Influence of boundary condition on the sound velocity in granular assembly: Spiral tube versus cylinder

The properties of elastic wave propagation in granular assemblies have become a subject of immense interest in recent years, however, the influence of different confinements on the sound velocity is seldom investigated. This study provides a method to determine the contact point between spherical, super-ellipsoidal particles and complex boundaries, in order to investigate how the anisotropy induced by particle shape or boundary affects velocity. Taking cylinder and spiral tube confinements as examples, the falling process of spherical and super-ellipsoidal assemblies are simulated to verify the validation by the discrete element method (DEM). The convergence of the kinetic energy during the falling process and the equilibrium state with zero residual kinetic energy guarantees the stability and correctness. On the basis, elastic wave propagation of spherical and super-ellipsoidal systems in spiral tube and cylindrical confinements under different pressures are modelled, and sound velocities are calculated. The effective medium theory (EMT), granular solid hydrodynamics (GSH), and elastic stiffness are used to interpret the relationship between velocity and stress in cylindrical confinement. However, the results in the spiral tube deviate from EMT and GSH, which means the boundary affects velocity significantly. The difference of velocity between spiral tube and cylinder is qualitatively explained from the perspective of anisotropy of contact force distribution in the system. The simulation results show that anisotropy introduced by the curved surface affects the acoustic properties greatly. The method used for spiral boundary is also suitable for other complicated confinements.     

Finite element study of the effect of material properties on reaction forces produced by solitary wave propagation in granular chains

The response of a granular chain to impulse loading was investigated as a function of material properties. Using COMSOL Multiphysics, the elastic modulus and density of the grains were varied while the piston and force sensor properties remained fixed. The result of solitary wave propagation through the granular chain was recorded at the force sensor as a series of reaction force waves. It was found that wave velocity and amplitude increased with elastic modulus. Increasing density caused a decrease in wave velocity and an increase in amplitude. In addition, higher density granular chains exhibited a decrease in the number of waves in their respective reaction force wave trains. LS-DYNA was then used to explore the response of a variety of ceramic and metallic granular chains. Density, elastic modulus, and Poisson’s ratio were all set to representative values for the respective material. It was found that solitary wave development and decay occurred at different rates for different materials. In addition, the kinetic energy decay of the impactor was slower for glass compared with tungsten. Finally, it was shown that a single reaction force wave with no train could be produced by impacting a high density, high modulus chain such as tungsten with a glass piston, which has relatively low density and elastic modulus. Increasing impact velocity for this case resulted in a single high-amplitude wave with no train.     

Wave propagation in elasto-plastic granular systems

Due to the nonlinear nature of the inter-particle contact, granular chains made of elastic spheres are known to transmit solitary waves under impulse loading. However, the localized contact between spherical granules leads to stress concentration, resulting in plastic behavior even for small forces. In this work, we investigate the effects of plasticity in wave propagation in elasto-plastic granular systems. In the first part of this work, a force–displacement law between contacting elastic-perfectly plastic spheres is developed using a nonlinear finite element analysis. In the second part, this force–displacement law is used to simulate wave propagation in one-dimensional granular chains. In elasto-plastic chains, energy dissipation leads to the formation and merging of wave trains, which have characteristics very different from those of elastic chains. Scaling laws for peak force at each contact point along the chain, velocity of the leading wave, local contact and total dissipation are developed.     

Influence of particle packed pattern on the transient granular flow in a wedge-shaped hopper

A hopper has very wide and vital applications in handing the granular materials in daily life and industrial production, and the full understanding of the granular flow inside a hopper is of great importance to control and optimize the discharge process. By employing experimental and numerical methods, the influence of particle packed pattern on the transient granular flow is investigated in terms of the particle-scale kinetics and structure. For the mono-sized particles packed pattern, despite the similar particle-scale structure, smaller particles achieve greater kinetic energy conversion efficiency, which helps shorten the discharge time. For the binary-sized particles uniform mixing pattern, the interaction between particles increases the individual kinetic energy and transient average coordination number (CN) of large particles, while decreases that of small ones. Then the in-between kinetic energy and the disperse structure are reached. For the layer by layer mixing pattern, the strong percolation effect caused by the upper small particles hinders the increase of the individual kinetic energy at the beginning of the discharge process, and the transient average CN at the layer interface abruptly reaches 8. By contrast, when the small particles are placed at the bottom, more particles are active in the larger space, and subsequently, a looser structure is achieved in a shorter period.     

