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Showing papers in "Granular Matter in 2003"


Journal ArticleDOI
TL;DR: A critical review on shear testers for IFPRI-members and it is clear that electrostatic forces are eminent in flows with a free surface – an issue not addressed in this review.
Abstract: The author was asked by the International Fine Particle Research Institue (IFPRI) to write a cri- tical review on shear testers for IFPRI-members. The re- view was delivered to IFPRI in summer 1999. Following the contract with IFPRI it was not allowed to publish the review elsewhere for at least two years. Granular Matter invited the author to submit the review in the original form; during the refereeing process (besides other chang- es) it turned out that some remarks should be added here for clarification: - Since 1999, the author is not aware of a really new device for testing bulk solid properties, which could lead to a change of the general comments and con- clusions provided in the review. - It was argued, that the review is referring too much to the work of Jenike, while the works of Johanson and Peschl were not adequately cited. Both are excellent en- gineers with a lot of experience, but their basic ideas are not available in published form, and if, they are not set in relation to alternative approaches so that an objec- tive comparison in detail would be a future research issue rather than a topic in this report. - A discussion on the influence of electrostatic char- ges was missing. There hardly is an influence, since the particles are in continuous contact. Only with non-con- ducting plastic particles electrostatic charges could cause problems. But no relevant experiments and results are known. In closed systems, the effect of electric charges is thus mainly neglected, but it is clear that electrostatic forces are eminent in flows with a free surface - an issue not addressed in this review.

316 citations


Journal ArticleDOI
TL;DR: Comparisons indicate that while this approach can successfully generate relatively dense two-dimensional particle assemblies, the three- dimensional implementation is less effective at generating dense systems than other available approaches.
Abstract: Discrete element methods are emerging as useful numerical analysis tools for engineers concerned with granular materials such as soil, food grains, or pharmaceutical powders. Obviously, the first step in a discrete element simulation is the generation of the geometry of the system of interest. The system geometry is defined by the boundary conditions as well as the shape characteristics (including size) and initial coordinates of the particles in the system. While a variety of specimen generation methods for particulate materials have been developed, there is no uniform agreement on the optimum specimen generation approach. This paper proposes a new triangulation based approach that can easily be implemented in two or three dimensions. The concept of this approach (in two dimensions) is to triangulate a system of points within the domain of interest, creating a mesh of triangles. Then the particles are inserted as the incircles of these triangles. Extension to three dimensions using a mesh of tetrahedra and inserting the inspheres is relatively trivial. The major advantages of this approach include the relative simplicity of the algorithm and the small computational cost associated with the preparation of an initial particle assembly. The sensitivity of the characteristics of the particulate material that is generated to the topology of the triangular mesh used is explored. The approach is compared with other currently used methods in both two and three dimensions. These comparisons indicate that while this approach can successfully generate relatively dense two-dimensional particle assemblies, the three- dimensional implementation is less effective at generating dense systems than other available approaches.

82 citations


Journal ArticleDOI
TL;DR: One dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels, and it was found that for both materials, creep strain is proportional to the logarithm of time.
Abstract: This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.

62 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the discrete element modeling of cyclic loading of an aggregate of crushable sand grains, where each grain of sand is modelled as an agglomerate of balls bonded together.
Abstract: This paper examines the discrete element modelling of cyclic loading of an aggregate of crushable sand grains. Each grain of sand is modelled as an agglomerate of balls bonded together. The aggregate is subjected to compaction followed by isotropic normal (plastic) compression, and then unloaded to half the maximum applied stress. The aggregate is then subjected to cyclic loading to a maximum stress ratio of 0.8. The aim of the paper is to examine the reduction of the rate of axial strain with number of cycles, and to determine the relative influences of volumetric strain and shear strain rates on the axial strain rate. In particular, the paper aims to show whether particle breakage is mainly related to the accumulation of volumetric strain. This is found to be the case, which is consistent with proposals by other authors that plastic hardening under monotonic loading is due to particle fracture.

58 citations


Journal ArticleDOI
TL;DR: In this article, the probability density functions of contact force components corresponding to the principle directions of average stress were analyzed and a theoretical prediction was derived for the distribution of these components, with the help of maximizing the statistical entropy.
Abstract: This paper analyses the probability density functions of contact force components corresponding to the principle directions of average stress. A theoretical prediction is derived for the distribution of these components, with the help of maximizing the statistical entropy. Limits of validity of the prediction are analyzed by numerical simulations on isotropic assemblies under hydrostatic pressure. The results show that the `history' of the assembly has a strong influence on the type of the force distributions.

