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.     

Effects of Material Properties on Granular Flow in a Silo Using DEM Simulation

In order to test the effect of material properties on flowability of particulate materials, discharge procedures of spherical particles within a flat-bottomed model silo with three sets of material properties, i.e., soft and hard without adhesion and adhesive hard, were simulated using the Discrete Element Method. For each system, three particles on the center line were selected and their instant vertical velocity components were traced. In addition, both discharge and the rate were recorded throughout the procedure. The predicted results show that, for both the systems without adhesion, though the soft has a material modulus only 1/1000 of the hard, there are no significant differences in f low pattern and discharge rate. This suggests that a soft system can be used to predict the behavior of a hard one to save CPU time in a gravity-driven granular flow. On the other hand, comparison between both hard systems shows that adhesion can significantly reduce the flowability in granular flow. By analyzing the velocity plot for the traced particles, free fall was clearly detected above the decompression zone, indicating the motion of a particle in a granular flow can be resolved as free fall together with the movement due to particle collision. In addition, select dynamic behavior related to the kinetic fluctuations affecting flow was observed. discrete element method silo granule flow particulate material     

Effects of Material Properties on Granular Flow in a Silo Using DEM Simulation

In order to test the effect of material properties on flowability of particulate materials, discharge procedures of spherical particles within a flat-bottomed model silo with three sets of material properties, i.e., soft and hard without adhesion and adhesive hard, were simulated using the Discrete Element Method. For each system, three particles on the center line were selected and their instant vertical velocity components were traced. In addition, both discharge and the rate were recorded throughout the procedure. The predicted results show that, for both the systems without adhesion, though the soft has a material modulus only 1/1000 of the hard, there are no significant differences in f low pattern and discharge rate. This suggests that a soft system can be used to predict the behavior of a hard one to save CPU time in a gravity-driven granular flow. On the other hand, comparison between both hard systems shows that adhesion can significantly reduce the flowability in granular flow. By analyzing the velocity plot for the traced particles, free fall was clearly detected above the decompression zone, indicating the motion of a particle in a granular flow can be resolved as free fall together with the movement due to particle collision. In addition, select dynamic behavior related to the kinetic fluctuations affecting flow was observed.

discrete element method silo granule flow particulate material     

Numerical investigation of reverse segregation in debris flows by DEM

Studies of the mechanisms and the effects on the flowing mobility for hazardous geophysical flows (e.g., debris flows) is crucial for hazard mitigation and prediction. Granular flows with grains of mixed sizes are numerically modeled and the contact behavior of solid particles is fundamentally studied using the discrete element method. The mechanical effects of particle contacts (shearing and collision) are contrasted with geometrical effects (kinetic sieving) to explain the mechanism of reverse segregation. Compared to granular flows with uniform solid particles, the effect of segregation on granular flowing mobility is investigated. It is found that reverse segregation can significantly influence the flowing mobility and the flowing regimes in the front head of the granular body. A mechanical explanation of the segregation mechanism can be presented by a new dimensionless number, which is correlated with the contact force.     

Force propagation speed in a bed of particles due to an incident particle impact

The force propagation speed in granular matter is a very difficult property to be measured. A new technique has been developed to calculate the force propagation speed in granular matter based on measuring experimentally the contact time. The contact time for a particle hitting a bed of particles is estimated as the time taken for a particle to strike a bed of particles till the time of its ejection, and it is calculated using the discrete element method. The speed of force propagation in a bed of particles is estimated by plotting the dependence of the path length of the contact force on the contact time and finding the gradient of such dependence. Such approach leads to accurate results if the impact speed is below the yield velocity, i.e. no plastic deformations. It is found that the force propagation speed in spherical granular matter is proportional to the impact speed of the incident particle, which is different from force propagation in continuum matter. It is also found that the propagation speed is dependent on the material and diameters ratio of the interacting particles, but it is not dependent on the number of bed layers. The propagation speed in granular matter is normalized by dividing it by a reference propagation speed, i.e. the propagation speed at an impact speed of 1 m/s. It is found that the normalized propagation speed is independent of the material and diameter of the interacting particles, but it is logarithmically proportional to the impact speed. The proportionality constant is equal to 0.16, which can be taken as a universal constant for force propagation in spherical granular matter.     

3D experimental quantification of fabric and fabric evolution of sheared granular materials using synchrotron micro-computed tomography

Many experimental studies have demonstrated that mechanical response of granular materials is highly influenced by micro-structural fabric and its evolution. In the current literature, quantification of fabric and its evolution has been developed based on micro-structural observations using Discrete Element Method or 2D experiments with simple particle shapes. The emergence of X-ray computed tomography technique has made quantification of such experimental micro-structural properties possible using 3D high-resolution images. In this paper, synchrotron micro-computed tomography was used to acquire 3D images during in-situ conventional triaxial compression experiments on granular materials with different morphologies. 3D images were processed to quantify fabric and its evolution based on experimental measurements of contact normal vectors between particles. Overall, the directional distribution of contact normals exhibited the highest degree of isotropy at initial state (i.e., zero global axial strain). As compression progressed, contact normals evolved in the direction of loading until reaching a constant fabric when experiments approached the critical state condition. Further assessment of the influence of confining pressure, initial density state, and particle-level morphology on fabric and its evolution was formed. Results show that initial density state and applied confining pressure significantly influence the fabric-induced internal anisotropy of tested specimens at initial states. Relatively, a higher applied confining pressure and a looser initial density state resulted in a higher degree of fabric-induced internal anisotropy. Influence of particle-level morphology was also found to be significant particularly on fabric evolution.     