A coupled CFD-DEM analysis of granular flow impacting on a water reservoir

Massive debris flows or rock avalanches falling into a water reservoir may cause devastating hazards such as overtopping or dam breakage. This paper presents a coupled Computational Fluid Dynamics and Discrete Element Method (CFD-DEM) analysis on the impacting behaviour of a granular flow falling from an inclined slope into a water reservoir. The coupling between CFD and DEM considers such important fluid–particle interaction forces as the buoyancy force, the drag force and the virtual mass force. It is found that the presence of water in the reservoir can generally help to reduce direct impact of granular flow on the check dam behind the reservoir, minimizes the intense collisions and bouncing among particles and helps form a more homogeneous final deposited heap as compared to the dry case. While the interparticle/particle–wall frictions and collisions dominate the energy dissipation in the dry granular flow, the majority of kinetic energy of the granular system in the wet case is first transferred to the water body, which leaves the granular flow itself to become a contact-shearing dominant one and causes impulse wave travelling between the check dam and the slope surface for a rather sustained period before settling down. A power law distribution is found for the velocity profile of the granular flow travelling on both the slope and the reservoir ground surfaces, and it may change temporarily to a linear distribution at the transition point of the slope toe where the Savage number depicts a peak. The consideration of rolling friction among particles may homogeneously reduce the travelling velocity of the granular flow and alleviate the overall impact on the check dam. The impact on the check dam depends on both the initial debris releasing height and the reservoir water level. Medium water levels in the reservoir have been found to be generally safer when the initial debris height is relatively high.     

Rheology of weakly wetted granular materials: a comparison of experimental and numerical data

Shear cell simulations and experiments of weakly wetted particles (a few volume percent liquid binders) are compared, with the goal to understand their flow rheology. Application examples are cores for metal casting by core shooting made of sand and liquid binding materials. The experiments are carried out with a Couette-like rotating viscometer. The weakly wetted granular materials are made of quartz sand and small amounts of Newtonian liquids. For comparison, experiments on dry sand are also performed with a modified configuration of the viscometer. The numerical model involves spherical, monodisperse particles with contact forces and a simple liquid bridge model for individual capillary bridges between two particles. Different liquid content and properties lead to different flow rheology when measuring the shear stress-strain relations. In the experiments of the weakly wetted granular material, the apparent shear viscosity $\eta _g$ η g scales inversely proportional to the inertial number $I$ I , for all shear rates. On the contrary, in the dry case, an intermediate scaling regime inversely quadratic in $I$ I is observed for moderate shear rates. In the simulations, both scaling regimes are found for dry and wet granular material as well.     

Segregation of cohesive granular materials during discharge from a rectangular hopper

Granular materials may readily segregate due to differences in particle properties such as size, shape, and density. Segregation is common in industrial processes involving granular materials and can occur even after a material has been uniformly blended. The specific objective of this work is to investigate via simulation the effect of particle cohesion due to liquid bridging on particle segregation. Specifically, a bi-disperse granular material flowing from a 3-D hopper is simulated using the discrete element method (DEM) for cohesive particles and the extent of discharge segregation is characterized over time. The cohesion between the particles is described by a pendular liquid bridge force model and the strength of the cohesive bond is characterized by the Bond number determined with respect to the smaller particle species. As the Bond number of the system increases, the extent of discharge segregation in the system decreases. A critical value of Bo = 1 is identified as the condition where the primary mechanism of segregation in the cohesionless hopper system, i.e. gravity-induced percolation, is essentially eliminated due to the liquid bridges between 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.     