58 citations


Journal ArticleDOI
TL;DR: In this paper, the statistical texture tensor is defined to quantify the notion of stored deformation in a material, which links microscopic and macroscopic descriptions of the material and extends the definition of elastic strain.
Abstract: Under mechanical deformation, most materials exhibit both elastic and fluid (or plastic) responses. No existing formalism derived from microscopic principles encompasses both their fluid-like and solid-like aspects. We define the statistical texture tensor to quantify the intuitive notion of stored deformation. This tensor links microscopic and macroscopic descriptions of the material, and extends the definition of elastic strain.

57 citations


Journal ArticleDOI
TL;DR: In this paper, a simple model of a particle assembly is used to compare average contact forces in typical single-particle AFM experiments and typical bulk experiments, and thus identify those regimes of powder flow where the two approaches overlap, and AFM measurements may be used with some confidence in more sophisticated modeling based on distinct element analysis.
Abstract: The atomic force microscope (AFM) has been used to study inter-particle contacts in air for a range of model particles and cohesive granular materials of commercial importance. Adhesion (or pull-off force), friction and its load dependence, and particle size, morphology and roughness were measured for glass ballotini, fumed silica, alumina, limestone, titania and zeolite. Particle-wall contacts and effects of relative humidity were also studied. Most of the results, after allowing for roughness, are consistent with JKR contact mechanics and capillary bridge theory; however, the main object of the present work is to demonstrate semi-quantitative links between the AFM measurements and related bulk flow and cohesion measurements performed in parallel on the same materials. A simple model of a particle assembly will be used to compare average contact forces in typical single-particle AFM experiments and typical bulk experiments, and thus identify those regimes of powder flow where the two approaches overlap, and AFM measurements may be used with some confidence in more sophisticated modeling based on distinct element analysis (DEA). Four areas will be discussed briefly: (1) The apparent analogy between bulk yield loci and single-particle friction-load data; (2) Cohesion data and particle size effects; (3) Bulk tensile strength and single particle pull-off force; (4) Bulk wall friction and single-particle-wall friction. It is found that typical single-particle AFM experiments and bulk shear experiments converge for small particles (~ 4 wm) and low consolidation stress, when the average inter-particle contact forces are of the order 20-100nN, involve single or few asperities, and are not much larger than pull-off forces. For large particles and high consolidation loads the data do not overlap and AFM measurements may be less useful as input to simulations where sliding friction is less important, and where large normal contact forces dominate over tangential forces and are responsible for the shear strength.

54 citations


Journal ArticleDOI
TL;DR: In this article, a number of chrome steel balls are arranged in a chain formation with monotonically decreasing size, and the incoming impulse is received by the largest ball at one end and propagates through the chain.
Abstract: This paper describes a unique way to disperse an impulse in granular material. A number of chrome steel balls are arranged in a chain formation with monotonically decreasing size. The incoming impulse is received by the largest ball at one end and propagates through the chain. Due to translation symmetry breaking, the classical solitary wave known to develop in a chain of particles of the same size quickly lose its signature, disperses itself throughout the balls in the chain, and finally manifests itself as a collection of smaller impulses. This paper presents experimental confirmation of this mechanism and a comparison with recent theoretical predictions of impulse dispersion in a chain of hard inelastic spheres. Some discrepancies with theory are interpreted in terms of energy transfer to rotational degrees of freedom.

53 citations


Journal ArticleDOI
TL;DR: Au et al. as discussed by the authors used a texture tensor to quantify deformation in a two-dimensional foam steadily flowing through a constriction, and proved that the foam has the elastic properties of a (linear and isotropic) continuous medium.
Abstract: In a continuum description of materials, the stress tensor field σ quantifies the internal forces the neighbouring regions exert on a region of the material. The classical theory of elastic solids assumes that σ de- termines the strain, while hydrodynamics assumes that σ determines the strain rate. To extend both successful theories to more general materials, which display both elastic and fluid properties, we recently introduced a de- scriptor generalizing the classical strain to include plastic deformations: the "statistical strain," based on averages of microscopic details ("A texture tensor to quantify de- formations" M.Au., Y.J., J.A.G., F.G, companion paper, Granular Matter, this issue). Here, we apply such a statis- tical analysis to a two-dimensional foam steadily flowing through a constriction, a problem beyond reach of both traditional theories, and prove that the foam has the elastic properties of a (linear and isotropic) continuous medium.

