DEM investigation of particle anti-rotation effects on the micromechanical response of granular materials

The importance of particle rotation to the mechanical behavior of granular materials subject to quasi-static shearing has been well recognized in the literature. Although the physical source of the resistance to particle rotation is known to lie in the particle surface topography, it has been conveniently studied using the rolling resistance model installed typically on spherical particles within the DEM community. However, there has been little effort on assessing the capability of the rolling resistance model to produce more realistic particle rotation behavior as exhibited by irregular-shaped particles. This paper aims to eliminate this deficiency by making a comprehensive comparison study on the micromechanical behavior of assemblies of irregular-shaped particles and spherical particles installed with the rolling resistance model. A variety of DEM analysis techniques have been applied to elucidate the full picture of micromechanical processes occurring in the two types of granular materials with different particle-level anti-rotation mechanisms. Simulation results show that the conventional rheology-type rolling resistance models cannot reproduce the particle rotation and strain localization behavior as displayed by irregular-shaped materials, although they demonstrate clear effects on the macroscopic strength and dilatancy behavior, as have been adequately documented in the literature. More insights into the effects of particle-level anti-rotation mechanism are gained from an in-depth inter-particle energy dissipation analysis.     

Micromechanical modelling of oval particulates subjected to bi-axial compression

One of the questions that still remain unanswered among researchers dealing with granular materials is how far the particle shape affects the micro-macroscopic features of granular assemblies under mechanical loading. The latest advances made with particle instrumentation allow us to capture realistic particle shapes and size distribution of powders to a fair degree of accuracy at different length scales. Industrial applications often require information on the micromechanical behaviour of granular assemblies having different particle shapes and varying surface characteristics, which still remains largely unanswered. Traditionally, simulations based on discrete element method (DEM) idealise the shape of individual particles as either circular or spherical. In the present investigation, we analyse the influence of particle shape on the shear deformation characteristics of two dimensional granular assemblies using DEM. We prepared the assemblies having nearly an identical initial packing fraction (dense), but with different basic shapes of the individual particles: (a) oval and (b) circular for comparison purposes. The granular assemblies were subjected to bi-axial compression test. We present the evolution of macroscopic strength parameters and microscopic structural/topological parameters during mechanical loading. We show that the micromechanical properties of granular systems are significantly influenced by the shape of the individual particles constituting the granular assemblies.     

Theoretical and experimental study of multi-compression particle breakage

By modifying Griffith's theory, a theoretical fatigue model was built to explain how the fatigue strength of a single particle changes under repeated compressions. The predictions of the model were validated by experimental results for two kinds of crystal particles: NaCl and MgO. We also performed experiments on granular particles whose properties were unknown. Here too the fatigue trends were similar to that of the model. The results show that as the compression stresses acting on the particles and the number of compressions increase, the fatigue compression strength decreases. In addition, fatigue trends we observed for the various particles demonstrate dependence on the material's properties.     

玻璃球宏细观冲击特性的SHPB试验和耦合数值模拟研究

为研究玻璃球的宏细观冲击特性,该文开展了不同相对密实度玻璃球的一维霍普金森杆(SHPB)冲击试验和离散元-有限差分法耦合数值模拟研究。结果表明：一维冲击荷载下玻璃球经历初始弹性、屈服、颗粒间互锁硬化和颗粒破碎硬化四个阶段。基于耦合数值模拟发现,颗粒平均配位数随着冲击荷载时程不断增加,但增加的速率逐渐下降,其原因是配位数变化取决于孔隙压缩和以旋转为主的颗粒重排,随着试样压缩变形的发展,孔隙压缩和颗粒重排需要克服更大的颗粒间互锁效应,因此逐渐变缓。而试样孔隙率在弹性阶段基本不变,在屈服阶段和互锁硬化阶段近似线性下降,其原因是孔隙率变化受控于颗粒整体移动,弹性阶段颗粒整体移动尚未发展,屈服之后颗粒整体移动产生的孔隙压缩随荷载时程呈线性发展。冲击荷载下,颗粒位移以整体移动为主,相对位移为辅,因此,颗粒位移对试样的初始密实度不敏感。颗粒旋转需要克服周围颗粒的互锁效应,互锁效应取决于试样级配和颗粒粒径,对密实度较敏感。     

Segregation behavior of particles with Gaussian distributions in the rotating drum with rolling regime

