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.     

An entropy-like parameter of particle size distributions as packing density index in complex granular media

Information entropy dimension (ED) has been used earlier in the characterization of the particle size distribution (PSD) in complex multi-particle granular media. In this work the ED is first proposed as an indicator of the packing density on the basis of the theoretical based interpretation of the ED in the granular media PSD context. A one-parametric exact self-similar PSD model, where the information ED is known, together with a 2-D computational random packing algorithm, are used to test the ability of the ED as an indicator of packing density. It is found that the packing density increases when the ED does. Moreover, results show a strong linear dependence between packing density and the ED. Empirical results from a large soil data base also reinforce the computational results. As ED may be estimated from field or laboratory data, the above mentioned results suggest its use as an indicator of packing density in complex granular media and material science in order to predict their properties.     

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.     

Measurement of rotation of individual spherical particles in cohesive granulates

To explore dynamical processes in granular matter, we use a combination of 3D imaging and mechanical testing. We analyze structural changes using confocal microscopy while applying a compression load simultaneously. Fluorescently labeled polydisperse silica particles were hydrophobized with long alkyl chains and dispersed in an index-matching liquid. The particles show a weak attraction. Photobleaching the central plane of individual particles generates an optical anisotropy without changing particle interaction. In a series of 3D images, we follow trajectories and rotation of single particles. We focus on particle translation and rotation in dependency of the local volume fraction. During compression, restructuring happens predominantly in regions of low packing density. We show that rotation plays an important role and is hence a key parameter for explaining dynamical processes in granular systems.     

Slow relaxation and compaction of granular systems

Granular materials are of substantial importance in many industrial and natural processes, yet their complex behaviours, ranging from mechanical properties of static packing to their dynamics, rheology and instabilities, are still poorly understood. Here we focus on the dynamics of compaction and its 'jamming' phenomena, outlining recent statistical mechanics approaches to describe it and their deep correspondence with thermal systems such as glass formers. In fact, granular media are often presented as ideal systems for studying complex relaxation towards equilibrium. Granular compaction is defined as an increase of the bulk density of a granular medium submitted to mechanical perturbation. This phenomenon, relevant in many industrial processes and widely studied by the soil mechanics community, is simple enough to be fully investigated and yet reveals all the complex nature of granular dynamics, attracting considerable attention in a broad range of disciplines ranging from chemical to physical sciences.     

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.     

Simulation of cutting processes using mesh-free Lagrangian particle methods

This contribution presents the model of a ‘granular solid’ based on the Discrete Element Method which is used to model cutting processes of cohesive and ductile materials, e.g. aluminum. The model is based on a conventional three-dimensional Discrete Element approach which employs rigid spheres as it is used to model granular media. Including cohesive interactions besides the repulsive interactions of the basic model allows for the particle agglomerate to display cohesive and ductile behavior. Using the thus generated granular solid the failure modes of ductile engineering materials like aluminum can be qualitatively and quantitatively reproduced. This is shown by comparison with experiments of a tensile and a Charpy impact test. To show the applicability of the approach for manufacturing problems an orthogonal cutting process of steel and aluminum is modelled and the cutting forces are compared to experiments. To further enhance the model thermal interactions between particles are included. The thermodynamics during cutting due to dissipative phenomena is evaluated and compared to experiments.     

Penetration of cement pastes into sand packings during 3D printing: analytical and experimental study

3D printing processes of concrete and cement based materials could bring architectural and structural innovation in construction industry. Additive manufacturing and digital fabrication methods in civil engineering have recently been developed at laboratory scale. Among the 3D printing processes that could bring new perspectives in innovative and designed architectural elements, one of the most interesting is called the selective paste intrusion method. The component is built layer by layer by selectively applying cement paste on an aggregate packing using a 3D printer nozzle and a subsequent penetration of the paste into the aggregate layer. The implementability of the selective paste intrusion method requires the prediction of the flow of a yield stress fluid through a porous media. The rheological behaviour of the cement paste must be adapted for its penetration through the porous network of the aggregate particle packing. An adequate penetration depth of the cement paste produces homogeneous materials that are capable of sustaining a high mechanical stress. We show in this paper that the compressive strength of component made by such a technique is directly linked to the penetration depth of the cement paste into the aggregate layer; consequently, this paper aims at predicting the penetration depth of cement pastes into sand layers. A theoretical framework has been developed to propose an evaluation of penetration depth as a function of the average sand grain diameter and the yield stress of the cement paste, which is experimentally validated with specific penetration measurements. Finally, we stress that the prediction of penetration with an analytical model is an effective technique to ensure building homogeneous cement based materials with the 3D printing selective binding method.     