48 citations


Journal ArticleDOI
TL;DR: In this paper, an Event Driven computer simulation of a diluted binary mixture of granular particles vertically vibrated in the presence of gravity was carried out to confirm that the kinetic energies of the two species are not equally distributed, as predicted by various theoretical models, and seem to reproduce rather well the density and temperature profiles measured experimentally.
Abstract: Motivated by recent experiments we have carried out an Event Driven computer simulation of a diluted binary mixture of granular particles vertically vibrated in the presence of gravity. The simulations not only confirm that the kinetic energies of the two species are not equally distributed, as predicted by various theoretical models, but also seem to reproduce rather well the density and temperature profiles measured experimentally. Rotational degrees of freedom do not seem to play any important qualitative role. Instead, simulation shows the onset of a clustering instability along the horizontal direction.

42 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined a simple linear string of particles in an attempt to estimate how much force is required to hold the chain together and how large a force imbalance can be tolerated.
Abstract: When a load is applied to a granular material, the stress is not uniformly distributed but concentrates into quasi-linear particle assemblies known as ‘‘force chains.’’ By the time they can be observed, force chains are apparently quasistatic in the sense that they persist over time scales much longer than elastic timescales (such as a contact time) over which an unstable chain breaks apart. But many force chains attempt to form, but are unstable and break apart after a few contact times. Stability requires that each particle in the chain be pressed against its neighbors by the forces in the chain. Furthermore, each particle must also be in quasistatic equilibrium in the sense that all forces on it must roughly balance. This paper examines a simple linear string of particles in an attempt to estimate how much force is required to hold the chain together and how large a force imbalance can be tolerated. There are two modes of instability, a simple case in which an overloaded contact pushes its particles apart breaking the chain as they separate, and a more complicated mode requiring the interaction of elastic waves traveling along the chain. Overall, dissipation acts as a stabilizing factor, first by reducing the initial energy of the overloaded contact as it unloads, and subsequently, by reducing the energy of the elastic waves.

Journal ArticleDOI
TL;DR: In this article, Burtally et al. reported that mixtures of fine equal-sized bronze and glass spheres separate into glass-rich and bronze-rich regions under sinusoidal verti- cal vibration.
Abstract: It has recently been reported that mixtures of fine equal-sized bronze and glass spheres separate into glass-rich and bronze-rich regions under sinusoidal verti- cal vibration (Burtally et al., Science 295, 1877 (2002)). Here we report a study of these separation effects, vary- ing both the bronze/glass size ratio and the composition of the mixture. For a wide range of mixtures we observe separation into bronze-rich and almost pure glass regions separated by extremely sharp boundaries. Either a bronze- rich region forms above a glass layer or a bronze-rich layer is sandwiched between two glass layers. Convection exists within each layer but does not act to cause mixing of the two regions. The separation into two regions is maintained even in the presence of a variety of spatial oscillations. The variations of behaviour with differing glass/bronze size ratios support the proposal of a differential air-damping separation mechanism, while experiments using a porous bottomed box indicate that separation requires air to be driven through the granular bed by the vibration.

Journal ArticleDOI
TL;DR: In this article, the axial limits of these cells correspond to the plane of rotation of ploughshare blades or of the mechanical supports for long flat blades, and a more physical approach reveals a cellular structure to the flow with transfers between cells limiting behaviour.
Abstract: The manufacture of a wide range of materials in particulate form currently has to rely upon a design basis that is not at all strong theoretically. The most developed methods exist in the design of storage vessels for particles but many weaknesses remain. In those areas of processing concerned with the development of product properties, the knowledge of the dynamics of granular motion is more rudimentary. However, we are now in a position where progress of a fundamental character elucidating the mechanisms operating in engineering systems can now be undertaken. This is illustrated by recent studies aimed at understanding how the axial motion of particles occurs in mixers which the particles are stirred mechanically by blades. Representation is possible in terms of an axial diffusion coefficient, for instance. A more physical approach reveals a cellular structure to the flow with transfers between cells limiting behaviour. The axial limits of these cells correspond to the plane of rotation of ploughshare blades or of the mechanical supports for long flat blades.

Journal ArticleDOI
TL;DR: In this paper, a Boltzmann type equation for the probability of contact force distribution is formulated and solved for model packings, and a new approach which employs statistical-mechanical concepts is offered for the description of jammed state results.
Abstract: In a static granular material all particles are touching their neighbours and given a sufficiently high density a jammed state results. A new approach which employs statistical-mechanical concepts is offered for the description of such states. We investigate the simplest statically determinate problem and derive equations of stress propagation. The simplest Boltzmann type equation for the probability of contact force distribution is formulated and solved for model packings. The theory predicts a distribution for the probability of finding a contact force of magnitude f as e − f / ¯f which is in a good agreement with experimental data. We also propose a pathway to calculating the macroscopic stress tensor as a function of compactivity in a static and slowly sheared granular media.