The mixing and segregation of granular materials are essential to provide valuable insights and references for practical industrial production. In this paper, the segregation behaviors of particles with Gaussian distributions and 40% filling level in the rotating drum with rolling regime were numerically studied by the discrete element method. The effects of rotation speed and particle size parameter λ (size ratio of the largest versus smallest particles) on the segregation behavior (mixing index, segregation rate), flow characteristics (particle velocity and trajectory, gyration degree and radius, particle size distributions) and the microscopic properties (collision, contact force, axial diffusion, and kinetic energy) of granular systems were systematically investigated. The results show that the segregation rate and degree of particles with Gaussian distributions gradually increase with the increase of the rotation speed and particle size parameter λ. The radial and axial segregation patterns become more obvious with the increase of λ. And the variation of the flow characteristics of particles with different sizes in the same system is also inconsistent. The microscopic properties of Gaussian-dispersed particles change with the rotation speed and λ. The rapid radial segregation depends on the larger pores existed in the granular system, which leads to a gradual increase of the axial dispersion coefficient of large particles and a gradual decrease of the axial dispersion coefficient of small particles.     

Freestanding loadbearing structures with Z-shaped particles

Architectural structures such as masonry walls or columns exhibit a slender verticality, in contrast to the squat, sloped forms obtained with typical unconfined granular materials. Here we demonstrate the ability to create freestanding, weight-bearing, similarly slender and vertical structures by the simple pouring of suitably shaped dry particles into a mold that is subsequently removed. Combining experiments and simulations we explore a family of particle types that can entangle through their non-convex, hooked shape. We show that Z-shaped particles produce granular aggregates which can either be fluid and pourable, or solid and rigid enough to maintain vertical interfaces and build freestanding columns of large aspect ratio (\(>\)10) that support compressive loads without external confinement. We investigate the stability of such columns with uniaxial compression, bending, and vibration tests and compare with other particle types including U-shaped particles and rods. We find a pronounced anisotropy in the internal stress propagation together with strong strain-stiffening, which stabilizes rather than destabilizes the structures under load.     

Formulation and numerical implementation of micro-scale boundary conditions for particle aggregates

Novel numerical algorithms are presented for the implementation of micro-scale boundary conditions of particle aggregates modelled with the discrete element method. The algorithms are based on a servo-control methodology, using a feedback principle comparable to that of algorithms commonly applied within control theory of dynamic systems. The boundary conditions are defined in accordance with the large deformation theory, and are imposed on a frame of boundary particles surrounding the interior granular micro-structure. Following the formulation presented in Miehe et al. (Int J Numer Methods Eng 83(8–9): 1206–1236, 2010), first three types of classical boundary conditions are considered, in accordance with (1) a homogeneous deformation and zero particle rotation (D), (2) a periodic particle displacement and rotation (P), and (3) a uniform particle force and free particle rotation (T). The algorithms can be straightforwardly combined with commercially available discrete element codes, thereby enabling the determination of the solution of boundary-value problems at the micro-scale only, or at multiple scales via a micro-to-macro coupling with a finite element model. The performance of the algorithms is tested by means of discrete element method simulations on regular monodisperse packings and irregular polydisperse packings composed of frictional particles, which were subjected to various loading paths. The simulations provide responses with the typical stiff and soft bounds for the (D) and (T) boundary conditions, respectively, and illustrate for the (P) boundary condition a relatively fast convergence of the apparent macroscopic properties under an increasing packing size. Finally, a homogenization framework is derived for the implementation of mixed (D)–(P)–(T) boundary conditions that satisfy the Hill–Mandel micro-heterogeneity condition on energy consistency at the micro- and macro-scales of the granular system. The numerical algorithm for the mixed boundary conditions is developed and tested for the case of an infinite layer subjected to a vertical compressive stress and a horizontal shear deformation, whereby the response computed for a layer of cohesive particles is compared against that for a layer of frictional particles.     

A packing algorithm for three-dimensional convex particles

Simulation of granular particles is an important tool in many fields. However, simulation of particles of complex shapes remains largely out of reach even in two-dimension. One of the major hurdles is the difficulty in representing particles in an efficient, flexible, and accurate manner. By representing particles as convex polyhedrons which are themselves the intersection of a set of half spaces, we develop a method that allows one to efficiently carry out key operations, including particle–particle and particle–container wall overlapping detection, precise identification of the overlapping region, particle shifting, particle rotation, and others. The simulation of packing 1,000 particles into a container takes only a few minutes with this approach. We further demonstrate the potential of this approach with a simulation that re-generates the “Brazil nut” phenomenon by mixing and shaking particles of two different sizes.     

