On the contact force distributions of granular mixtures under 1D-compression

We investigate the distribution of the inter-particle contact forces inside granular mixtures of a sand-particle-size material and of a finer-particle-size material using the Discrete Element Method for frictional spherical grains. The numerical granular samples were compressed vertically with no lateral expansion following a common stress path in soil mechanics; the material states varied from jammed states towards highly jammed states with increasing solid fraction. The inter-particle contacts were categorized depending on the particle sizes of the two contacting entities. The force distributions of the contact networks were calculated depending on the contact types. It was found that different contact networks possess a similar shape of the probability distribution function of the contact forces when the populations of the respective particle sizes are involved in the percolation of the strong forces in the systems. For systems of a small percentage of the fine particles, the fine particles do not actively participate in the strong force transmission and the related contact force distributions reflect the characteristic of an unjammed state for the subsystem consisted of these particles.     

Tensile stress relaxation in unsaturated granular materials

The mechanics of granular media at low liquid saturation levels remain poorly understood. Macroscopic mechanical properties are affected by microscale forces and processes, such as capillary forces, inter-particle friction, liquid flows, and particle movements. An improved understanding of these microscale mechanisms is important for a range of industrial applications and natural phenomena (e.g. landslides). This study focuses on the transient evolution of the tensile stress of unsaturated granular media under extension. Experimental results suggest that the stress state of the material evolves even after cessation of sample extension. Moreover, we observe that the packing density strongly affects the efficiency of different processes that result in tensile stress relaxation. By comparing the observed relaxation time scales with published data, we conclude that tensile stress relaxation is governed by particle rearrangement and fluid redistribution. An increased packing density inhibits particle rearrangement and only leaves fluid redistribution as the major process that governs tensile stress relaxation.     

From Single Particle AFM Studies of Adhesion and Friction to Bulk Flow: Forging the Links

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 μm) 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.     

Distinct simulation of earth pressure against a rigid retaining wall considering inter-particle rolling resistance in sandy backfill

The focus of this paper is to analyze earth pressure against a rigid retaining wall under various wall movement modes with a contact model considering inter-particle rolling resistance implemented into the distinct element method (DEM). Firstly, a contact model considering rolling resistance in particles was generally explained and implemented into the DEM. The parameters of the contact model are determined from DEM simulation of biaxial tests on a sandy specimen. Then, the influence of inter-particle rolling resistance in the backfill is discussed by comparing the active and passive earth pressure against a rigid wall subjected to a translational displacement with and without inter-particle rolling resistance in the material. Third, the DEM model considering the rolling resistance is used to investigate active and passive earth pressures while the rigid wall moves in a more general manner such as rotation or translation. The influence of rolling resistance on the earth pressures is examined from the microscopic particle scale (e.g., shear strain field) as well as the macroscopic scale (e.g., the magnitude and action point of resultant earth pressures). Finally, the effect of the initial density and the particle size of the backfill are discussed. The results show that when rolling resistance in the particles is taken into account in the DEM simulation, the simulation results are more appropriate and are in line with practical situation. Hence, particles rolling resistance should be taken into account to get more realistic results in DEM analyses.     

Evaluation of energy contributions using inter-particle forces in granular materials under impact loading

A drop-tower based experimental setup was developed for the impact testing of 2D assembly of cylinders with impactor velocity of around 6 m/s. This drop tower setup was used to load 2D granular assemblies of polyurethane and polycarbonate cylinders of 1\(^{\prime \prime }\)–1.25\(^{\prime \prime }\) length with three different diameters of 1/4\(^{\prime \prime }\), 3/8\(^{\prime \prime }\) and 1/2\(^{\prime \prime }\). A high speed camera was used for recording the images at speeds between 10,000 and 55,000 fps to monitor the deformation of the cylinders. Kinematic and strain fields in individual grains during each experiment were measured using digital image correlation. These experimentally measured strain and kinematic fields were used as inputs for the granular element method (GEM) based force inference technique and the inter-particle forces in normal and tangential direction were determined at every contact in each experiment. The inter-particle forces at each contact can facilitate the calculation of frictional work done at each contact. The GEM based inter-particle forces for a simple 2 particle granular assembly were found to be in good agreement with predictions from ABAQUS explicit based FEM simulation. The influence of different model parameters was also characterized such as grain stiffness, frictional co-efficient was investigated qualitatively. The impact response of the various ordered granular assemblies was also investigated using the GEM approach and the effect of local defects such as voids or layering of granular materials on the wave propagation phenomena is also studied. The presence of the point or line defects have significant effects on the wave propagation in the granular assemblies due to wave scattering and attenuation.     