Evolution of mesoscale structure in fluidized beds with non-spherical dry and wet particles

Fluidized beds with non-spherical dry and wet particles are widely used in industrial processes, and the mesoscale structure in the bed has an important influence. In this study, CFD-DEM simulations are performed to evaluate the flow behaviors and mesoscale structure in fluidized beds with non-spherical dry and wet particles. The accuracy of the model is validated by comparison with the results of the particle image velocimetry experiment. The force distributions at bubble boundaries are analyzed to explain the influence mechanism of different shapes of bubbles in non-spherical dry and wet particle systems. The factor analysis indicates the interaction of particle shape and viscous liquid on the translational and rotational kinetic energy of particles. When the bed height is low, as the particle aspect ratio increases, the bubble equivalent diameter gradually increases. In addition, as the liquid viscosity increases, the particle and bubble granular temperature gradually decrease, indicating the reduction of particle velocity fluctuate and the decrease of turbulent kinetic energy of bubble. These findings have guiding significance for the fluidization of non-spherical dry and wet particles and can be used to optimize related industrial processes.     

Amplitude-dependent attenuation of compressive waves in curved granular crystals constrained by elastic guides

We study the wave propagation in a curved chain of spherical particles constrained by elastic guides under the axial impact of a falling mass. We characterize the force transmission properties of the chain by varying the striker’s mass and the chain’s curvature. Experimental tests demonstrate amplitude-dependent attenuation of compressive waves propagating through the curved chain. In particular, we observe that the curved systems present an improved transmission of small dynamic disturbances relative to that of strong excitations, resulting from the close interplay between the granular particles and the softer elastic medium. We also find that the transmission of the compressive waves through the chains is dependent on the initial curvature imposed to the system. Numerical simulations, based on an approach that combines discrete element and finite element methods, corroborate the experimental results. The findings suggest that hybrid structures composed of granular particles and linear elastic media can be employed as new passive acoustic filtering materials that selectively transmit or mitigate excitations in a desired range of pressure amplitudes.     

Mechanical and electrical behaviors of polymer particles. Experimental study of the contact area between two particles. Experimental validation of a numerical model

The present paper is devoted to the analysis of mechanical and electrical behaviors observed on particulate polymer granular materials. The constituting particles obtained these physical properties by coating the polymer spherical substrate with a conducting polymer: polypyrrole (PPy) which confers electrical conducting properties to the particle, while preserving its mechanical properties. Particle contacts dominate the behavior of the granular media and, consequently, size, morphology, roughness and plasticity of the particles play a crucial role in this behavior. Scanning electron microscope (SEM) and atomic force microscope (AFM) were used to study the surface state and the contact area between neighbors. An experimental set up, based on the measurement of the displacement of contacting particles subjected to a normal force and of the variation of the electrical resistance of the packing, allowed the study of both the mechanical and electrical behaviors of the particle system. The experimental results took into account the plastic deformation under varying loading and unloading conditions; they were consistent with theories of contact mechanics, thus validating the existing models.     

Effect of base roughness on size segregation in dry granular flows

This paper presents simulations of dry granular flows along a sloping channel using the discrete element method. The kinetic sieving and squeeze expulsion theories are utilized to study the effects of base roughness on size segregation and the underlying mechanisms. Basal friction has a significant influence on flowing regimes inside the granular body, and a larger base friction accelerates the size segregation process. The front zone of the granular body is more likely to be collision dominated with increasing base friction; as a result, the energy dissipated by frictional shearing decreases, and damping energy due to particles collisions is enhanced. Meanwhile, granular flows become much looser, and collisions between particles increase rapidly. It is shown that the differences in the kinetics among grains of mixed sizes and the mechanical effects of particle contacts can explain the mechanism of size segregation. The parameter representing the intensity of particles exchange also increases as base friction increases. The forces acting on particles are also affected by base friction. The dimensionless contact force describing the contribution of contact channel-normal stress increases as base friction increases, which indicates that a higher dispersive trend has developed inside the granular body.     

DEM simulations: mixing of dry and wet granular material with different contact angles

In solid mixing the raw materials typically differ at least in one material property, such as particle size, solid density and wetting properties, which in turn influence particle mobility. For example, smaller particles can percolate through the voids of larger ones under the influence of strain and gravity. This may produce fine particle accumulation at the bottom of the mixing vessel which results in undesired, inhomogeneous final products. When wet particles with different wetting properties need to be mixed, heteroagglomeration may occur as another segregation mechanism. We present a new capillary bridge force model to study segregation in moist cohesive mixing processes using DEM. New analytical equations of best fit are derived by solving the Young–Laplace equation and performing a regression analysis, in order to investigate discontinuous mixing processes of dry and moist materials with different particle sizes and different contact angles. Compared to a dry mixing process, mixing efficiency is improved by the addition of a small amount of liquid. While percolating segregation is reduced, heteroagglomerates occur in the wet mixing process.     

