Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles

In the present article, we study the effect of inherent anisotropy, i.e., initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials, by numerical simulation of several biaxial compression tests using the discrete element method (DEM). Particle shape is considered to be irregular convex-polygonal. The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading. As experimental tests have already shown, numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies. Comparison of simulations with tests using oval particles, shows that angularity influences both the mobilized shear strength and the volume change regime, which originates from the interlocking resistance between particles.     

Effect of aspect ratio on triaxial compression of multi-sphere ellipsoid assemblies simulated using a discrete element method

Here, we present a numerical investigation of the mechanical behavior of ellipsoids under triaxial compression for a range of aspect ratios. Our simulations use a multi-sphere approach in a three-dimensional discrete element method. All assemblies were prepared at their densest condition, and triaxial compression tests were performed up to extremely large strains, until a critical state was reached. The stress–strain relationship and the void ratio–strain behavior were evaluated. We found that the stress–dilatancy relationship of ellipsoids with different aspect ratios could be expressed as a linear equation. In particular, the aspect ratio influenced the position of the critical state lines for these assemblies. Particle-scale characteristics at the critical state indicate that particles tend to be flat lying, and the obstruction of particle rotation that occurs with longer particles affects their contact mechanics. Lastly, anisotropic coefficients related to aspect ratio were investigated to probe the microscopic origins of the macroscopic behavior. A detailed analysis of geometrical and mechanical anisotropies revealed the microscopic mechanisms underlying the dependency of peak and residual strengths on aspect ratio.     

Effect of particle shape on micro- and mesostructure evolution of granular assemblies under biaxial loading conditions

Discrete element method (DEM) numerical biaxial tests on samples with different particle shapes are performed to investigate how the multiscale evolves with varying particle shape. The samples used in such simulations are composed of circular, square, and elongated particles, respectively. For the numerical results, analyses are conducted in terms of microscopic evolution, i.e. particle rotation and evolution of fabric, and mesoscopic evolution, i.e. the evolution of loops and improved clustering coefficient. At the microscale, the mean particle rotation of circular particles is remarkably larger than those of square and elongated particles, and the shear band localization phenomenon is more obvious when the aspect ratio (AR) decreases. Considering the fabric evolving with particle shape, the value of anisotropy gradually increases when particle shape becomes irregular, and contacts of circular particles are pronouncedly less than those of irregular particles from the coordination number and curves of degree distribution. At the mesoscale, when the particle relationship is considered, the isotropic particles (i.e. circular and square particles) have similar evolutions of loops and modified clustering coefficient, whereas the elongated particles have remarkable three loops and modified clustering coefficient, which are both larger than those of isotropic particles.     

Flow fields and packing states in the discharge flow of noncircular particles—A SIPHPM simulation

Although the discharge flow of spherical materials has been extensively explored, the effect of particle shape on discharge is still poorly understood. The present work explores the two-dimensional discharge flow fields of noncircular particles using the soft-sphere-imbedded pseudo-hard particle model method. Rectangular particles having different aspect ratios (R_a = 1, 1.5, 2–5) and regular polygonal particles having different numbers of sides (N_s = 3–8, 10) are discharged through hopper beds having different orifice widths (D_i = 40, 70.77, 99.13, 125.74, 151.13 mm). The discharge rates of differently shaped particles in different beds are consistent with Beverloo’s relation. Moreover, the flow fields are computed and evaluated to study the effects of R_a, N_s, and D_i on particle discharge. The characteristics of particle–particle connections in the discharge process are evaluated according to the temporal evolution and spatial distribution of the contact points. Additionally, the effect of the initial packing on the discharge profile is investigated. The findings help clarify the discharge of noncircular particles.     

DEM investigation on the effect of sample preparation on the shear behavior of granular soil

The effect of initial fabric anisotropy produced by sample preparation on the shear behavior of granular soil is investigated by performing discrete element method (DEM) simulations of fourteen biaxial tests in drained conditions. Numerical test specimens are prepared by three means: gravitational deposition, multi-layer compression, and isotropic compression, such that different initial inherent soil fabrics are created. The DEM simulation results show that initial fabric anisotropy exerts a considerable effect on the shear behavior of granular soil, and that the peak stress ratio and peak dilatancy increase with an increase in the fabric index a_n that is estimated from the contact orientations. The stress–dilatancy relationship is found to be independent of the initial fabric anisotropy. The anisotropy related to the contact orientation and contact normal force accounts for the main contribution to the mobilized friction angle. Also, the occurrence of contractive shear response in an initial shearing stage is accompanied by the most intense particle rearrangement and microstructural reorganization, regardless of the sample preparation method. Furthermore, the uniqueness of the critical state line in e–log p′ and q–p′ plots is observed, suggesting that the influence of initial fabric anisotropy is erased at large shear strains.     