On the influence of inter-particle friction and dilatancy in granular materials: a numerical analysis

Mechanical behavior of granular soils is a classic research realm but still yet not completely understood as it can be influenced by a large number of factors, including confining pressure, soil density, loading conditions, and anisotropy of soil etc. Traditionally granular materials are macroscopically regarded as continua and their particulate and discrete nature has not been thoroughly considered although many researches indicate the macro mechanical behavior closely depends on the micro-scale characteristics of particles. This paper presents a DEM (discrete element method)-based micromechanical investigation of inter-particle friction effects on the behavior of granular materials. In this study, biaxial DEM simulations are carried out under both ‘drained’ and ‘undrained’ (constant volume) conditions. The numerical experiments employ samples having similar initial isotropic fabric and density, and the same confining pressure, but with different inter-particle friction coefficient. Test results show that the inter-particle friction has a substantial effect on the stress-strain curve, peak strength and dilatancy characteristics of the granular assembly. Clearly, it is noted that apart from the inter-particle friction, the shear resistance is also contributed to the dilation and the particle packing and arrangements. The corresponding microstructure evolutions and variations in contact properties in the particulate level are also elaborated, to interpret the origin of the different macro-scale response due to variations in the inter-particle friction.     

Isostaticity in Cosserat continuum

Under conditions of isostaticity in granular media, the contact forces for all particles are statically determinate and forces can be computed without recourse to deformation equations or constitutive relationships. Given that stresses represent spatial averages of inter-particle forces, the stress-equilibrium equations for the isostatic state form a hyperbolic system of partial differential equations that describe the internal stress state using only boundary tractions. In this paper, we consider a Cosserat medium and propose closure relationships in terms of stresses and couple stresses from observations of stress variations in the critical state regime from discrete element simulations and experiments on sand, even though the isostatic condition is only satisfied in an average sense. It is shown that the governing equations are hyperbolic, which can be solved using the method of characteristics. Examples of both analytic and numerical solutions are presented. These examples clearly demonstrate that stress chains (characteristic lines) form oblique angles with the assumed direction of the force chains.     

Mechanistic modelling of tests of unbound granular materials

Various tests are used to characterise the strength and resilience of granular materials used in the subbase of a pavement system, but there is a limited understanding of how particle properties relate to the bulk material response under various test conditions. Here, we use discrete element method (DEM) simulations with a mechanistically based contact model to explore influences of the material properties of the particle on the results of two such tests: the dynamic cone penetrometer (DCP) and the resilient modulus tests. We find that the measured resilient modulus increases linearly with the particle elastic modulus, whereas the DCP test results are relatively insensitive to particle elastic modulus. The DCP test results are also relatively insensitive to inter-particle friction coefficient but strongly dependent on the particle shape. We discuss strengths and weaknesses of our modelling approach and include suggestions for future improvements.     

Dynamic evolution of oxide scale on the surfaces of feed stock particles from cracking and segmenting to peel-off while cold spraying copper powder having a high oxygen content

The oxide scale present on the feedstock particles is critical for inter-particle bond formation in the cold spray(CS)coating process,therefore,oxide scale break-up is a prerequisite for clean metallic contact which greatly improves the quality of inter-particle bonding within the deposited coating.In general,a spray powder which contains a thicker oxide scale on its surface(i.e.,powders having high oxygen content)requires a higher critical particle velocity for coating formation,which also lowers the deposition efficiency(DE)making the whole process a challenging task.In this work,it is reported for the first time that an artificially oxidized copper(Cu)powder containing a high oxygen content of 0.81 wt.%with a thick surface oxide scale of 0.71μm.,can help achieve an astonishing increment in DE.A transition of surficial oxide scale evolution starting with crack initiations followed by segmenting to peeling-off was observed during the high velocity particle impact of the particles,which helps in achieving an astounding increment in DE.Single-particle deposit observations revealed that the thick oxide scale peels off from most of the sprayed powder surfaces during the high-velocity impact,which leaves a clean metallic surface on the deposited particle.This makes the successive particles to bond easily and thus leads to a higher DE.Further,owning to the peeling-off of the oxide scale from the feedstock particles,very few discontinuous oxide scale segments are retained at inter-particle boundaries ensuring a high electrical conductivity within the resulting deposit.Dependency of the oxide scale threshold thickness for peeling-off during the high velocity particle impact was also investigated.     