Analysis of elastic wave propagation in a functionally graded thick hollow cylinder using a hybrid mesh-free method

In this paper, a hybrid mesh-free method based on generalized finite difference (GFD) and Newmark finite difference (NFD) methods is presented to calculate the velocity of elastic wave propagation in functionally graded materials (FGMs). The physical domain to be considered is a thick hollow cylinder made of functionally graded material in which mechanical properties are graded in the radial direction only. A power-law variation of the volume fractions of the two constituents is assumed for mechanical property variation. The cylinder is excited by shock loading to obtain the time history of the radial displacement. The velocity of elastic wave propagation in functionally graded cylinder is calculated from periodic behavior of the radial displacement in time domain. The effects of various grading patterns and various constitutive mechanical properties on the velocity of elastic wave propagation in functionally graded cylinders are studied in detail. Numerical results demonstrate the efficiency of the proposed method in simulating the wave propagation in FGMs.     

基于统计方法的NOPD耗能机理定量分析

非阻塞性微颗粒阻尼（NOPD）是在传统颗粒阻尼和冲击阻尼技术基础上发展起来的新型阻尼技术。本文从湍流物理模型出发,基于统计方法定量分析了NOPD技术的耗能机理。经分析认为,高频振动中的NOPD颗粒群其运动状态和湍流运动相似,故引入Kolmogorov的局部各向同性假设,得到NOPD的结构函数表达式及能谱密度表达式。研究结果表明,同种材料,相同颗粒直径情况下,能量耗散率随颗粒群体积比的增加而增大;相同颗粒群体积比时,能量耗散率随颗粒直径的增加而增大。统计方法的引入,为NOPD的工程应用提供了一种有效的定量分析方法。     

Physico-mechanical properties and water absorption of cement composite containing shredded rubber wastes

The main objective of this study was to investigate the potential utilisation of rubber waste in cementitious matrix, as fine aggregates, to develop lightweight construction materials. Composites containing different amounts of rubber particles, as partial replacement to cement by volume, were characterised by destructive and non-destructive testing. Five designated rubber contents varying from 10% to 50% by volume were used. The 28-days physical, mechanical and hydraulic transport properties of the cement composite were determined. Analyses included dry unit weight, elastic dynamic modulus, compressive and flexural strengths, strain capacity, and water absorption. Test results of the physico-mechanical behaviour indicated that the increase in rubber content decreases the sample unit weight with a large reduction in the strengths and elastic modulus values of the composites. Results have only shown that the introduction of rubber particles significantly increases the strain capacity of the materials. However, rubbers into cement paste enhances the toughness of the composite. Although the mechanical strengths were reduced, the composite containing 50% of rubber particles satisfies the basic requirement of lightweight construction materials and corresponds to “class II”, according to the RILEM classification. Test-results of the hydraulic transport properties revealed that the addition of rubber particles tends to restrict water propagation in the cement matrix and reduces water absorption of the composite. The decrease of the sorptivity-value is favourable to the durability of the specimen structures.     

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.     

Propagation of solitary waves in 2D granular media: A numerical study

The impact-induced wave propagation in a model granular material composed of closely packed linearly elastic spherical particles interacting through Hertzian contact is investigated numerically using a specially adapted molecular dynamics framework. Of particular interest is the effect of the stiffness and density mismatch between main and interstitial beads on the anisotropic nature and speed of propagation of the primary compressive wave generated by a localized impact event in an extended square-packed granular medium. Two propagation regimes are observed in the numerical simulations: the first one described by a solitary wave pattern emanating from the point of impact, and the other characterized by a directional propagation of the impact energy in the principal directions of the pack. A simple model is proposed to describe the bounds between these two propagation regimes in the parametric space defined by the mass and stiffness ratios between main and interstitial particles. Maps of the normalized maximum compressive force and wave speed are presented to quantify the anisotropy of the wave propagation response.