Slow steady-shear of plastic bead rafts

Experimental measurements of the response of a two dimensional system of plastic beads subjected to steady shear are reported. The beads float at the surface of a fluid substrate and are subjected to a slow, steady-shear in a Couette geometry. The flow consists of irregular intervals of solid-like, jammed behavior, followed by stress relaxations. We report on statistics that characterize the stress fluctuations as a function of several parameters including shear-rate and packing density. Over a range of densities between the onset of flow to the onset of buckling (overpacking) of the system, the probability distribution for stress fluctuations is essentially independent of the packing density, particle dispersity, and interaction potential (varied by changing the substrate). Finally, we compare the observed stress fluctuations with those observed in other complex fluids.     

A new theory of recording media noise

Previous investigations of the noise in particulate or grainy recording media have considered statistical variations in the processes by which the particles become magnetized. The theory of noise presented includes also statistical variations in the packing density of the particles. An extremely simple analysis shows that, when both of these phenomena are included properly, the noise power of recording media may always be expected to depend upon the magnetization, or signal level, and the particle packing factor. It is found that the recording media should always provide higher signal-to-noise ratios (SNRs) than was previously supposed. It is pointed out that the signal recovery or detection techniques employed today in magnetic storage devices cannot yield optimum SNRs or bit error rates. Some algebraic and/or conceptual errors in the published literature on noise are discussed.<>     

Coupled effects of capillary suction and fabric on the strength of moist granular materials

This paper discusses the coupled effects of capillary suction and fabric on the behavior of partially saturated granular materials at pendular state when discrete liquid bridges form around particle contacts. Experimental results show that the soil–water characteristic curves of granular materials are affected by the internal structure formed during reconstitution of the specimen. The effect of capillary suction on the shear strength of moist sand varies with the direction of shearing relative to the bedding plane which is generally perpendicular to the major principal direction of the fabric tensor. When treating capillary attraction as interparticle forces at particle contacts, a micromechanics analysis shows that the coupling between capillary-attracting forces and fabric results in an additional stress tensor, which describes the anisotropic effect of capillary suction on the behavior of moist sand.     

Effect of liquid phase on densification in electric-discharge compaction

The effect of liquid phase on densification in electric-discharge compaction (EDC) was explored in the present work. The temperature at contact area of particles in EDC was estimated from random packing model incorporated with electric current distributions. Consolidation of cemented carbide and tungsten heavy alloys was conducted under varying current densities. WC-11Co/Fe/WC-11Co sandwich powder compacts were designed to investigate the effect of liquid phase flow. It is found that the densification occurred only when liquid phase formed, and relative density increased with the increasing of liquid phase volume. In the case of WC-11Co powders, the faceted grain evolution occurred but the significant grain growth was hardly observed, which meant the densification was mainly induced by particle rearrangement. The depth of liquid penetration of Fe in WC-11Co/Fe/WC-11Co sandwich compact also agreed with that caused by particle rearrangement processing. The possible effects of electric current on densification were also discussed.     

Dynamics of an intruder in dense granular fluids

We investigate the dynamics of an intruder pulled by a constant force in a dense two-dimensional granular fluid by means of event-driven molecular dynamics simulations. In a first step, we show how a propagating momentum front develops and compactifies the system when reflected by the boundaries. To be closer to recent experiments (Candelier and Dauchot in Phys Rev 81(1):011304, 2010; Phys Rev 103(12):128001, 2009), we then add a frictional force acting on each particle, proportional to the particle’s velocity. We show how to implement frictional motion in an event-driven simulation. This allows us to carry out extensive numerical simulations aiming at the dependence of the intruder’s velocity on packing fraction and pulling force. We identify a linear relation for small and a nonlinear regime for high pulling forces and investigate the dependence of these regimes on granular temperature.     

