A discrete model of a two-particle contact applied to cohesive granular materials

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.     

Characterization of fluctuations in granular hopper flow

We present a 2D discrete modelling of sand flow through a hopper using realistic grain shapes. A post-processing method is used to assess the local fluctuations in terms of void ratio, coordination number, velocity magnitude, and mean stress. The characteristics of fluctuations associated with the four considered quantities along the vertical axis of the hopper and across the entire hopper are carefully examined. The flow fluctuations for coordination number, velocity magnitude and mean stress are all found to take the form of radial waves originating from the lower centre of the hopper and propagating in the opposite direction of the granular flow. Quantitative characteristics of these waves (shape, amplitude, frequency, velocity, etc.) are identified. The fluctuations in void ratio however are not supportive of the observation of density waves in the granular flow as mentioned in some experiments. The possible reasons for this apparent contradiction are discussed, as well as possible extensions of this work.     

Falling process of a rectangular granular step

This study experimentally investigates the falling process of a dry granular step in a transparent plexiglass chute by particle image analysis. Three types of uniform spherical beads and one type of quartz sand were piled up with various bed slopes and widths to elucidate their flow characteristics. The surface angles during the early slipping phase are close to the failure angles that are associated with the active earth pressure, based on the Mohr-Coulomb friction law. For a given size of particles (d) and slope (θ), the retreating upper granular surface follows a theoretical curve, and dimensionless mobile length decreases as the dimensionless time parameter t* increases. Velocity profiles measured at the side wall exhibit an exponential-like tail close to the static region at the bottom of the chute. As determined by the conservation of mass and momentum, the relationship between the characteristic velocity and the characteristic depth is linear in the transient flow.     

Segregation and stability of a binary granular heap

We measure stability of two-dimensional granular mixtures in a rotating drum and relate grain configurations to stability. We use two types of grains which differ in both size and shape, with the larger grains reaching a larger average angle before an avalanche. In our mixtures, the smaller grains cluster near the center of the drum, while the larger grains remain near the outer edge, a pattern suggesting that grain size rather than avalanche angle determines the segregation behavior. One consequence of the size segregation is that the smaller grains heavily influence the stability of the heap. We find that the maximum angle of stability is a non-linear function of composition, changing particularly rapidly when small grains are first added to a homogeneous pile of large grains. We conclude that the grain configuration within the central portion of the heap plays a prominent role in stability. This work was supported in part by the National Science Foundation’s Research Experience for Undergraduates Program under PHY-0243904.     

On the influence of gas filtration on the discharge of loose material from a hopper

Experimental results on the influence of gas filtration on the discharge of loose material from a hopper in a broad range of variation of the parameters are classified.     

Analysis of the velocity field of granular hopper flow

We report the analysis of radial characteristics of the flow of granular material through a conical hopper. The discharge is simulated for various orifice sizes and hopper opening angles. Velocity profiles are measured along two radial lines from the hopper cone vertex: along the main axis of the cone and along its wall. An approximate power law dependence on the distance from the orifice is observed for both profiles, although differences between them can be noted. In order to quantify these differences, we propose a Local Mass Flow Index that is a promising tool in the direction of a more reliable classification of the flow regimes in hoppers.     

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.     

Micromechanic modeling and analysis of unsteady-state granular flow in a cylindrical hopper

This paper presents a numerical study of the micro- and macro-dynamic behavior of the unsteady-state granular flow in a cylindrical hopper with flat bottom by means of a modified discrete-element method (DEM) and an averaging method. The results show that the trends of the distributions of the microscopic properties such as the velocity and forces, and the macroscopic properties such as the velocity, mass density, stress and couple stress of the unsteady-state hopper flow are similar to those of steady-state hopper flow, and do not change much with the discharge of particles. However, the magnitudes of the macroscopic properties in different regions have different rates of variation. In particular, the magnitudes of the two normal stresses vary little with time in the orifice region, but decrease in other regions. The magnitude of the shear stress decreases with time when far from the bottom wall and central axis of the hopper. The results also indicate that DEM can capture the key features of the granular flow, and facilitated with a proper averaging method, can also generate information helpful to the test and development of an appropriate continuum model for granular flow.     