Application of the Voronoï tessellation to study transport and segregation of grains inside 2D and 3D packings of spheres

This article provides a simple method to simulate the transport of a small bead through a static granular medium as a random walk on a network. This kind of displacement is strongly related to the geometry of the porous structure. A way to map the interparticle space is to calculate the Voronoï tessellation of the packing whose edges describe the network of pores of the medium. Then, the calculation of the probabilities to use each bond and a Monte-Carlo method for the choice of them, can simulate the displacement of the sphere. We introduce this technique for the inter-particle percolation of a fine particle through a packing of monosize spheres. We compare our numerical simulation with experiments performed in our laboratory. Then this technique is extended to the surface segregation. For the two kinds of segregation, we study the transverse diffusion and obtain a good agreement with experimental results. That our numerical simulation based on a rigorous geometric analysis of the medium is in agreement with inter-particle percolation and surface segregation experiments shows the importance of the study of the geometry of granular materials.     

A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method

It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.     

Kinematic and static hypotheses for constitutive modelling of granulates considering particle rotation

Summary The granular material perceived as a collection of particles is modelled as a Cosserat or multipolar continuum taking into account the effect of material microstructure. The macro-scale constitutive law for a granular material is derived from the micro-scale of two interacting particles. We adopt an approach based on a static hypothesis and establish two relationships: i) macro-to-micro static relationship, and ii) micro-to-macro kinematic relationship. We derive macro-scale constitutive constants for granular materials with idealized isotropic packing structure. The effects of inter-particle stiffness on the macro-scale constitutive constants are discussed. In addition, Green's function for concentrated force and couple is derived to be expressed in terms of inter-particle stiffness. Using the expressions of Green's function, the physical meaning and the effect of the internal characteristic length for granular materials are discussed.     

Particle size induced heterogeneity in compacted powders: Effect of large particles

We investigated the effect of particle size distribution on heterogeneity of compacted powders. We used experiments and discrete particle based simulations to compact powders, test the mechanical strength of the compact, and study the microstructure of the compact. A metallic powder which has a wide particle size distribution was used in the experiments. We found that the compaction profile is not reproducible when particles larger than 1/6 of the die diameter are present in the powder sample. The presence of these large particles generate a highly heterogeneous inter-particle contact and bonding forces. The discrete particle simulations showed that for these heterogeneous compacts the tensile strength exhibits high variability, even for one compact if the diametrical compression force is applied along different axes. Based on these results, it is recommend that the largest particle in a powder compact should not exceed one sixth of the die diameter, which is the same as the recommendation of ASTM International D4767 - 11 for compression test of cohesive soils.     

Photophoretic velocimetry for the characterization of aerosols

Aerosols are particles in a size range from some nanometers to some micrometers suspended in air or other gases. Their relevance varies as wide as their origin and composition. In the earth's atmosphere they influence the global radiation balance and human health. Artificially produced aerosols are applied, e.g., for drug administration, as paint and print pigments, or in rubber tire production. In all these fields, an exact characterization of single particles as well as of the particle ensemble is essential. Beyond characterization, continuous separation is often required. State-of-the-art separation techniques are based on electrical, thermal, or flow fields. In this work we present an approach to apply light in the form of photophoretic (PP) forces for characterization and separation of aerosol particles according to their optical properties. Such separation technique would allow, e.g., the separation of organic from inorganic particles of the same aerodynamic size. We present a system which automatically records velocities induced by PP forces and does a statistical evaluation in order to characterize the particle ensemble properties. The experimental system essentially consists of a flow cell with rectangular cross section (1 cm(2), length 7 cm), where the aerosol stream is pumped through in the vertical direction at ambient pressure. In the cell, a laser beam is directed orthogonally to the particle flow direction, which results in a lateral displacement of the particles. In an alternative configuration, the beam is directed in the opposite direction to the aerosol flow; hence, the particles are slowed down by the PP force. In any case, the photophoretically induced variations of speed and position are visualized by a second laser illumination and a camera system, feeding a mathematical particle tracking algorithm. The light source inducing the PP force is a diode laser (lambda = 806 nm, P = 0.5 W).     

Discrete-particle simulations of cohesive granular flow using a square-well potential

In the present study, rapid granular flows with attractive inter-particle forces are investigated. In particular, cohesive forces are incorporated into hard-sphere (molecular dynamics) simulations via a square-well potential. The square-well potential treats cohesive forces as both binary and instantaneous. For simple shear flows, an investigation of the input parameter space indicates that two distinct flow regimes are present. For relatively large cohesive forces, the formation of a large, single agglomerate is observed. For moderate cohesive forces, the sheared system is composed of mostly 2-particle, dynamic agglomerates that are fairly evenly distributed throughout the domain. Furthermore, the results for this latter regime indicate that cohesion attenuates the magnitude of the stress components at higher solids fractions (in the collisional regime) as compared to the non-cohesive case. At lower solids fractions (kinetic regime), however the presence of cohesive forces has little impact on the observed stress.The authors would like to thank the U.S. Department of Education GAANN Program in Microparticle and Nanoparticle Technology (Grant No. P2004980454) and the U.S. Department of Energy National Energy Technology Laboratory (via subcontract from Ames National Laboratory) for funding support. The Ames Laboratory is operated for the Department of Energy by Iowa State University under Contract No. W-7405-ENG82.     