Analysis and optimisation of particle mixing performance in fluid phase resonance mixers based on Euler/Lagrange calculations

A novel mixing principle utilising oscillating liquid columns was analysed numerically with regard to particle dispersion characteristics. For producing fluid oscillations a pipe (diameter 100 mm) was immersed centrally into a vessel (diameter 450 mm) filled with liquid (filling height 700 mm) and periodically pressurised (frequency 1.2 Hz). The outlet geometry of the central pipe, just ending near the vessel bottom, has a strong effect on mixing and was optimised in this study. The principle of a FPR-mixer does not require rotating stirrers and in the turbulent regime it has power numbers comparable to propellers. The numerical calculations were conducted by a Euler/Lagrange approach neglecting two-way coupling as well as inter-particle collisions for clarity in order to only focus on the effect of interfacial forces on particle dispersion. The continuous phase was calculated in an unsteady way based on the Reynolds-averaged equations combined with the k-ω-SST (shear stress transport) turbulence model. Lagrangian tracking was conducted considering all relevant forces; drag, gravity/buoyancy, fluid inertia, added mass, Basset force and transverse lift forces due to shear and particle rotation. The importance of these forces was analysed with respect to the turbulent particle Stokes number (considered range 0.004 < St < 10.0) and particle/liquid density ratio (i.e. 1.05, 1.5 and 2.5). Finally, the significance of Basset force and shear-rotation lift force (i.e. Magnus effect) on the dispersion process was quantified by mixing parameters.     

On thermal runaway and local endothermic/exothermic reactions during flash sintering of ceramic nanoparticles

Numerical analysis of the heat balance at the flash event during flash sintering of granular ceramic nanoparticles was performed assuming continuum solid state as well as simultaneous surface softening/liquid formation and current percolation through the nanoparticle contacts. Assuming inter-particle radiations in the specimen volume, the electric Joule heat generated at the nanoparticle contacts partially lost by radiation from the specimen external surfaces. Considering the thermal effects due to rapid heating rate and free-molecular heat conduction regime, high-temperature gradients between the nanoparticle surfaces and the surrounding gas were developed. The attractive capillary forces, induced by the particle surface softening/liquid at the percolation threshold, lead to rapid rearrangement and densification of the nanoparticles. The excess Joule heat, already at the flash event, suffices the excess internal heat that is necessary for partial or full melting. Particle surface softening/liquid formation is a transient process, hence followed by crystallization immediate after the nanoparticle rearrangement. Thermal runaway is associated with local surface softening/melting and its solidification.     

Multiscale modeling of solid propellants: From particle packing to failure

We present a theoretical and computational framework for modeling the multiscale constitutive behavior of highly filled elastomers, such as solid propellants and other energetic materials. Special emphasis is placed on the effect of the particle debonding or dewetting process taking place at the microscale and on the macroscopic constitutive response. The microscale is characterized by a periodic unit cell, which contains a set of hard particles (such as ammonium perchlorate for AP-based propellants) dispersed in an elastomeric binder. The unit cell is created using a packing algorithm that treats the particles as spheres or discs, enabling us to generate packs which match the size distribution and volume fraction of actual propellants. A novel technique is introduced to characterize the pack geometry in a way suitable for meshing, allowing for the creation of high-quality periodic meshes with refinement zones in the regions of interest. The proposed numerical multiscale framework, based on the mathematical theory of homogenization, is capable of predicting the complex, heterogeneous stress and strain fields associated, at the microscale, with the nucleation and propagation of damage along the particle–matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples involving simple unit cells are presented to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes.     

Effect of the particle size ratio on the structural properties of granular mixtures with discrete particle size distribution

In this study, the discrete element method was used to examine the structural properties and geometric anisotropy of polydisperse granular packings with discrete uniform particle size distributions. Confined uniaxial compression was applied to granular mixtures with different particle size fractions. The particle size fraction (class) was defined as the fraction of the sample composed of particles with a certain size. The threshold value of number of particle size fractions (i.e., the value above which structural properties of assemblies remain constant) was determined. The effect of heterogeneity in particle size on the critical value of number of particle size fractions was investigated for packings with different ratios between diameters of the largest and smallest grains. The threshold number of particle size classes decreased from five to three as the diameter ratio between the largest and smallest grains increased. Regardless of the diameter ratio, the critical number of particle size fractions (above which the packing density and coordination number of the granular mixtures remained constant) was determined to be five. The study has also shown an increase in packing density of binary mixtures with particle size ratio increasing up to 2.5, which was followed by decrease in density of mixtures with larger particle size ratios, which has not so far been reported in the literature.