Particle Deposition in Porous Media: Analysis of Hydrodynamic and Weak Inertial Effects

We have studied the transport and capture of non-Brownian particles in porous media, when the particles are mainly submitted to hydrodynamic and weak inertial effects. Visualization experiments have been performed using several models of porous media which consist of transparent etched networks of interconnected channels. Typical particle deposits have been observed at the corners of the grains of the porous medium. Their shape and their orientation were dependent on flow rate and on the anisotropy of the flow field. A trajectory analysis model has been applied to a porous medium made of a doubly periodic array of rectangular grains very close to the experimental model. This numerical model has been used to localize particle deposits and to determine particle capture efficiency on the grains over a range of low Stokes numbers, grain aspect ratios and flow-field anisotropy ratios. The results have been interpreted in terms of shape of particle deposits and compared successfully to experimental observations.     

Micromechanics of breakage in sharp-edge particles using combined DEM and FEM

By combining DEM （Discrete Element Method） and FEM （Finite Element Method）, a model is established to simulate the breakage of twodimensional sharp-edge particles, in which the simulated particles are assumed to have no cracks. Particles can, however, crush during different stages of the numerical analysis, if stress-based breakage criteria are fulfilled inside the particles. With this model, it is possible to study the influence of particle breakage on macro- and micro-mechanical behavior of simulated angular materials. Two series of tests, with and without breakable particles, are simulated under different confining pressures based on conditions of biaxial tests. The results, presented in terms of micromechanical behavior for different confining pressures, are compared with macroparameters. The influence of particle breakage on microstructure of sharp-edge materials is discussed and the related confining pressure effects are investigated. Breakage of particles in rockfill materials are shown to reduce the anisotropy coefficients of the samples and therefore their strength and dilation behaviors.     

粒料固有各向异性的离散元模拟与细观分析

料在摊铺后形成的颗粒定向排列将导致其力学性质的固有各向异性. 依据粒料的实际不规则形状, 构建了可模拟粒间咬合嵌挤作用的三维离散元复杂形状颗粒; 生成了5 种不同沉积方向的各向异性试件和1种各向同性试件, 对比了各试件在三轴压缩试验中的宏观力学特性差异; 引入组构张量以量化各向异性程度, 利用玫瑰图表达接触法向与接触力的分布特征, 探究了粒料各向异性的细观发展规律. 结果表明: 颗粒长轴愈趋向水平排布, 峰值应力比愈大, 剪缩与剪胀程度愈明显; 相较于各向同性试件, 沉积角$\theta$为料在摊铺后形成的颗粒定向排列将导致其力学性质的固有各向异性. 依据粒料的实际不规则形状, 构建了可模拟粒间咬合嵌挤作用的三维离散元复杂形状颗粒; 生成了5 种不同沉积方向的各向异性试件和1种各向同性试件, 对比了各试件在三轴压缩试验中的宏观力学特性差异; 引入组构张量以量化各向异性程度, 利用玫瑰图表达接触法向与接触力的分布特征, 探究了粒料各向异性的细观发展规律. 结果表明: 颗粒长轴愈趋向水平排布, 峰值应力比愈大, 剪缩与剪胀程度愈明显; 相较于各向同性试件, 沉积角$\theta$为$0^\circ$时, 峰值应力比和最大体积压缩应变分别提高了12.6\%和18.8\%, 其原因在于加载过程中颗粒旋转和滑动百分比更小, 内部调整时间更短、更易被剪密; 固有各向异性对颗粒法向接触力分布的影响不大, 但显著影响接触法向分布特征; 剪切过程中, $\theta$为$90^\circ$时的接触法向各向异性系数先快速减小后逐渐增大, 而$\theta$为$0^\circ$到$60^\circ$时则呈现出增大后稍有回落或趋于稳定的趋势, 且$\theta$ 愈小的试件各向异性系数增大愈快.     

Particle Lagrangian Tracking with Hydrodynamic Interactions and Collisions

Hydrodynamic interactions between particle pairs are included in a Lagrangian approach for the simulation of the turbulent dispersion of a discrete particle. Several particles are simultaneously followed, and the set of equations of motion involves a coupling between particles through the use of a resistance matrix pertaining to the sedimentation theory. Results are presented for particle behavior in low turbulence fields, where collisions between particle pairs are assumed to be perfectly elastic. The influence of the turbulence anisotropy is considered and the anisotropy of the particle fluctuating motion is shown to be reduced by collisions.     

