基于球形颗粒几何排列的离散元试样高效生成方法

在球体离散元数值模拟中,颗粒的初始排列状态是影响计算效率和计算结果的重要环节。本文采用前进面几何构造算法,提出了一种基于网格搜索的球形颗粒随机排列高效算法。通过求解空间三边方程,满足了粒径设置的任意大小的颗粒依次置入前进面的外侧,并与构成前进面的三个颗粒相互接触。为获得高体积分数的颗粒簇,该算法允许颗粒改变其粒径大小。采用颗粒网格化方法可以简化前进面的搜索,并由此提高排列效率。通过计算平均配位数、体积分数和二阶结构张量的特征值,对不同粒径比下得到的立方体试样进行了分析,得到试样配位数及体积分数均随着粒径比的增大而增大,且得到的试样为各向同性。此外,空间网格的大小和初始颗粒的生成点对随机排列的效率均会产生显著的影响。最后,对非规则铁路道砟进行了精细构造及压碎模拟,发现DEM模拟得到的应力-应变曲线与试验结果基本吻合,验证了该算法得到的颗粒试样在模拟道砟裂纹起裂、扩展等过程的有效性。     

A nonlocal contact formulation for confined granular systems

We present a nonlocal formulation of contact mechanics that accounts for the interplay of deformations due to multiple contact forces acting on a single particle. The analytical formulation considers the effects of nonlocal mesoscopic deformations characteristic of confined granular systems and, therefore, removes the classical restriction of independent contacts. This is in sharp contrast to traditional contact mechanics theories, which are strictly local and assume that contacts are independent regardless the confinement of the particles. For definiteness, we restrict attention to elastic spheres in the absence of gravitational forces, adhesion or friction. Hence, a notable feature of the nonlocal formulation is that, when nonlocal effects are neglected, it reduces to Hertz theory. Furthermore, we show that, under the preceding assumptions and up to moderate macroscopic deformations, the predictions of the nonlocal contact formulation are in remarkable agreement with detailed finite-element simulations and experimental observations, and in large disagreement with Hertz theory predictions—supporting that the assumption of independent contacts only holds for small deformations. The discrepancy between the extended theory presented in this work and Hertz theory is borne out by studying periodic homogeneous systems and disordered heterogeneous systems.     

On flows of granular materials

This article reviews the behavior of materials made up of a large assemblage of solid particles under rapid and quasi static deformations. The focus is on flows at relatively high concentrations and for conditions when the interstitial fluid plays an insignificant role. The momentum and energy exchange processes are then primarily governed by interparticle collisions and Coulomb-type frictional contact. We first discuss some physical behavior —dilatancy, internal friction, fluidization and particle segregation — that are typical to the understanding of granular flows. Bagnold's seminal Couette flow experiments and his simple stress analysis are then used to motivate the first constitutive theories that use a microstructural variable — the fluctuation energy or granular temperature — governing the subscale fluctuating motion. The kinetic theories formalize the derivation of the field equations of bulk mass, momentum and energy, and permit derivation of constitutive relations for stress, flux of fluctuation energy and its dissipation rate for simple particle assemblages and when frictional rubbing contact can be ignored. These statistical considerations also show that formulation of boundary conditions needs special attention. The frictional-collisional constitutive behavior in which both Coulomb-type rubbing contact and collisional encounters are significant are discussed. There is as yet no rigorous formulation. We finally present a phenomenological approach that describes rapid flows of granular materials under simultaneous transport of heat and close with a summary of stability analyses of the basic flow down an inclined plane.Dedicated to Professor Dr.-Ing. Franz Gustav Kollmann on the occasion of his sixtieth brithday     

Random close packing and relative viscosity of multimodal suspensions

Multimodal suspensions, consisting of non-colloidal spherical particles and a Newtonian matrix, are considered. A new differential (or multi-scale mean field approach) model for the relative viscosity of multimodal suspensions has been developed. The problem of the random close packing fraction of the solid phase is also investigated. We suppose that the multimodal suspension has a dominant large particle composition and that the smaller particles are embedded in the empty space between the larger particles. The relative viscosity model can therefore be based on the theory of monomodal suspensions. Experimental data of Eveson are compared to the predictions given by using three different models of monomodal suspensions respectively. The Maron–Pierce approach appears to give the best agreement with Eveson’s experiments. However, due to experimental uncertainties, we recommend that the Mendoza and Santamaria-Holek (MSH) formula be adopted.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method (DEM) when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method （DEM） when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles

We use a two-dimensional model of polygonal particles to investigate granular ratcheting. Ratcheting is a long-term response of granular materials under cyclic loading, where the same amount of permanent deformation is accumulated after each cycle. We report on ratcheting for low frequencies and extremely small loading amplitudes. The evolution of the sub-network of sliding contacts allows us to understand the micromechanics of ratcheting. We show that the contact network evolves almost periodically under cyclic loading as the sub-network of the sliding contacts reaches different stages of anisotropy in each cycle. Sliding contacts lead to a monotonic accumulation of permanent deformation per cycle in each particle. The distribution of these deformations appears to be correlated in form of vortices inside the granular assembly.     

Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles

We use a two-dimensional model of polygonal particles to investigate granular ratcheting. Ratcheting is a long-term response of granular materials under cyclic loading, where the same amount of permanent deformation is accumulated after each cycle. We report on ratcheting for low frequencies and extremely small loading amplitudes. The evolution of the sub-network of sliding contacts allows us to understand the micromechanics of ratcheting. We show that the contact network evolves almost periodically under cyclic loading as the sub-network of the sliding contacts reaches different stages of anisotropy in each cycle. Sliding contacts lead to a monotonic accumulation of permanent deformation per cycle in each particle. The distribution of these deformations appears to be correlated in form of vortices inside the granular assembly.     

Micro-rheology of dense particulate flows: Application to immersed avalanches

We rely here on a non-smooth contact dynamics (NSCD) approach to treat particle collisions in a direct numerical simulation of a dense particulate flow. Interactions between particles are considered by a non-smooth formulation of particle dynamics at the microscopic scale, which enables one to straightforwardly implement complex contact laws. The hydrodynamic coupling is achieved by a distributed Lagrange multiplier/fictitious domain (DLM/FD) method. As a preliminary step, the relevance of our NSCD-DLM/FD method is assessed by comparing results of 2D sedimentation simulations with those obtained with a usual molecular dynamics collision model. Then, we use it to investigate how a fully immersed granular packing collapses depending on its initial particle volume fraction, providing clues on the micro-rheology of dense particulate flows.     

Neighborhood Relationships of Widely Distributed and Irregularly Shaped Particles in Partially Dewatered Filter Cakes

A more thorough understanding of the properties of bulk material structures in solid–liquid separation processes is essential to understand better and optimize industrially established processes, such as cake filtration, whose process outcome is mainly dependent on the properties of the bulk material structure. Here, changes of bulk properties like porosity and permeability can originate from local variations in particle size, especially for non-spherical particles. In this study, we mix self-similar fractions of crushed, irregularly shaped Al₂O₃ particles (20 to 90 µm and 55 to 300 µm) to bimodal distributions. These mixtures vary in volume fraction of fines (0, 20, 30, 40, 50, 60 and 100 vol.%). The self-similarity of both systems serves the improved parameter correlation in the case of multimodal distributed particle systems. We use nondestructive 3D X-ray microscopy to capture the filter cake microstructure directly after mechanical dewatering, whereby we give particular attention to packing structure and particle–particle relationships (porosity, coordination number, particle size and corresponding hydraulic isolated liquid areas). Our results reveal widely varying distributions of local porosity and particle contact points. An average coordination number (here 5.84 to 6.04) is no longer a sufficient measure to describe the significant bulk porosity variation (in our case, 40 and 49%). Therefore, the explanation of the correlation is provided on a discrete particle level. While individual particles?<?90 µm had only two or three contacts, others?>?100 µm took up to 25. Due to this higher local coordination number, the liquid load of corresponding particles (liquid volume/particle volume) after mechanical dewatering increases from 0.48 to 1.47.

