Stress transmission in systems of faceted particles in a silo: the roles of filling rate and particle aspect ratio

We present experimental and numerical results for particle alignment and stress distribution in packings of faceted particles deposited in a small-scale bi-dimensional silo. First, we experimentally characterize the deposits’ morphology in terms of the particles’ aspect ratio and feeding rate. Then we use the experimental results to validate our discrete element method (DEM) based on spheropolygons. After achieving excellent agreement, we use contact forces and fabric provided by the simulations to calculate the coarse-grained stress tensor. For low feeding rates, square particles display a strong tendency to align downwards, i.e., with a diagonal parallel to gravity. This morphology leads to stress transmission towards the walls, implying a quick development of pressure saturation, in agreement with the Janssen effect. When the feed rate is increased, both the disorder and the number of horizontal squares in the silo increase, hindering the Janssen effect. Conversely, for elongated particles the feed rate has a weak effect on the final deposit properties. Indeed, we always observe highly ordered structures of horizontal rods where the stress is transmitted mainly in the vertical direction.     

CFD-DEM numerical study on air impacted packing densification of equiaxed cylindrical particles

A CFD-DEM model was developed to reproduce the packing densification process of mono-sized equiaxed cylindrical particles under air impact. The effects of operating parameters on packing density were firstly studied. Then various microscopic properties of packing structures such as coordination number (CN), contact types, particle orientations, pore features were characterized and compared. And corresponding densification mechanisms were analysed based on particle motion behaviour, local structure evolution, and forces. Results indicate that the air impact can realize the packing densification of cylindrical particles under appropriate conditions. The pore size distribution in the packing of cylindrical particles shows a tail at larger pore sizes compared with that in the packing of equal spheres. Both the size and the sphericity of the pores decrease in the final dense packing; also, more surface-surface and less surface-edge contacts between two particles therein can be formed. More cylindrical particles tend to be in parallel or perpendicular contact with each other to form more stable local structures during air impact. Most particles at higher position move down (direction of gravity/air impact) with about one particle length during the densification process and most particles exhibit translational motion to realize the local rearrangement for pore filling through air impact induced inter-particle forces.     

Domain and network aggregation of CdTe quantum rods within Langmuir-Blodgett monolayers

Control over the organization of quantum rods was demonstrated by changing the surface area at the air-liquid interface by means of the Langmuir-Blodgett (LB) technique. The LB isotherm of CdTe quantum rods capped with a mixture of alkylphosphines shows a transition point in the liquid-solid state, which is caused by the inter-rod reorganization. As we observed, at low surface pressure the quantum rods are assembled into round-shaped aggregates composed of a monolayer of nanorods packed in limited-size clusters with random orientation. The increase of the surface pressure leads to the rearrangement of these aggregates into elongated bundles composed of uniformly oriented nanorod clusters. Further compression results in denser packing of nanorods aggregates and in the transformation of monolayered domains into a continuous network of locally ordered quantum rods.     

Packing of fine particles in an electrical field

A numerical model based on the Discrete Element Method (DEM) is developed to study the packing of fine particles in an electrical field related to the dust collection in an electrostatic precipitator (ESP). The particles are deposited to form a dust cake mainly under the electrical and van der Waals forces. It is shown that for the packing formed by mono-sized charged particles, increasing either particle size or applied electrical field strength increases packing density until reaching a limit corresponding to the density of random loose packing obtained under gravity. The corresponding structural changes are analyzed in terms of coordination number, radial distribution function and other topological and metric properties generated from the Voronoi tessellation. It is shown that these properties are similar to those for the packing under gravity. Such structural similarities result from the similar changes in the competition of the cohesive forces and the driving force in the packing. In particular, it is shown that by replacing the gravity with the electrical field force, the previous correlation between packing density and the ratio of the cohesive force to the packing-driven force can be applied to the packing of fine particles in ESP.     

Untersuchungen zu Zusammenhängen zwischen Schichtmorphologie und Herstellungsbedingungen an amorphen Siliziumnitridschichten

Electron microscopic investigations of magnetron sputtered amorphous SiN_x-coatings showed, that morphology changes with variation of working gas pressure and substrate position corresponding to the Structure Zone Model by Thornton. Increasing working gas pressure and displacement of substrate to larger radial distances influence columnar structures. Energy of particles and adatom mobility decrease with increasing pressure. In positions far from the centre of deposition there are more particles with oblique incidence. This leads to a shadowing mechanism. Columnar diameter increases and packing density decreases. The influence of working gas pressure and angle of incidence bears also an effect on the behaviour of mechanical stress. Coatings with coarse columnar structures have lower mechanical stress than coatings with fine columnar structures.     