Micromechanic modeling and analysis of unsteady-state granular flow in a cylindrical hopper

This paper presents a numerical study of the micro- and macro-dynamic behavior of the unsteady-state granular flow in a cylindrical hopper with flat bottom by means of a modified discrete-element method (DEM) and an averaging method. The results show that the trends of the distributions of the microscopic properties such as the velocity and forces, and the macroscopic properties such as the velocity, mass density, stress and couple stress of the unsteady-state hopper flow are similar to those of steady-state hopper flow, and do not change much with the discharge of particles. However, the magnitudes of the macroscopic properties in different regions have different rates of variation. In particular, the magnitudes of the two normal stresses vary little with time in the orifice region, but decrease in other regions. The magnitude of the shear stress decreases with time when far from the bottom wall and central axis of the hopper. The results also indicate that DEM can capture the key features of the granular flow, and facilitated with a proper averaging method, can also generate information helpful to the test and development of an appropriate continuum model for granular flow.     

Nonlinear fracture of cohesive materials

The cohesive crack is a useful model for describing a wide range of physical situations from polymers and ceramics to fiber and particle composite materials. When the cohesive zone length is of the order of the specimen size, the influence method—based on finite elements—may be used to solve the fracture problem. Here a brief outline of an enhanced algorithm for this method is given. For very large specimen sizes, an asymptotic analysis developed by the authors allows an accurate treatment of the cohesive zone and provides a powerful framework for theoretical developments. Some recent results for the zeroth order and first order asymptotic approaches are discussed, particularly the effective crack concept and the maximum load size effect. These methods are used to analyze the effect of the size and of the shape of the softening curve on the value at the peak load of several variables for three point bent notched beams. The results show, among other things, that for intermediate and very large sizes the size effect curves depend strongly on the shape of the softening curve, and that only the simultaneous use of asymptotic and influence methods may give an adequate estimate of the size effect in the intermediate range.     

Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model

An adhesive elasto-plastic contact model for the discrete element method with three dimensional non-spherical particles is proposed and investigated to achieve quantitative prediction of cohesive powder flowability. Simulations have been performed for uniaxial consolidation followed by unconfined compression to failure using this model. The model has been shown to be capable of predicting the experimental flow function (unconfined compressive strength vs. the prior consolidation stress) for a limestone powder which has been selected as a reference solid in the Europe wide PARDEM research network. Contact plasticity in the model is shown to affect the flowability significantly and is thus essential for producing satisfactory computations of the behaviour of a cohesive granular material. The model predicts a linear relationship between a normalized unconfined compressive strength and the product of coordination number and solid fraction. This linear relationship is in line with the Rumpf model for the tensile strength of particulate agglomerate. Even when the contact adhesion is forced to remain constant, the increasing unconfined strength arising from stress consolidation is still predicted, which has its origin in the contact plasticity leading to microstructural evolution of the coordination number. The filled porosity is predicted to increase as the contact adhesion increases. Under confined compression, the porosity reduces more gradually for the load-dependent adhesion compared to constant adhesion. It was found that the contribution of adhesive force to the limiting friction has a significant effect on the bulk unconfined strength. The results provide new insights and propose a micromechanical based measure for characterising the strength and flowability of cohesive granular materials.     

Heat transport in granular materials during cyclic fluid flow

Heat transfer takes place between grains and the fluids that saturate the pore space in granular materials, when the fluid is static or moving. This study explores effective heat transport in granular materials during cyclic fluid flow. Controlled particle-scale experiments, complementary analyses and numerical simulations help us identify the governing variables and ensuing time scales. We show that fluid-grain heat transfer leads to effective heat transport along the granular medium during cyclic fluid flow. At the macro-scale, the process resembles diffusion where the effective diffusion coefficient is proportional to the square of the fluid invasion length in each cycle and inversely proportional to the cycle period. Both experimental and numerical results confirm improved heat transfer by cyclic fluid flow over thermal diffusion under hydrostatic conditions. The formulation can be used to identify optimal operation conditions for maximum transport.     