Micromechanics of breakage in sharp-edge particles using combined DEM and FEM

By combining DEM (Discrete Element Method) and FEM (Finite Element Method),a model is established to simulate the breakage of two-dimensional sharp-edge particles,in which the simulated particles are assumed to have no cracks.Particles can,however,crush during different stages of the numerical analysis,if stress-based breakage criteria are fulfilled inside the particles.With this model,it is possible to study the influence of particle breakage on macro- and micro-mechanical behavior of simulated angular materials.Two series of tests,with and without breakable particles,are simulated under different confining pressures based on conditions of biaxial tests.The results,presented in terms of micromechanical behavior for different confining pressures,are compared with macroparameters.The influence of particle breakage on microstructure of sharp-edge materials is discussed and the related confining pressure effects are investigated.Breakage of particles in rockfill materials are shown to reduce the anisotropy coefficients of the samples and therefore their strength and dilation behaviors.     

An Examination of Anisotropic Void Evolution in Aluminum Alloy 7075

This paper investigates the anisotropy of void evolution and its relation with ductility in the high strength rolled aluminum alloy 7075-T7351. Smooth tension specimens are extracted from three principal material orientations, i.e. rolling (R), transverse (T), and short transverse (S). The mechanical behavior of these specimens is characterized and the varying ductility in the three orientations is clearly observed. Electron Backscattered Diffraction (EBSD), optical microscopy, and Scanning Electron Microscopy (SEM) are employed to characterize the grain structure and the size, location, and chemical composition of the intermetallic particles. In-situ X-ray Tomography (XCT) experiments are performed to obtain tomographic images of the specimens at critical loading steps. The radiographs acquired during the tensile test are then reconstructed and examined through quantitative analysis to partition particles and voids. These tomographic images enable us to visualize void evolution as the specimens are loaded along material orientations. The tomographic images clearly illustrate anisotropy in the void evolution and highlight the importance of local coalescence in developing 1D and 2D void structures prior to global coalescence. Fractography confirms tomography. These findings motivate model forms with appropriate internal variables to adequately describe the dominant mechanisms which govern anisotropic void evolution.     

Global flow instability in a lid‐driven cavity

The stability of flow in a lid‐driven cavity is investigated using an accurate numerical technique based on a hybrid scheme with spectral collocation and high‐order finite differences. A global stability analysis is carried out and critical parameters are identified for various aspect ratios. It is found that while there is reasonable agreement with the literature for the critical parameters leading to loss of stability for the square cavity, there are significant discrepancies for cavities of aspect ratios 1.5 and 2. Simulations of the linearized unsteady equations confirm the results from the global stability analysis for aspect ratios A = 1, 1.5 and A = 2. Copyright © 2009 John Wiley & Sons, Ltd.     

A simple plasticity model for prediction of non-coaxial flow of sand

A bounding surface plasticity model for non-coaxiality, another aspect of anisotropic behavior of sands under rotation of principal stress axes; is developed in the critical state framework. Numerous experimental evidences exist that corroborate dependence of plastic shear strain rate direction on inherent fabric anisotropy. At first, general expressions for plastic strain rate with respect to possible emerge of non-coaxial flow are obtained. Consequently, using an anisotropy state parameter that is specially developed for this model and accounts for the interaction between imposed loading and soil fabric; effect of anisotropy on plastic flow direction is taken into account. Besides, novel circumstances are proposed for plastic modulus and dilatancy under rotation of principal stress axes. Finally, it is shown that the model is able to simulate successfully the non-coaxial behavior of sands subjected to principal stress axes rotation.     

On the orientation of ellipsoidal particles in a turbulent shear flow

Direct numerical simulation (DNS) of small prolate ellipsoidal particles suspended in a turbulent channel flow is reported. The coupling between the fluid and the particles is one-way. The particles are subjected to the hydrodynamic drag force and torque valid for creeping flow conditions. Six different particle cases with varying particle aspect ratios and equivalent response times are investigated. Results show that, in the near-wall region, ellipsoidal particles tend to align with the mean flow direction, and the alignment increases with increasing particle aspect ratio. When the particle inertia increases, the particles are less oriented in the spanwise direction and more oriented in the wall-normal direction. In the core region of the channel, the orientation becomes isotropic.     

Influence of aspect ratio and arrangement direction on the shear behavior of ellipsoids

This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method (DEM) simulation. To avoid the boundary effect, a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing. The shape features of ellipsoids are investigated, including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids. The macroscopic properties of ellipsoidal particle samples, such as the deviatoric stress, volumetric strain, internal friction angle, as well as dilatancy angles are explored. Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips. In addition, it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains. The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior.     