     

The elastic response of a cohesive aggregate—a discrete element model with coupled particle interaction

A model is presented for the deformation of a cohesive aggregate of elastic particles that incorporates two important effects of large-sized inter-particle junctions. A finite element model is used to derive a particle response rule, for both normal and tangential relative deformations between pairs of particles. This model agrees with the Hertzian contact theory for small junctions, and is valid for junctions as large as half the nominal particle size. Further, the aggregate model uses elastic superposition to account for the coupled force–displacement response due to the simultaneous displacement of all of the neighbors of each particle in the aggregate. A particle stiffness matrix is developed, relating the forces at each junction to the three displacement degrees of freedom at all of the neighboring-particle junctions. The particle response satisfies force and moment equilibrium, so that the model is properly posed to allow for rigid rotation of the particle without introducing rotational degrees of freedom. A computer-simulated sintering algorithm is used to generate a random particle packing, and the stiffness matrix is derived for each particle. The effective elastic response is then estimated using a mean field or affine displacement calculation, and is also found exactly by a discrete element model, solving for the equilibrium response of the aggregate to uniform-strain boundary conditions. Both the estimate and the exact solution compare favorably with experimental data for the bulk modulus of sintered alumina, whereas Hertzian contact-based models underestimate the modulus significantly. Poisson's ratio is, however, accurately determined only by the full equilibrium discrete element solution, and shown to depend significantly on whether or not rigid particle rotation is permitted in the model. Moreover, this discrete element model is sufficiently robust, so it can be applied to problems involving non-homogeneous deformations in such cohesive aggregates.     

Heat Transfer and Particle Behaviours in Dispersed Two-Phase Flow with Different Heat Conductivities for Liquid and Solid

Liquid-solid two-phase flow with heat transfer is directly simulated, to investigate the effects of the ratios of heat conductivities (solid to liquid) and bulk solid volume fraction from dense to dilute situations. The interaction between fluid and particles is solved by our original immersed solid approach on a rectangular grid system. A discrete element method with a soft-sphere collision model is applied for particle-particle and particle-wall interactions. Governing equation of temperature is time-updated with an implicit treatment for the diffusion term, which enables robust simulation with particles of very high/low ratios of heat conductivities (from 1/1000 to 1000) to the fluid. The local heat flux at the fluid-solid interface is modelled by a new flux decomposition technique, and incorporated into the implicit scheme of the temperature. The method is applied to a 2-D particulate flow in a natural convection in a square domain at a relatively low Rayleigh number. In the dense condition, for the cases with high ratios of heat conductivity, the heat transfer is promoted by strong convection, while the particles of low ratios of heat conductivity tend to hinder the development of the temperature rise in the flow field, causing a weak convection and low Nusselt number. Under a condition of relatively low solid volume fraction, fixed particles only depress the heat convection as the number of particles and heat conductivity ratio increase. For the cases with freely-moving particles, on the other hand, heat conductivity of particles has a stronger influence on the heat transfer of the system than the number of particles. The above simulation results highlight the effect of temperature distributions within the particles and liquid.     

Multi-level DEM study on silo discharge behaviors of non-spherical particles

The silo discharge of non-spherical particles has been widely practiced in engineering processes, yet the understanding of multi-level mechanisms during solid transportation is still lacking. In this study, a high-fidelity super-ellipsoid Discrete Element Method (DEM) model is established to investigate the discharge behaviors of non-spherical particles with different size distributions. After the comprehensive model validations, we investigated the effects of particle shape (aspect ratio and particle sharpness) on the particle level discharge behaviors. The discharge rates of the ellipsoid particles used in the current work are larger than the spherical particles due to the larger solid fraction. The discharge rates of the cuboid-like particles are determined by the combined effect of the solid fraction and the contact force. Parcel level data show that the translational movements of the ellipsoid particles are more ordered, which is supported by the global level data. Strong correlations exist between the particle level and parcel level data, especially the ellipsoid particles and the large particles in the polydispersed cases.     

Effect of temperature gradient within a solid particle on the rotation and oscillation modes in solid-dispersed two-phase flows

Liquid–solid two-phase flow with heat transfer is simulated, and the effect of temperature gradient within a solid particle on the particle behaviour and heat transfer is studied. The interaction between fluid and particles is considered with our original immersed solid approach on a rectangular grid system. The local heat flux at the fluid–solid interface is described with an anisotropic heat conductivity matrix, and the governing equation of temperature is time-updated with an implicit treatment for the diffusion term. The method is applied to a 2-D natural convection flow of a relatively low Rayleigh number including multiple particles. Heat transfer and particle behaviours are studied for different solid heat conductivities (ratio to the fluid conductivity ranging between 10⁻³ and 10³) and solid volume fractions. Under a condition of relatively low heat conductivity ratio, the particles show a simple circulating flow. By increasing the heat conductivity ratio, a transition of the particulate flow is observed to oscillation mode around the domain centre due to the buoyancy force as a restitution force. The oscillation period is found to vary with the heat conductivity ratio, and it is related to the time scales for the heat transfer via fluid and solid.     