Journal ArticleDOI
TL;DR: In this paper, the authors classified heterogeneity in topologic, geometric, kinematic, static, and constitutive topologies in a numerical DEM simulation of biaxial compression and showed that the topology and geometric fabric become more variable during loading.
Abstract: Heterogeneity is classified in five categories– topologic, geometric, kinematic, static, and constitutive–and the first four categories are investigated in a numerical DEM simulation of biaxial compression. The simulation experiments show that the topology and geometric fabric become more variable during loading. The measured fluctuations in inter-particle movements are large, they increase with loading, and they extend to distances of at least eight particle diameters. Deformation and rotation heterogeneity are large and are expressed in spatial patterning. Stress heterogeneity is moderate throughout loading.

Journal ArticleDOI
TL;DR: In this paper, a novel expression for the repulsive force which controls dynamically the transfer and dissipation of energy in granular media is proposed, where a fractional derivative accumulates the whole history of the virtual overlap over time in weighted form.
Abstract: In this paper, we consider the complex problem of how to simulate particle contacts, taking into account the cohesion effect. In accordance with the molecular dynamics models, we propose a novel expression for the repulsive force which controls dynamically the transfer and dissipation of energy in granular media. This expression is formulated under fractional calculus, where a fractional derivative accumulates the whole history of the virtual overlap over time in weighted form. We then discuss and illustrate the basic properties of the repulsive force in a normal direction to the contacting surfaces. This approach allows us to perform simulations of arbitrary multiparticle contacts as well as granular cohesion dynamics.

Journal ArticleDOI
TL;DR: In this article, an extension to kinetic theory and hydrodynamic models is proposed that accounts for the existence of multi-particle contacts and leads to a correction of the cooling rate.
Abstract: An extension to kinetic theory and hydrodynamic models is proposed that accounts for the existence of multi-particle contacts and leads to a correction of the cooling rate. The other hydrodynamic terms remain unchanged. In the presence of multi-particle contacts a class of different models leads to deviations from the classical inelastic hard sphere (IHS) results. For the homogeneous cooling state (HCS), as examined here, the theoretical results are found to be in perfect agreement with the numerical simulations.

Journal ArticleDOI
TL;DR: In this article, the authors studied the Brazil Nut effect and found that the rise of a large intruder particle within a vertically vibrated bed of smaller particles was influenced by humidity of the air within the interstices of the particle bed and on the electrostatic charge developed on the bed particles during preparation and vibration.
Abstract: We have studied the Brazil Nut effect – the rise of a large intruder particle within a vertically vibrated bed of smaller particles. In our study both intruder and bed particles were spherical and the vibration was such that bed convection was negligible. The rise of the intruder was found to be influenced by humidity of the air within the interstices of the particle bed and on the electrostatic charge developed on the bed particles during preparation and vibration. High relative humidity and high electrostatic charge each had the effect of slowing the rise of the intruder. Because increasing relative humidity of the interstitial air caused the electrostatic charge to diminish, the rise rate of the intruder achieved a maximum at a relative humidity of around 55%. Under controlled humidity and charge conditions, the time for the intruder to rise through the bed was found to decrease with increase in intruder diameter. As intruder density was varied under controlled humidity and charge conditions, the intruder rise time was found to exhibit a maximum when the intruder density of approximately one half of the bulk density of the bed of particles. This interesting trend was modelled by taking account of the pressure gradient that is generated across a bed of particles vertically vibrated within a gas. The tentative model suggests that the gas flows associated with this pressure gradient restrict the motion of the bed more than that of the intruder and that it is this difference that accounts for the rise of the intruder. Also incorporated in the model is the buoyancy force on the intruder that results from the pressure gradient across the bed. KeywordsBrazil nut effect, Vibration, Granular solids, Humidity, Electrostatics, Interstitial air

Journal ArticleDOI
TL;DR: In this article, the Boltzmann kinetic theory is used to analyze the effect of energy nonequipartition on the pressure and the shear viscosity of a granular binary mixture under simple shear flow.
Abstract: The Boltzmann kinetic theory is used to analyze the effect of energy nonequipartition on the pressure and the shear viscosity of a granular binary mixture under simple shear flow. Theory and Monte Carlo simulations show that both quantities exhibit a non−monotonic behaviour with the mass ratio in contrast to the predictions made from previous theories based on the equipartition assumption. Our results agree qualitatively well with recent molecular dynamics simulations performed by Alam and Luding [Granular Matter 4, 139 (2002)].