An approach to simulate the motion of spherical and non-spherical fuel particles in combustion chambers

The objective of this paper is to identify a numerical method to simulate motion of a packed or fluidized bed of fuel particles in combustion chambers, such as a grate furnace and a rotary kiln. Therefore, the various numerical methods applied in the areas of granular matter and molecular dynamics were reviewed extensively. As a result, a time driven approach was found to be suited for the numerical simulation of particle motion in combustion chambers. Furthermore, this method can also be employed to moving boundaries which are required for the present application e.g. travelling grate. The method works in a Lagrangian frame of reference, which uses the position and orientation of particles as independent variables. These are obtained by time integration of the three-dimensional dynamics equations derived from the classical Newtonian approach for each particle. This includes the keeping track of all forces and momentums acting on each particle at every time step. Viscoelastic contact forces include normal and tangential components with viscoelastic models for energy dissipation and friction. The particle shapes are approximated by spheres and ellipsoids with a varying size and ratio of the semi-axis accounting for the variety of particle geometries in a combustion chamber. For these shapes the overlap of particles during contact is expressed by a polynomial of 4th order in the two-dimensional case and a polynomial of 6th order in the three-dimensional case. A new algorithm to detect two-dimensional elliptical particle contact with sufficient accuracy was developed. It is based on a sequence of coordinate transformations and has demonstrated its reliability in numerous applications. Finally, the method was applied to simulate the motion of spherical and elliptical particles in a rectangular enclosure, on a travelling grate, and in a rotary kiln. Received: 16 November 2001     

颗粒接触摩擦系数空间变异性对颗粒流双轴数值试验的影响

提出了考虑颗粒摩擦系数空间变异性的砂土双轴剪切响应分析方法。采用随机场模型表征颗粒摩擦系数空间变异性,通过Karhunen-Loève展开方法离散接触摩擦系数随机场,编写了基于颗粒流程序PFC^2D和MATLAB的随机模拟耦合分析程序。研究了摩擦系数空间变异性对密砂试样的双轴剪切响应影响规律。结果表明：1） 提出方法可有效地考虑颗粒间接触摩擦系数变异性对土体材料双轴压缩宏观力学行为影响;2） 密砂试样在剪切过程中的应力-应变关系曲线、体积-应变关系曲线的变化规律与颗粒间接触摩擦系数不确定性密切相关,在初始加载阶段随机模拟的偏应力曲线、体积应变曲线基本重合,继续加载后曲线开始发散;3） 垂直相关距离对峰值偏应力均值与标准差影响明显大于水平相关距离。颗粒接触摩擦系数的均值对峰值偏应力的影响大于摩擦系数空间分布的影响。摩擦系数的空间分布会影响剪切带的形成位置。     

Numerical investigations of strong hydrodynamic interaction between neighboring particles inertially driven in microfluidic flows

Dispersed particles traveling at a high throughput in microchannels laterally migrate and focus into a streamline at each channel face. The focusing attractors within the cross-section are determined by the balance between the lift forces. However, particles in close proximity (e.g. due to high concentration and abrupt particle contact) suffer a breakdown of distinct focusing due to excessive hydrodynamic interaction. Here, I present numerical investigations into the effects of the strong hydrodynamic interaction on the inertial focusing. The direct numerical simulation is used to calculate the focusing/defocusing of particles, specifically since the particle-induced disturbance flows vary at the particle scale and hence affect the individual particle motion. The simulated defocusing of many-body systems prefer finite inter-particle separation, in contrast with sedimentation of two mobile particles, whereby the trailing particle catches up with the leading particle due to reduced drag in its wake. I numerically demonstrate that the finite separation between nearest neighbors is a consequence of hydrodynamic repulsive motion unique to wall-bound shear flows. The author further presents direct demonstrations of the effects of the strong hydrodynamic interaction on the inertial focusing in an experimentally unachievable manner. The excessive hydrodynamic interaction drastically dissipates the near-wall focusing attractors and thus causes irreversible defocusing by breaking the balance between the lift forces. Unexpectedly, I also find that moderate hydrodynamic interaction can alter focusing speed on specific conditions, suggesting that an optimum concentration may significantly boost the inertial focusing in microfluidic-based applications.