Numerical direct shear tests for outwash deposits with random structure and composition

Outwash deposits is a kind of special geological material composed of soil and stone particles. Since the shear behaviors of outwash deposits are mainly dominated by its complicated structure and composition the strength parameters of which are difficult to be determined accurately. In this work, samples of outwash deposits with random structure and composition taking account of the effects of sizes, shapes and distributions of stone blocks were simulated based on the granular discrete element method. The meso-scale parameters of soil and stone particles were first calibrated by comparing numerical predictions with experimental data. Then a series of numerical direct shear tests for the simulated samples were conducted. Results show that the effects of strain hardening of shear stress–displacement curves become increasingly apparent with the increase of stone content. The shear strength of outwash deposits is dominated by the content as well as by the random distribution of stone blocks. There is an approximate linear relationship between the mean value of shear strength and the stone content lying between 30 and 60  \(\%\) , while a larger fluctuation in shear strength mainly due to the random distribution of stone blocks. Compared with the mean value of shear strength, the maximum fluctuation of internal friction angle reaches up to 4.26 \(^{\circ }\) while the maximum fluctuation of cohesion approximates up to 1/3 of its mean value. Results also indicate that the improvement of cementation degree between soil particles increases mainly the macro cohesion of outwash deposits but has almost no influence on the macro internal friction angle. And because of a relative higher strength of stone blocks, the shear yield bands of outwash deposits detours significantly around stone blocks and shows numerous local cracks, which frequently accompanies an acute release of strain energy owing to the geometric redistribution of stone blocks. The integration of laboratory investigations and numerical direct shear tests can be an effective approach to determine the statistical mechanic’s parameters of outwash deposits.     

Influence of particle shape on sheared dense granular media

We study by means of molecular dynamics simulations of periodic shear cells, the influence of particle shape on the global mechanical behavior of dense granular media. At large shear deformation samples with elongated particles, independent of their initial orientation, reach the same stationary value for both shear force and void ratio. At the micro-mechanical level the stress, the fabric and the inertia tensors of the particles are used to study the evolution of the media. In the case of isotropic particles the direction of the principal axis of the fabric tensor is aligned with the one of the principal stress, while for elongated particles the fabric orientation is strongly dependent on the orientation of the particles. The shear band width is shown to depend on the particle shape due to the tendency of elongated particles to preferential orientations and less rotation.     

On contact numbers in random rod packings

Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well with experiments on granular packings. Contact numbers are also compared to caging numbers calculated for sphero-cylinders with arbitrary aspect-ratio. The caging number for rods arrested by uncorrelated point contacts asymptotes towards at high aspect ratio, strikingly close to the experimental contact number for thin rods. These and other findings confirm that thin-rod packings are dominated by local arrest in the form of truly random neighbor cages. The ideal packing law derived for random rod–rod contacts, supplemented with a calculation for the average contact number, explains both absolute value and aspect-ratio dependence of the packing density of randomly oriented thin rods.     

DEM investigations of two-dimensional granular vortex- and anti-vortex-structures during plane strain compression

The paper presents simulation results of a quasi-static plane strain compression test on cohesionless initially dense sand under constant lateral pressure using a three-dimensional discrete element method. Grains were modelled by means of spheres with contact moments imitating irregular particle shapes. The material behaviour was studied at both global and local levels. The stress–strain and volumetric-strain curves, distribution of void ratio, resultant grain rotation and contact forces were calculated. The main attention was paid to the appearance of plane strain granular micro-structures like vortex and anti-vortex structures in the granular specimen during deformation. In order to detect two-dimensional vortex and anti-vortex structures, a method based on orientation angles of displacement fluctuation vectors of neighbouring single spheres was used. The effect of the method parameters was also analyzed.     

A discrete element analysis of elastic properties of granular materials

The elastic properties of a regular packing of spheres with different tolerances were evaluated using the discrete element method to elucidate the mechanisms behind the discrepancies between laboratory experiments and theoretical predictions of the classic Hertz-Mindlin contact law. The simulations indicate that the elastic modulus of the packing is highly dependent on the coordination number and the magnitude and distribution of contact normal forces, and this dependence is macroscopically reflected as the influence of confining pressure and void ratio. The increase of coordination number and the uniformity of contact normal forces distribution with increasing confining pressure results in the stress exponent $n$ for elastic modulus being higher than 1/3 as predicted by the Hertz-Mindlin law. Furthermore, the simulations show that Poisson’s ratio of a granular packing is not a constant as commonly assumed, but rather it decreases as confining pressure increases. The variation of Poisson’s ratio appears to be a consequence of the increase of the coordination number rather than the increase of contact normal forces with confining pressure.     