DEM simulation on the one-dimensional compression behavior of various shaped crushable granular materials

In order to investigate the effects of particle shape on the compression behavior of granular materials, a series of simulations was conducted using a two-dimensional discrete element method employing moment springs. Fracturable granular assemblies were constructed from particles of the same shape and size. The range of possible particle shapes includes disk, ellipse and hexagon, with different aspect ratios. Simulations of single particle crushing tests on elliptical particles showed that crushing could be classified into three types: cleavage destruction, bending fracture and edge abrasion, depending on the manner of compression. A series of simulations of one-dimensional compression tests was then conducted on six types of crushable particle assemblies; the three types of crushing mentioned above were also observed, but their rates of occurrence depended on the particle shape. Cleavage destruction was mainly observed with circular and elliptical particles; bending fracture was observed only with elongated particles; edge abrasion was frequently observed with angular particles. Despite the difference in crushing type, all samples, when subjected to intense compression, converged to a critical grading with unique void ratio, grain size distribution and aspect ratio, with a similar distribution of number of contact points.     

Granular segregation studies for the development of a radar-based three-dimensional sensing system

The behavior of dense granular materials is difficult to measure in three-dimensions due to the opacity of the materials. We present a new radar-based sensing system that has the capability of measuring three-dimensional particle movement throughout the bulk of high solids fraction granular systems. A key component of the new system involves retroreflectors imbedded in objects resembling the particles in the bulk granular systems. These embedded retroreflectors may be used as tracers in systems comprised of relatively large particles. However, in systems of smaller particles the most versatile use of this new sensing system requires an understanding of the details of relative particle movement based on particle size and other particle properties. Towards this, we present new ongoing experimental and computational results toward building a versatile sensing system for high solids fraction granular systems. We then comment on additional research needed on the behavior of the components in granular mixtures for a fully versatile sensing system.     

基于离散元方法的RDX-Al颗粒混合数值模拟分析

基于离散元方法,以旋转筒内RDX-Al二元颗粒体系的搅拌过程为研究对象进行模拟。采用离散元软件(EDEM),首先研究RDX-Al二元颗粒各自随转速的变化趋势,并进一步得出二元颗粒变化率的特点,做出分布上的拟合,得出最吻合模拟试验的函数为指数函数。然后,将旋转筒细分为多个单元空间,考察旋转轴与单元空间之间的距离对二元颗粒混合效果的影响。结果表明:单元空间离旋转轴越远,即旋转半径越大,颗粒之间的变化率也就越快,越容易达到均匀状态。最后,考察加入抄板的影响,结果表明:RDX-Al二元颗粒趋于的稳定值分别发生了改变。     

Particle modeling of dynamic fragmentation—II: Fracture in single- and multi-phase materials

The second paper of this series adopts particle modeling (PM) to simulation of dynamic fracture phenomena in homogeneous and heterogeneous materials, such as encountered in comminution and blasting processes in mining industry. As the basis for such simulations, we first develop a new method to prevent particles from topologically interpenetrating themselves within the material domain, when actual fracture does not actually take place. We then move to a number of application studies: (i) fragmentation of 2-D single- and multi-phase materials—including a simulation of a drop-weight test—and (ii) fragmentation of 3-D single-phase materials under either very rapid extension or compression. These investigations show patterns and trends of fragmentation of materials in function of their constitutive properties, their geometric shapes, and the loading conditions.     

Segregation pattern of binary-size mixtures in a double-walled rotating drum

Size-induced granular segregation was performed systematically and experimentally in an almost fully filled double-walled rotating drum at 10 different rotation speeds and two different side wall types. The motion of the granular materials was recorded using a high-speed camera for image analysis of particle segregation development in the drum. With continual tracking of the particle movements, the velocity, fluctuations, and granular temperatures were measured. The experimental results indicate that both rotation speeds and friction coefficient of side walls significantly affect segregation phenomena in binary-size mixture granular flows. The results demonstrate similar situations to the Brazil-nut effect and its reverse in the radial direction at either high or a low rotational speed (where the Froude number (Fr) is far from 1). At these instances, the maximum granular temperature occurs near the side walls. Specifically, a double segregation effect (DSE) is found at Froude number (Fr) close to 1. These results can be used in many industrial processes, for example, size grading of materials, screening of impurities, and different structures of functionally graded materials. Moreover, the maximum granular temperature occurs in the middle of the ring space. It causes small particles to move toward both side walls as it pushes bigger particles to accumulate in the middle of the ring space of rotating drum.     

Numerical analysis of restitution coefficient,rotational speed and particle size effects on the hydrodynamics of particles in a rotating drum

Hydrodynamic behavior of two dimensional horizontal rotating drum was studied by using finite volume method and granular kinetic theory. In this work, the effects of the different parameters such as rotation speed, restitution coefficient and particle size on the hydrodynamic and especially on the granular temperature of particles were investigated. At first, the results of present work were verified with previous experimental results. Packing limit of 0.6 and restitution coefficient of 0.95 with Gidaspow inter-phase momentum coefficient showed the good agreement with experimental works. It is found that by increasing the restitution coefficient, the granular temperature at different depth of bed increased and affected the hydrodynamic behavior of the bed. Also, particle size and rotation speed directly changed the granular temperature. Moreover, augmentation of the rotation speed leads to increasing the repose angle which caused better mixing of bed, granular temperature rising and consequently particle velocity alteration in the bed.     