Multiscale modeling of heterogeneous propellants from particle packing to grain failure using a surface-based cohesive approach

In the present work,a computational framework is established for multiscale modeling and analysis ofsolid propellants.A packing algorithm,considering the ammonium perchlorate(AP) and aluminum(Al) particles asspheres or discs is developed to match the size distributionand volume fraction of solid propellants.A homogenizationtheory is employed to compute the mean stress and strainof a representative volume element(RVE).Using the meanresults,a suitable size of RVE is decided.Without considering the interfaces between particles and matrix,several numerical simulations of the relaxation of propellants are performed.The relaxation effect and the nonlinear mechanicalbehavior of propellants which are dependent on the appliedloads are discussed.A new technology named surface-basedcohesive behavior is proposed to describe the phenomenonof particle dewetting consisting of two ingredients:a damageinitiation criterion and a damage evolution law.Several examples considering contact damage behavior are computedand also nonlinear behavior caused by damaged interfaces isdiscussed in this paper.Furthermore the effects of the critical contact stress,initial contact stiffness and contact failuredistance on the damaged interface model have been studied.     

Filler-reinforcement of elastomers viewed as a triboelastic phenomenon

A triboelastic approach is offered for modeling the reinforcement phenomenon in particulate elastomeric composites. The structural unit is composed of two solid substrates, modeling the surface of filler particles, and an adjoining nonlinear elastic spring, modeling a rubber molecule adsorbed by the surfaces of substrates. The strength of the adhesive bond is represented as a specified frictional resistance appearing when the string is sliding along the substrate. The tensile curve of this model gives a clearer insight into the reinforcement mechanism, which may by regarded as the frictional resistance experienced by the spring on its sliding along the substrates at lower and moderate deformations.     

Constitutive model for predicting dynamic interactions between soil ejecta and structural panels

A constitutive model is developed for the high-rate deformation of an aggregate comprising of mono-sized spherical particles with a view to developing an understanding of dynamic soil-structure interactions in landmine explosions. The constitutive model accounts for two regimes of behaviour. When the particle assembly is widely dispersed (regime I), the contacts between particles are treated as collisions, analogous to those between molecules in a gas or liquid. At high packing densities (regime II) the contacts are semi-permanent and consolidation is dominated by particle deformation and inter-particle friction. Regime I is modelled by extending an approach proposed by Bagnold (1954. Experiments on a gravity-free dispersion of large solid particles in a Newtonian fluid under shear. Proceedings of the Royal Society of London A 225, 49-63) to a general strain history comprising volumetric and deviatoric deformation. For regime II, classical soil mechanics models (such as Drucker-Prager) are employed. The overall model is employed to investigate the one-dimensional impact of sand against a rigid stationary target. The calculations illustrate that, unlike single-particle impact, the momentum transmitted to a rigid target is insensitive to the particle co-efficient of restitution, but strongly dependent on initial density. The constitutive model is also used to examine the spherical expansion of a shell of sand (both dry and water saturated). In line with initial experimental observations, the wet sand is predicted to form clumps while the dry sand fully disperses. The model shows that this clumping of explosively loaded wet sand exerts higher pressures on nearby targets compared to equivalent dry sand explosions.     

环空钻柱三维二重非线性动力学问题的研究

通过对大挠度钻柱受力变形特点及其环空旋转状态下与井壁接触机理的分析，根据动力学原理，建立和进一步完善钻柱与井壁动态摩擦接触模型．根据有限元理论，提出了Ｗｉｌｓｏｎ－θ法与Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法相结合的模式，解决钻柱二重非线性动力学问题．计算分析结果说明，文中理论模型是可行的，不仅更完善，而且更简便；动态非线性效应分析得到了与静态分析相似的结论；钻柱与井壁各种接触形式或并存或交替都有可能；转速较高时动态影响不容忽视．     

Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.