SiC粒子非均布引起铝基复合材料的损伤分析

 根据电镜断面考察结果，以Gurson模型为本构方程的有限单元 法对包体模型及三维非均匀模型进行了详细分析. 为了评价应力-应变 关系及损伤的主要因素，考虑了基体中SiC粒子的体积率和径比的非均 匀分布. 其结果表明，用这种非均匀模型能很好地仿真铝基体在大量塑 性变形之后所发生的韧窝破坏过程. SiC粒子体积率、径比及其位置的 非均匀性，对局部和整体损伤过程与应力-应变关系的影响相当大. 当 Sic粒子径比为1.0，并在基体中均匀分布时，断裂应变会大幅度增大.     

微流道内椭圆粒子黏弹性聚焦数值模拟研究

黏弹性聚焦技术借助微尺度黏弹性流体的惯性和弹性耦合效应,能够实现生物粒子在流道中心的单一位置聚焦排列,被认为是未来生物粒子计数以及检测的理想预处理单元,因而引起了广泛的关注．自然界中的生物粒子往往是非球形的,故而研究不同形状粒子在黏弹性流体中的迁移特性具有十分重要的价值．本文通过格子玻尔兹曼方法耦合浸入边界法,对椭球粒子在直流道内黏弹性流体中的聚焦行为进行了系统的数值模拟研究．结果表明,面积相同但长径比不同的椭圆粒子在黏弹性流体中有不同的旋转周期与迁移速度．长径比更大的粒子旋转周期更长,且长径比大于3.5 的粒子甚至不再有明显的旋转．长径比更大的粒子上下两侧的黏弹性力分布更加平缓,受到指向流道中心的弹性力更小,使得粒子横向迁移速度更慢从而导致了长径比不同的椭圆粒子聚焦至流道中心所需时间的差异．此外,Weissenberg 数Wi 的增加同样能够减弱粒子的旋转,使得长径比稍小的粒子也能和长径比为1.0 的圆形粒子产生明显的分离．上述数值模拟的结论,为不同长径比粒子在黏弹性流体中的聚焦与分选应用提供了重要的理论指导．     

Inertial Particles in Homogeneous Shear Turbulence: Experiments and Direct Numerical Simulation

The properties of the transport of heavy inertial particles in a uniformly sheared turbulent flow have been investigated by combining experimental and numerical data at particle Stokes number St?≈?0.3?÷?0.5 respectively. As in isotropic turbulence, particles are observed to avoid zones of intense enstrophy and to cluster in strain-dominated regions, resulting in highly intermittent spatial distributions. Moreover, the anisotropy of the mean flow is found to imprint a clear preferential orientation of the particle clusters in the direction of the maximum mean strain. These features are observed both in the numerics and in the experiments, and have been consistently quantified by a number of complementary statistical tools, such as the Voronoï tessellations and the pair correlation function. The latter quantity has been generalized in the form of the Angular Distribution Function and has allowed to evaluate the anisotropy content of the particle field at each scale. The behavior of this observable exhibits the same trend in the two datasets and suggests that, owing to increased inertia, the particle distribution starts to recover isotropy at scales smaller than the carrier velocity field. A proper rescaling of the two datasets in terms of their respective values of the shear scale allows to account for differences in the Reynolds number of experiments and numerics in the range of scales dominated by the mean shear.     

Influence of obstacle aspect ratio on tripped cylinder wakes

The influence of an asymmetrically mounted, single tripwire on the shedding and wake characteristics of a vertical, surface-mounted finite circular cylinder is investigated experimentally. Height-to-diameter aspect ratios of 3 and 6 are considered. It is shown that a critical position for the tripwire exists, which is characterised in an abrupt change in the shedding frequency and wake structure. Results further suggest that the tripwire can strengthen 2D wake properties. The influence of the aspect ratio is due to tip-wake flow interactions and thus differs fundamentally from two-dimensional geometries.     

Cold flow experiments in an entrained flow gasification reactor with a swirl-stabilized pulverized biofuel burner

Short particle residence time in entrained flow gasifiers demands the use of pulverized fuel particles to promote mass and heat transfer, resulting high fuel conversion rate. The pulverized biomass particles have a wide range of aspect ratios which can exhibit different dispersion behavior than that of spherical particles in hot product gas flows. This results in spatial and temporal variations in temperature distribution, the composition and the concentration of syngas and soot yield. One way to control the particle dispersion is to impart a swirling motion to the carrier gas phase. This paper investigates the dispersion behavior of biomass fuel particles in swirling flows. A two-phase particle image velocimetry technique was applied to simultaneously measure particle and gas phase velocities in turbulent isothermal flows. Post-processed PIV images showed that a poly-dispersed behavior of biomass particles with a range of particle size of 112–160 µm imposed a significant impact on the air flow pattern, causing air flow decelerated in a region of high particle concentration. Moreover, the velocity field, obtained from individually tracked biomass particles showed that the swirling motion of the carrier air flow gives arise a rapid spreading of the particles.