Journal ArticleDOI
TL;DR: In this paper, the behavior of fine-grained granular materials at small shear strains cannot only be described by their density and stress state, but also particle surface forces have to be taken into account.
Abstract: Resonant column experiments were conducted with an extremely fine-grained material, viz. an α-aluminum oxide (Al2O3), which serves as a model material for cohesive soils with particle diameters in the range of μm. With this particle size interparticle forces from van der Waals and Coulombic interaction have an influence on the behavior of the material in dynamic shear tests. By adjusting the surface charge, and hence the Coulombic repulsion, we obtain repulsive or attractive particles, which influences sample fabric and shear stiffness. From the increase of shear stiffness at small strain (γ≤10−6) with effective pressure we have estimated the net interparticle pressure from surface forces in the range of some kPa for a mean particle diameter of 0.8 μm. Our results show that the behavior of fine-grained granular materials at small shear strains cannot only be described by their density and stress state. Particle surface forces have to be taken into account.

Journal ArticleDOI
TL;DR: In this paper, the intruder segregation dependence on size and density is investigated in the framework of a hydrodynamic theoretical model for vibrated granular media, and a segregation mechanism based on the difference of densities between different regions of the granular system, which give origin to a buoyant force that acts on the intruder, is proposed.
Abstract: The intruder segregation dependence on size and density is investigated in the framework of a hydrodynamic theoretical model for vibrated granular media. We propose a segregation mechanism based on the difference of densities between different regions of the granular system, which give origin to a buoyant force that acts on the intruder. From the analytic solution of the segregation velocity we can analyze the transition from the upward to downward intruder's movement.

Journal ArticleDOI
TL;DR: In this article, the rheology of dense granular surface flow is investigated and a non-local biphasic rheological law is proposed to account for the unusual shape of the velocity profile within granular flow as well as for the different scalings observed in rotating drum experiments.
Abstract: We investigate here the rheology of dense granular surface flow. First, steady surface flows in a rotating drum are studied experimentally and a large number of clusters of `jammed' grains embedded in the flowing layer is evidenced. The clusters size is power-law distributed, from the grain size scale up to the thickness of the flowing layer. Theoretical implications are then discussed and a non-local biphasic rheological law is proposed. The resulting model succeeds quantitatively to account for the unusual shape of the velocity profile within granular surface flows as well as for the different scalings observed in rotating drum experiments.

Journal ArticleDOI
TL;DR: In this article, a simple method to determine the density of contacts and the fraction of bonded contacts by two macroscopic measurements for materials that belong to this class is suggested, and the simplicity and similar structure of the effective-medium estimates for the properties of these two qualitatively different materials indicate that the number of contacts may play a similar role in an appropriate effective medium description of a large class of materials formed by processes similar to random deposition.
Abstract: Effective-medium theories for both random packings of elastic discs and mats of randomly sedimented elastic fibers can be constructed such that the effective material stiffness depends on the stiffness and geometry of the constituents of the material, and the number density of contacts. It is demonstrated that the number density of contacts together with the geometry of the constituents also determine the porosity of these materials. The simplicity and similar structure of the effective-medium estimates for the properties of these two qualitatively different materials indicate that the number density of contacts may play a similar role in an appropriate effective-medium description of a large class of materials formed by processes similar to random deposition. A simple method to determine the density of contacts and the fraction of bonded contacts by two macroscopic measurements for materials that belong to this class is suggested.

Journal ArticleDOI
TL;DR: In this article, a concept of an equivalent normal ball stiffness based on averaging the work done by the nonlinear Hertz force during the impact is introduced and a numerical assessment is made on its efficiency in simulating collinear collisions.
Abstract: In the paper a concept of an equivalent normal ball stiffness based on averaging the work done by the nonlinear Hertz force during the impact is introduced and a numerical assessment is made on its efficiency in simulating collinear collisions. The systems of balls investigated, ranging from 2 to 30, are considered to be coupled and conservative. The energy and momentum conservation principles are used to assess the accuracy of simulation results. The effect of the time step for both linear and nonlinear models is investigated and it is shown that the linear model allows an increased time step compared to a nonlinear one while meeting energy and momentum conservation requirements with the same accuracy. In the paper also the pattern of break up for both models and different number of balls is investigated. It is found that for both models the pattern is the same: the balls are disconnected one at the time with constant rate and this rate does not depend on the number of balls.