Granular packing: numerical simulation and the characterisation of the effect of particle shape

The packing of granular particles is investigated using a combined finite-discrete element approach. One of the aims of this paper is to present an application of a recently improved numerical simulation technique for deformable granular material with arbitrary shapes. Our study is focused on the influence of the effect of the particle shape on (1) the emergent properties of a granular pack (packing density, coordination number, force distribution), and on (2) the spatial distribution of the stress. A set of simulations that mimick the sedimentation process is carried out, with varying input parameters, such as contact friction and particle shape. It is shown that the eccentricity of the particles not only significantly influences the final density of the pack but also the distribution of the stress and the contact forces. The presence of surface friction increases the amount of disorder within the granular system. Stress heterogeneities and force chain patterns propagate through the particles more efficiently than for the frictionless systems. The results also suggest that for the monodisperse systems investigated the coordination number is one of the factors that controls the distribution of the stress within a granular medium.     

注射成型聚苯乙烯的取向和残余应力

设计带压力传感器和热电偶的矩形模具,进行聚苯乙烯不同工艺条件注射成型实验,通过测试双折射３个热直方向的分量,分析工艺条件对制品性能的影响。最后讨论注射成型制品中的取向分布和残余应力。     

Examining the mechanisms of sand creep using DEM simulations

In this study, DEM simulations of triaxial creep tests on dense and loose sand samples were carried out to examine the micromechanics involved during creep. The simulated creep responses reproduce qualitatively the published experimental results. During the primary creep, the creep stress is gradually borne by the contact normal forces instead of contact tangential forces so that the columnar particle structures can be formed. This process also leads to a continuous decrease in the creep rate. The columnar structures eventually are completely formed and the creep rate reaches a minimum. However, the structures become meta-stable and susceptible to buckling. This explains why a sand packing does not show an extended period of secondary creep in the experiment. Buckling of the columnar structures also gives rise to maximum dilatancy and a sharp transition of the major fabric orientation of weak forces from horizontal to vertical. The continuous buckling process of columnar structures increases the creep rate and sliding ratios of contacts during the tertiary creep. In addition, the trend of contact tangential forces decreasing and contact normal forces increasing is reversed. Finally creep rupture occurs as the creep stress–strain line intersects the complete stress–strain curve. All the creep samples follow their original volume-change tendency to continue their dilation or contraction response during creep.     

Powder assembly simulation by particle dynamics method

The aim of the present study is to show that the developed particle dynamics method is able to describe important characteristics of powder assemblies. In the method, the interaction forces that are introduced between the particles are electrostatic attractive forces and elastic repulsive forces. Energy dissipation by friction at contact surfaces and damping during cohesive collision were also considered. Several numerical experiments on the angle of repose, packing and compaction are carried out. The initial position and the size of the particles are randomly distributed based on the Monte-Carlo method. The simulation results show that the method can be used to evaluate the effect of particle characteristics on flowability of powder assemblies.     

利用强磁场控制过共晶铝硅合金的凝固组织

研究了静磁场和梯度磁场的强度和方向对Al-15.7%Si合金宏观和微观凝固组织的影响.结果表明,在不同的磁场条件下,从过共晶合金中析出的初晶硅粒的分布状况和共晶硅的形态和密度有显著不同.通过改变磁感应强度和磁场梯度的大小和方向可有效控制初晶硅的分布;合理控制强磁场的操作参数可达到细化铝硅共晶体的目的.强磁场的磁化力和洛伦兹力通过控制初晶硅颗粒迁移行为来改变其在合金基体中的分布状态,通过影响凝固过程中的对流现象改变合金的凝固组织.     

Properties of force networks in jammed granular media

Discrete element method simulations are conducted to investigate the effects of applied uniaxial compressive load, and bidisperse particle size distributions on force networks within jammed granular media. The differences between the strong and weak networks are examined through investigating the spatial correlation and distribution of contact angles, and emergence of chainlike structures. The simulation results show that the chainlike structures are more prevalent in the strong network due to the larger cumulative probabilities of contact angles, but not all the contacts belonging to the strong or weak networks are able to constitute the chainlike structures. Although the contacts of coarse-fine particles are dominant for the bidisperse systems, the contacts of coarse–coarse particles dominate the strong network, as well as the linear chainlike structures. Upon increasing the pressure from very low to high, the probability of contact orientations with respect to the compression direction in the strong network increases for contact orientation less than \(60^{\circ }\) and decreases for contact orientation greater than \(60^{\circ }\), while the opposite trends are observed in the weak network. The tails of normalized normal contact forces distributions are quantified by \(\hbox {P}(\hbox {f}) = \hbox {exp}(-\hbox {cf}^{\mathrm{n}})\), and it is found that the value of n depends on the applied pressure and particle size distribution. Statistical analysis shows that the degree of homogeneity of contact force increases with increasing pressure, which is also validated by participation number.     