Hybrid and collocation Trefftz methods for traction boundary conditions in linear elastostatics

For linear elastostatics, the particular solutions and the fundamental solutions can be used for the admissible functions, so that only the boundary conditions need to be satisfied, thus called the boundary methods (or Trefftz methods). Hence, how to couple the boundary conditions is a crucial issue. There are basically two types of boundary conditions: (I) the displacement (i.e., Dirichlet) condition and (II) the traction (i.e., Neumann) condition. In this paper, the coupling techniques for the traction (i.e., Neumann condition) are the main theme for boundary methods, because the traction condition may be regarded as the basic condition and the displacement condition as the natural condition. The Lagrange multiplier used for the displacement (i.e., Dirichlet) condition is well known in mathematics community (see Babu?ka, 1973 [1]; Babu?ka et al., 1978 [2]; Li, 1998 [20]; Pitkäranta, 1979 [40]), but the Lagrange multiplier used for the traction (i.e., Neumann) condition is popular for elasticity problems by the Trefftz method in engineering community, which is called the hybrid Trefftz method (HTM) (see de Freitas, 1998 [7]; de Freitas and Ji, 1996 [8], [9]; Jirousek, 1978 [12]; Jirousek and Venkstesh, 1992 [13]; Jirousek and Wroblewski, 1996 [14]; Qin, 2000 [42]). On the other hand, the collocation Trefftz method (CTM) can also be used to directly couple the traction condition without extra-multipliers. In this paper, a brief error analysis for the HTM is given, to provide the optimal convergence rates. Numerical experiments of simple models are carried out to support this analysis. The HTM has the merits: flexibility and robustness, so that it has been widely used in engineering problems. Since the optimal convergence rates are the most important criterion in evaluation of numerical methods, the global performance of the HTM is as good as that of the CTM, although the HTM causes larger condition numbers and requires more CTU time for the computation of the simple models in this paper. More numerical comparisons also show that using the particular solutions is more advantageous than using the fundamental solutions in both HTM and CTM.     

Computer generation of binary Fresnel holography

Binarization of Fresnel holograms by direct thresholding based on the polarity of the fringe pattern is studied. It is found that if the hologram is binarized (i.e., for black and white hologram pixels) in this manner, only the edges of the object are preserved in the reconstructed image. To alleviate the errors caused by binarization, the use of error diffusion has been routinely employed. However, the reconstructed image using such standard technique is heavily contaminated with random noise. In this paper, we propose a novel noniterative method for generating Fresnel holograms that are suitable for binarization. Our method is capable of preserving good visual quality on the reconstructed images.     

B样条曲线的小波光顺法

本文研究了B样条曲线的小波光顺法。首先介绍了利用准均匀B样条曲线逼近具有任意节点矢量的B样条曲线的方法，从而将任意B样条曲线转化为多分辨率表示，进而提出了基于小波的曲线光顺误差控制算法。小波光顺法在光顺曲线的同时具有减少控制顶点的作用，兼具简单性和通用性的优点。     

Effect of the anisotropy of confining field on the structure of dusty plasma clusters

The structure of dusty plasma clusters in the ground state for various configurations of the confining field has been simulated using the molecular dynamics method with the interaction between spherical particles of dusty plasma described in terms of an isotropic Yukawa pair potential. Depending on the degree of the confining field anisotropy (i.e., a difference between forces in the vertical and horizontal directions), conditions for which a three-dimensional (3D) structure in the ground state (isotropic confining field) transforms into a 2D structure are determined. The shape, dimensions, and structure of dusty plasma clusters have been studied in systems with various numbers of particles and degrees of anisotropy of the confining field.     