The role of rolling friction in granular packing

In order to study the effects of the rolling friction of the particles on granular packing, we present a detailed analysis of circular disk assemblies with the rolling friction under macroscopic one-dimensional compression. The rolling friction of the particles produces a resisting moment to the rolling at each contact. A series of 2-D DEM simulations are performed with various values for the rolling friction parameter. We focus on several macroscopic and microstructural properties of granular media and analyze them as a functions of the rolling friction. From these results, we show that the rolling resistance, which results from the rolling friction of the particles, contributes to the inhibition of the rearrangement of the particles and increases the magnitude of the fabric anisotropy under packing. In addition, from both microscopic and macroscopic points of view, we describe that the stress state in a granular packing can vary considerably depending on the rolling resistance.     

DEM investigations of failure mode of sands under oedometric loading

It will be practically useful to explore the evolutions of the failure modes of sand grains within a sand specimen subject to compression for the particle breakage research. This paper attempts to deal with this challenge by conducting a discrete element method (DEM) simulation study on oedometric compression of two kinds of sands (spherical and non-spherical particles). In this study, particle morphologies reconstructed by the spherical harmonic (SH) analysis were created using the agglomerate method, and the micro-parameters used to define the contact model and the properties of walls and balls were adopted based on the single particle crushing tests. The effects of particle shape on the crushing behavior of granular materials and on the evolutions of failure modes of sand grains were captured, and the experimental data was used to evaluate the feasibility and reliability of the proposed DEM modelling strategy. The simulation results show that particle shape affects not only the number, type and orientation of cracks but also the evolution of the particle failure modes. The failure mode of chipping is the most common way to crush for both spherical and non-spherical particles. The particles that have less aspect ratio, sphericity and convexity are more likely to experience the failure mode of comminution. These findings shed light on the key role of particle shape in the investigation of the failure mode of sand grains and facilitate a better understanding of grain-scale behavior of granular materials.     

Wavelet analysis of DEM simulations of samples under biaxial compression

The results of a wavelet analysis of data from discrete element modelling (DEM) simulations of samples under biaxial compression are presented. We show how a wavelet technique may be used to find the strain scales on which critical events occur and to identify regions both in space and in strain when particles in the sample undergo significant activity. The wavelet analysis indicates that most activity occurs along a line, and this line coincides with a localization or shear band that develops in the specimen during compression. The location of this shear band can be visually identified by considering the cumulative particle rotation. Furthermore, using cross-correlation we show that the principal stress ratio is correlated with the porosity of the sample along this line. In order to investigate the robustness of the technique, the wavelet analysis is carried out on two different size specimens that both show the same general phenomena.     

Discrete element modeling of granular hopper flow of irregular-shaped deformable particles

Many natural and engineered granular materials have relatively deformable particles. Besides particle size and shape, particle deformability is another salient factor that significantly impacts the material’s flow behavior. In this work, the flow of irregular-shaped deformable particles in a wedge-shaped hopper is investigated using discrete element simulations. A bonded-sphere model is developed to simultaneously capture irregular particle shapes and particle-wise deformations (e.g., compression, deflection, and distortion). Quantitative analysis of the effects of irregular shapes and particle deformations shows that the increase in particle stiffness tends to increase initial packing porosity and decrease the flow rate in the hopper. Rigid particles tend to have clogging issues, whereas deformable particles have less chance to, indicating particle deformation reduces the critical bridging width in the hopper flow. Detailed analysis of stress fields is also conducted to provide insights into the mechanism of particle flow and clogging. Stresses and discharge rates calculated from numerical simulations are compared and show good agreement with Walker’s theory and the extended Beverloo formula. Simulations with various particle shape combinations are also performed and show that the initial packing porosity decreases with an increasing percentage of fibers while the discharge rate has a complex dependency on particle shapes.     

Effects of particle shapes to achieve angle of repose and force displacement behaviour on granular assembly

Circular or spherical particles in Discrete Element Method (DEM) possess limitations on achieving desired angle of repose for some granular assemblies. However, by using various shapes/clumps of particles, the limitation posed by the circular or spherical particles on achieving angle of repose can be minimized. In this paper, 2D DEM simulation has been used to investigate the effect of particle shapes on (a) angle of repose, where the aim is to achieve the angle of repose of 35° observed in a laboratory scale sand pile experiment, and (b) force displacement behaviour of granular assembly. The simulated results show that the particle shapes have strong influence on the angle of repose but have a less effect on force displacement behaviour on the granular assembly.