Studying nanostructure gradients in injection-molded polypropylene/montmorillonite composites by microbeam small-angle x-ray scattering

The core–shell structure in oriented cylindrical rods of polypropylene (PP) and nanoclay composites (NCs) from PP and montmorillonite (MMT) is studied by microbeam small-angle x-ray scattering (SAXS). The structure of neat PP is almost homogeneous across the rod showing regular semicrystalline stacks. In the NCs the discrete SAXS of arranged crystalline PP domains is limited to a skin zone of 300 μm thickness. Even there only frozen-in primary lamellae are detected. The core of the NCs is dominated by diffuse scattering from crystalline domains placed at random. The SAXS of the MMT flakes exhibits a complex skin–core gradient. Both the direction of the symmetry axis and the apparent perfection of flake-orientation are varying. Thus there is no local fiber symmetry, and the structure gradient cannot be reconstructed from a scan across the full rod. To overcome the problem the rods are machined. Scans across the residual webs are performed. For the first time webs have been carved out in two principal directions. Comparison of the corresponding two sets of SAXS patterns demonstrates the complexity of the MMT orientation. Close to the surface (< 1 mm) the flakes cling to the wall. The variation of the orientation distribution widths indicates the presence of both MMT flakes and grains. The grains have not been oriented in the flowing melt. An empirical equation is presented which describes the variation from skin to core of one component of the inclination angle of flake-shaped phyllosilicate filler particles.     

双曲壳结构非均匀风压作用局部稳定验算

风荷载条件大型双曲旋转壳体结构局部稳定性为结构设计关键控制因素。为考虑双曲旋转壳体结构在风载荷作用下的局部稳定性问题,现行国内外水工规范多采用20世纪70年代提出的基于环向均匀荷载加载试验方案的Mungan局部稳定验算公式（亦称为Buckling Stress State（BSS）方法）。首先,以Mungan提出的静水压力试验为基础,基于结构有限元分析算法,构建了早期壳体物理试验模型的有限元模型,分析了双曲旋转壳体在环向均布平均风压作用下的稳定性与试验结果的差异,验证了早期试验在特定条件下的正确性。为进一步评价该算法应用于以超大型冷却塔为代表的壳体结构设计的适用性和合理性,计算了水工规范（GB/T 50102-2003）中21种线型的双曲旋转壳体在环向非均布风压作用下的极限荷载,探讨了Mungan局部稳定验算公式有待改进的方向,提出了适用于非均布荷载作用下环向应力临界荷载计算公式,拟合得到改进的局部稳定验算公式。研究表明:水工规范建议的双曲旋转壳体结构局部稳定验算公式难于描述壳体实际情况下的非均布风压变化受力特征,推荐适用于非均匀风压分布变化的更新局部稳定验算公式,可以兼顾结构设计过程的便捷性与合理性。     

Measurements of normal stress distributions experienced by rigid liquid composite moulding tools

Mould tools used for LCM processes such as Resin Transfer Moulding (RTM) and Injection/Compression Moulding (I/CM) must withstand local forces due to compaction of the fibre reinforcement, and due to resin pressure generated within the laminate. A series of RTM and I/CM experiments have been carried out, with the focus placed on measurement of normal stress distributions exerted on the mould surface. In addition, total mould clamping force and injection gate pressure histories have been recorded. I/CM experiments using force-controlled secondary compaction were also undertaken, and compared to the velocity-controlled cases. Observed fluid pressure fields showed good agreement with theory, namely a logarithmic distribution during fluid injection and a quadratic distribution during the compression driven filling phase of I/CM. Significant spatial variation in normal stress due to reinforcement compaction was observed. The influence of the fluid pressure on the total stress experienced by the mould was observed to be a function of both the fibre volume fraction of the part and the applied injection pressure, the latter being more pronounced at lower part volume fractions.     

Effect of particle size ratio and contribution of particle size fractions on micromechanics of uniaxially compressed binary sphere mixtures

This paper is an extension of the recent work of Wi?cek (Granul Matter 18:42, 2016), wherein geometrical parameters of binary granular mixtures with various particle size ratio and contribution of the particle size fractions were investigated. In this study, a micromechanics of binary mixtures with various ratio of the diameter of small and large spheres and contribution of small particles was analyzed using discrete element simulations of confined uniaxial compression. The study addressed contact normal orientation distributions, global and partial contact force distributions and pressure distribution in packings of frictional spheres. Additionally, the effect of particle size ratio and contribution of particle size fractions on energy dissipation in granular mixtures was investigated. The particle size ratio in binary packings was chosen to prevent small particles from percolating through bedding. The bimodality of mixtures was found to have a strong effect on distribution of contact normal orientation and distribution of normal contact forces in binary mixtures. Stress transfer in binary packing was also determined by both, particle size ratio and volume fraction of small particles. Dissipation of energy was higher in mixtures with higher particle size ratios and decreased with increasing contribution of small spheres in system.