Mixtures of granular materials

Balance laws are given for a mixture of granular materials of a type described by Goodman and Cowin. Constitutive equations are given for the case of two dry granular constituents, and consequences of the entropy principle are found.     

Creep of granular materials

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.     

Steady-state granular flow in a 3D cylindrical hopper with flat bottom: macroscopic analysis

The information of a hopper flow at a particle scale, obtained from discrete particle simulation, is used to investigate the macroscopic dynamic behaviour of granular flow in a cylindrical hopper with flat bottom by means of an averaging technique. The macroscopic properties including velocity, mass density, stress and couple stress are quantified under the cylindrical coordinate framework, and an effort is made to link these variables to the microscopic variables considered. The velocity and density distributions are first illustrated to match qualitatively the experimental and numerical results, confirming the validity of the proposed averaging method. Four components of stress, T_zz, T_rr, T_rz and T_zr, and two dominant components of couple stress, M_{r θ} and M_{z θ}, are then investigated in detail. It is shown that large vertical normal stress is mainly observed in the region close to the bottom corner, large radial normal stress is observed within the particle bed as well as the bottom corner, and large shear stresses in the region adjacent to the vertical wall. The four stresses are relatively small in a region close to the orifice. Their magnitudes are mainly contributed by the interaction forces between particles and between particles and walls. However, the transport of particles also plays a significant role at the orifice, especially, in the vertical normal stress. The couple stress can be ignored except for the regions close to the vertical and bottom walls, where the most dominant components are M_{r θ} adjacent to the vertical wall and M_{z θ} close to the bottom wall. The magnitudes of these macroscopic variables depend on the geometric and physical parameters of the hopper and particles such as the orifice size and wall roughness of the hopper, and the friction and damping coefficients between particles although their spatial distributions are similar.     

Segregation due to particle shape of a granular mixture in a slowly rotating tumbler

Using DEM particle simulations we consider segregation of a binary granular particle mixture in a slowly rotating cylindrical tumbler where the particles differ only in their shape—spherical versus more cubical particles. We find that the more cubical particles segregate to the inner core of the particle bed while the spherical particles segregate to the curved walls of the tumbler. The main mechanism for this segregation is different energy dissipation rates for the different particle shape types when avalanching down along the free surface. The cubical particles, due to their sharper corners, dissipate energy much faster than the spherical particles. This results in spherical particles reaching the bottom end of the sloped, free surface which are then transported around the cylinder adjacent to the cylinder wall, as rigid body motion. In contrast to size or density segregation, the segregation due to shape is much weaker and takes longer to reach its equilibrium or steady state. In addition, the segregation occurs along the top surface rather than through the top surface (as occurs for size and density segregation). In general, in situations where two particles differ in their ease of flow (viz flowability) the more rapidly flowing particle will segregate to the base of the free surface (which in the case of the tumbler results in spherical particles near the periphery) and the more slowly flowing particle will segregate underneath.     

料仓中湿颗粒的卸料流型

基于离散单元法,构建湿颗粒料仓卸料模型,研究料仓卸料流型量化指标(MFI)与湿颗粒摩擦特性、料仓半顶角、料仓开口尺寸以及仓壁摩擦特性之间的相互关系,并与Jenike理论预测结果进行对比。结果表明:湿颗粒-壁面摩擦系数和料仓半顶角对MFI的影响很大,随着壁面摩擦系数或半顶角的增加,MFI值减小,卸料流型可由整体流变为中心流,该结果与Jenike理论预测结果一致;料仓开口尺寸、湿颗粒-颗粒摩擦系数、颗粒Bond数(Bo)和无因次含水量则对MFI的影响较小。