(v). Dense suspension and granular media are thus unified under a common framework. These results are shown to be compatible with classical empirical models of suspension rheology and provide a clear determination of constitutive laws close to the jamming transition.     

双轴压缩下颗粒物质剪切带的形成与发展

本文采用离散元方法,研究了双轴压缩的颗粒体系在刚性边界约束下,局部剪切带的形成和发展过程,注重分析了细观的体积分数、配位数、颗粒旋转角度等参数以及力链结构形态的演变.并从颗粒体系jamming 相图中J点附近的边壁压强和配位数随体积分数的标度规律出发,分析了剪切带内外的体积分数和配位数的变化.结果表明:剪切带形成于颗粒体系的塑性变形开始阶段,此时体系发生剪胀,颗粒体积分数减小,颗粒体系抵抗旋转的能力降低,开始出现细小剪切带,随着轴向应变的继续,细小剪切带发生连接,最终导致贯穿性优势剪切带形成 关键词： 颗粒物质 力链 双轴压缩 剪切带     

Arches and contact forces in a granular pile

Assemblies of granular particles mechanically stable under their own weight contain arches. These are structural units identified as sets of mutually stable grains. It is generally assumed that these arches shield the weight above them and should bear most of the stress in the system. We test such hypothesis by studying the stress born by in-arch and out-of-arch grains. We show that, indeed, particles in arches withstand larger stresses. In particular, the isotropic stress tends to be larger for in-arch grains whereas the anisotropic component is marginally distinguishable between the two types of particles. The contact force distributions demonstrate that an exponential tail (compatible with the maximization of entropy under no extra constraints) is followed only by the out-of-arch contacts. In-arch contacts seem to be compatible with a Gaussian distribution consistent with a recently introduced approach that takes into account constraints imposed by the local force balance on grains.     

Some remarks on the rheology of dense granular flows

The paper reviews some peculiar properties exhibited by granular flows. We emphasize the inability of kinetic theory and of Bagnolds heuristic approach to describe the rapid regime of densely packed flows, characterized by the breakdown of the binary collision picture and by multibody long-lasting contacts. We suggest that deformation waves through the continuous paths of contacts can be effective to transport momentum and energy through the bulk, in a time very short compared to the inverse of the shear rate. This mechanism could explain some key rheological features encountered in dense granular materials.Received: 25 June 2004, Published online: 31 August 2004PACS: 45.70.-n Granular systemsJ. Rajchenbach: On leave from LMDH (CNRS-UMR 7603), Université P. et M. Curie, 75005 Paris, France.     

Constitutive relations for steady flows of dense granular liquids

The micropolar model is a continuum-mechanical model suited to describe a collection of particles interacting via forces and couples. When applied to dense granular liquids that model must display some specific features because of the peculiarities of the frictional forces. We want here to stress on some of those specific features including the existence of two kinds of fluctuating kinetic energies (for translation and rotation), their evolution equations in which enters the mean dissipation rate, and how an estimation (or numerical calculation) of the dissipation rate can lead to the constitutive laws of dense granular liquids in steady flows.     

Numerical simulation of particle size effects on contact electrification in granular systems

Based on the contact charge transfer model between two particles due to a single collision proposed by Apodaca, the contact charges carried on a particle is derived due to multiple collisions, including the repeat collisions between two particles and the collisions with different particles, in mixed-size granular system of identical material. The effect of the particle size on the charges carried on the particle is simulated. The results indicate that for a mixed-size granular system, due to multiple collisions among particles, there exists a threshold particle radius, the particles with radius higher than which and the particles with radius lower than which carry opposite charges. The threshold particle radius is equal to mean value of particle size in the mixed-size granular system. Basically, the polarity of the charges carried on the largest particle is same as the polarity of the transfer charge carrier, and in case of the positive charge transferred, the largest particle will be positively charged and the smallest particle will be negatively charged, and vice versa. In the same size region, the more dispersive the particle size is, the more the net charges can be produced. In normal-distributed granular system, the magnitude of contact charge is determined mainly by the particle size distribution, size region, total particle number and the relative impact velocity.     

Fluctuating velocity and momentum transfer in dense granular flows

We show experimentally that in a free-surface granular flow the fluctuating velocity brings about momentum transfer at a considerable rate only very close to the free surface. Away from the free surface, where the flow is dense and stratified (or laminar), the fluctuating velocity plays no prominent dynamic role and stems passively from a kinematic constraint: The strata of particles must shake laterally as they slip past one another in the direction of the mean flow. Based on this insight, we formulate a simple model for the fluctuating velocity of dense granular flows. The predictions of the model agree well with our experimental measurements.     

Random networks of fibres display maximal heterogeneity in the distribution of elastic energy

Above a small length scale, the distribution of local elastic energies in a material under an external load is typically Gaussian, and the dependence of the average elastic energy on strain defines the stiffness of the material. Some particular materials, such as granular packings, suspensions at the jamming transition, crumpled sheets and dense cellular aggregates, display under compression an exponential distribution of elastic energies, but also in this case the elastic properties are well defined. We demonstrate here that networks of fibres, which form uncorrelated non-fractal structures, have under external load a scale invariant distribution of elastic energy (epsilon) at the fibre-fibre contacts proportional to 1/epsilon. This distribution is much broader than any other distribution observed before for elastic energies in a material. We show that for small compressions it holds over 10 orders of magnitude in epsilon. In such a material a few 'hot spots' carry most of the elastic load. Consequently, these materials are highly susceptible to local irreversible deformations, and are thereby extremely efficient for damping vibrations.     

Slip, yield, and bands in colloidal crystals under oscillatory shear

We study dense colloidal crystals under oscillatory shear using a confocal microscope. At large strains the crystals yield and the suspensions form shear bands. The pure harmonic response exhibited by the suspension rules out the applicability of nonlinear rheology models typically used to describe shear banding in other types of complex fluids. Instead, we show that a model based on the coexistence of linearly responding phases of the colloidal suspension accounts for the observed flows. These results highlight a new use of oscillatory measurements in distinguishing the contribution of linear and nonlinear local rheology to a globally nonlinear material response.     

Microstructure characterization of granular materials

This paper presents techniques and algorithms to compute microstructure properties of irregular-shaped granulate assemblies utilizing 3D images. The techniques are capable of extracting microstructure properties of particles such as centeroid, particle size distribution, shape indices (i.e., sphericiy and angularity), number of contacts (i.e., distribution of coordination numbers), contact network, packing efficiency, distribution of local void ratio and radial distribution function. Such properties are critical parameters for micromechanical-based numerical models to capture micro- and macromechanical behavior of geomaterials. X-ray microtomography was used to reconstruct high-resolution 3D image of a natural sand system to represent granular materials. Microstructure properties of the sand system were computed and compared with properties of a computer-simulated image of periodic random spheres. Findings indicate that the use of simplified systems of idealized spheres to model micro- and macromechanical behavior of granular systems can lead to inaccurate results due to the differences in the microstructure between both systems. Methods presented in this paper enabled capturing a more realistic microstructure that can be incorporated in micromechanical models to better simulate, understand, or explain macroscale behavior of granular materials based on their actual microstructure.