Visualizing the effect of gold nanocages on absorption, imaging, and lower critical solution temperature phase transition of individual poly(NiPAM)-based hydrogel particles by near infrared multispectral imaging microscopy

We have successfully utilized the near-infrared multispectral imaging (NIR-MSI) microscope to observe and measure directly images and spectra of individual hydrogel particles alone or with added gold nanocages (GNs). The NIR-MSI is suited for this task because it can simultaneously record spectral and spatial information of a sample with high sensitivity (single pixel resolution) and high spatial resolution (～0.9 μm/pixel). Because both images and spectra of the individual particles can be directly and simultaneously measured by the microscope, it is possible to detect any changes in the spectroscopic properties and/or nature (size, volume) of individual hydrogel particles induced by external factors (e.g., temperature and/or pH). These features make it possible to determine lower critical solution temperature (LCST) values based on monitoring either changes in the NIR spectra or the volume of the hydrogel particle in response to variations in temperature. More importantly, the measured volume transition temperature or LCST value is not of a collection of many hydrogel particles, but rather of individual hydrogel particles. GNs were found to significantly affect not only absorption but also images and properties of individual hydrogel particles. Specifically, GNs were found to enhance absorption of individual hydrogel particles, particularly the C-H band at 1716 nm, by about 25%. Of particular interest is the fact that not all individual hydrogel particles were enhanced by GNs; only about 50% of total number of particles were enhanced by GNs. GNs were also found to make it difficult to observe individual hydrogel particles, i.e., it seems that GNs defocused images of hydrogel particles. The defocusing effect by GNs might be due to photothermal generation of heat and vapor bubbles by the GNs. Of particular interest is the effect of GNs on the volume transition temperature of individual hydrogel particles. It seems that individual hydrogel particles lose their LCST in the presence of GNs, i.e., when heated, they undergo a gradual decrease in the volume but do not exhibit any clear and observable discontinued phase transition temperature.     

Granular element method (GEM): linking inter-particle forces with macroscopic loading

We present a new method capable of inferring, for the first time, inter-particle contact forces in irregularly-shaped natural granular materials (e.g., sands), using basic Newtonian mechanics and balance of linear momentum at the particle level. The method furnishes a relationship between inter-particle forces and corresponding average particle stresses, which can be inferred, for instance, from measurements of average particle strains emanating from advanced experimental techniques (e.g., 3D X-ray diffraction). Inter-particle forces are the missing link in understanding how forces are transmitted in complex granular structures and the key to developing physics-based constitutive models. We present two numerical examples to verify the method and showcase its promise.     

Image analysis of liberation spectrum of coarse particles

Determination of liberation spectrums by using MLA and QEMSCAN techniques require polished sections and fine particles. These techniques cannot be performed in-situ and for coarse particles. Thus, the focus of this technical note is to investigate whether the image analysis method can be used for the determination of liberation spectrum for coarse particles. Two methods were used to determine the liberation spectrum. In the first method, the liberation spectrum was obtained using the small and large diameter of particles. In the second method, the liberation spectrum was determined using the small and large diameter of particles as well as the shape correction diameter. The results showed that the image analysis can be used to successfully determine the liberation spectrum. The composition of composite particles was significantly improved when the stereological correction was used i.e. the square root of the mean square error for the particle composition using the method 1 was 1.25% while that using the method 2 was 0.60%. The proposed method might be used for the determination of liberation spectrum of high-grade real coarse particles. However, this requires a significant amount of future work.     

Using PIV to measure granular temperature in saturated unsteady polydisperse granular flows

The motion of debris flows, gravity-driven fast moving mixtures of rock, soil and water can be interpreted using the theories developed to describe the shearing motion of highly concentrated granular fluid flows. Frictional, collisional and viscous stress transfer between particles and fluid characterizes the mechanics of debris flows. To quantify the influence of collisional stress transfer, kinetic models have been proposed. Collisions among particles result in random fluctuations in their velocity that can be represented by their granular temperature, T. In this paper particle image velocimetry, PIV, is used to measure the instantaneous velocity field found internally to a physical model of an unsteady debris flow created by using “transparent soil”—i.e. a mixture of graded glass particles and a refractively matched fluid. The ensemble possesses bulk properties similar to that of real soil-pore fluid mixtures, but has the advantage of giving optical access to the interior of the flow by use of plane laser induced fluorescence, PLIF. The relationship between PIV patch size and particle size distribution for the front and tail of the flows is examined in order to assess their influences on the measured granular temperature of the system. We find that while PIV can be used to ascertain values of granular temperature in dense granular flows, due to increasing spatial correlation with widening gradation, a technique proposed to infer the true granular temperature may be limited to flows of relatively uniform particle size or large bulk.     

Parallel image restoration with a two-dimensional likelihood-based algorithm

We describe a pixelwise parallel algorithm for the restoration of images that have been corrupted by a low-pass optical channel and additive noise. This new algorithm is based on an iterative soft-decision method of error correction (i.e., turbo decoding) and offers performance on binary-valued imagery that is comparable to the Viterbi algorithm. We quantify the restoration performance of this new algorithm on random binary imagery for which it is superior to both the Wiener filter and the projection onto convex sets algorithms over a wide range of channels. For typical optical channels, the new algorithm is within 0.5 dB of the two-dimensional Viterbi restoration method [J. Opt. Soc. Am. A 17, 265 (2000)]. We also demonstrate the extension of our new algorithm to correlated and gray-scale images using vector quantization to mitigate the associated complexity burden. A highly parallel focal-plane implementation is also discussed, and a design study is presented to quantify the capabilities of such a VLSI hardware solution. We find that video-rate restoration on 252 x 252 pixel images is possible using current technology.