Showing papers in "Granular Matter in 2013"

Generating realistic 3D sand particles using Fourier descriptors

Abstract: This paper presents a novel method of generation of random realistic sand grains for use in three dimensional (3D) DEM simulations. Based on the concept of Fourier descriptors for sand grains proposed recently by the same authors, we first randomly generate three 2D contours of cross-section for a real sand particle in three orthogonal planes, and then develop a morphing technique to construct the external 3D surface of the particle to match these cross-sections. The proposed method is examined by application to the generation of six sands reported in the literature using the Fourier spectrums available for these sands. We show that with a proper correction on the smoothness and roundness of the orthogonal projection calibrated from the six sands, the method can generate fairly consistent results as compared to the real sands. Further validation of the proposed method on another three sands shows satisfactory performance. The advantages and limitations of the method, as well as relevant future applications of the work to granular material modelling are discussed.

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

Abstract: 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.

Polyhedral particles for the discrete element method

Abstract: The geometry of convex polyhedra is described by a set of half spaces. This geometry representation is used in the discrete element method to model polyhedral particles. An algorithm for contact detection and the calculation of the interaction forces for these particles is presented. Finally the presented model is exemplified by simulating the particle flow through a hopper.

A discrete element analysis of elastic properties of granular materials

Abstract: 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.

Dependence of shape on particle size for a crushed rock railway ballast

Abstract: Laboratory testing of railway ballast poses practical difficulties because the particle size is often too large for most standard apparatus. There are therefore advantages in developing a scaled material whose behavior is representative of the full size material. A first stage in validating such an approach is to investigate whether the particle shape is affected by the change in scale. This paper sets out methods for evaluating form and roundness (aspects of shape) and proposes a new measure for evaluating roundness, termed ellipseness. These methods are then applied to a crushed rock railway ballast over a range of particle sizes. Statistical analysis demonstrates a measurable variation in the distributions of form and roundness with particle size over a range of sieve intervals, although the differences are slight and do not necessarily rule out the use of a scaled material for investigating the factors influencing macro mechanical behavior.

Dynamic simulation of particle packing influenced by size, aspect ratio and surface energy

Abstract: The multi-sphere method and JKR model are used in the discrete element method simulation to investigate the effect of the particle size, aspect ratios, and cohesiveness on the packing structure, characterized by porosity, radial distribution function (RDF), coordination number and contact geometry. In the absence of cohesive force, the porosity is nearly invariable with fixed aspect ratio, regardless of the size of the particles. In contrast, as surface energy increases, the porosity increases with decreasing particle size and increasing aspect ratio. The RDF results show that the number of peaks for different aspect ratios changes and show trends similar to the relaxation algorithm, expected for the finer particles. In the case of finer, cohesive particles, the most novel outcome of contact analysis is the existence of single contact, attributed to the formation of a cage structure, which has not been previously reported. The peak position and the width of the contact distributions are affected by higher surface energy because fewer contacts are required to achieve the mechanical equilibrium. Another interesting observation is that higher porosity does not always imply fewer contacts for particles with non-zero aspect ratios and high surface energies. The analysis of the distribution of the contact vector angles is found to better explain increased porosity in spite of higher coordination numbers. The results presented shed light on the packing density and structure, revealing features not easily discerned via experiments, and confirming the important role of the cohesion and aspect ratio in packing.

Breakage of an artificial crushable material under loading

Abstract: The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percentage of fine material to increase. It follows that the frictional properties of the material and the critical states are modified as a consequence of the changes in grain size distribution and the available range of packing densities. This paper illustrates an extended experimental investigation of the evolution of the grading of an artificial granular material, consisting of crushed expanded clay pellets under different loading conditions. The changes of grading of the material after isotropic, one-dimensional and constant mean effective stress triaxial compression were described using a single parameter based on the ratio of the areas under the current and an ultimate cumulative particle size distribution, which were both assumed to be consistent with self similar grading with varying fractal dimension. Relative breakage was related to the total work input for unit of volume. For poorly graded samples, the observed maximum rate of breakage is practically independent of initial uniformity. Further experiments at higher confining stress are required to investigate the mechanics of breakage of better graded samples.

Discrete modelling results of a direct shear test for granular materials versus FE results

Abstract: The intention of this paper is to present a comparison of the results of discrete element and finite element simulations of a simple shear test for medium dense cohesionless sand. Such a comparison may provide useful information on the limitations and possible advantages of micro-polar continuum models for granular media as compared with discrete element models. To simulate the discrete nature of sand at the micro-level during shearing, the 3D discrete open-source model YADE developed at Grenoble University was used. Contact moments at spheres were assumed to capture the influence of force eccentricities due to grain roughness. Attention was paid to some micro-structural events (such as vortices, force chains, vortex structures, local void ratio fluctuations) appearing in a shear zone and kinetic, elastic and dissipated energies in granular specimen. The results of the discrete element simulations were compared with the corresponding finite element (FE) solutions based on a micro-polar hypoplastic constitutive model for granular material. A satisfactory agreement between discrete and FE results was achieved. Advantages and disadvantages of both approaches are outlined.

An investigation on loose cemented granular materials via DEM analyses

Abstract: This paper presents the results of a numerical study carried out by 2D discrete element method analyses on the mechanical behavior and strain localization of loose cemented granular materials. Bonds between particles were modeled in order to replicate the mechanical behavior observed in a series of laboratory tests performed on pairs of glued aluminum rods which can fail either in tension or shear (Jiang et al. in Mech Mater 55:1–15, 2012). This bond model was implemented in a DEM code and a series of biaxial compression tests employing lateral flexible boundaries were performed. The influence of bond strength and confinement levels on the mechanical behavior and on the onset of shear bands and their propagation within the specimens were investigated. Comparisons were also drawn with other bond models from the literature. A new dimensionless parameter incorporating the effects of both bond strength and confining pressure, called BS, was defined. The simulations show that shear strength and also dilation increase with the level of bond strength. It was found out that for increasing bond strength, shear bands become thinner and oriented along directions with a higher angle over the horizontal. It also emerged that the onset of localization coincided with the occurrence of bond breakages concentrated in some zones of the specimens. The occurrence of strain localization was associated with a concentration of bonds failing in tension.

DEM simulations of the small strain stiffness of granular soils: effect of stress ratio

Abstract: DEM (discrete element method) simulations are carried out to evaluate the small strain stiffness (i.e. Young’s modulus and shear modulus) of a granular random packing with focus on the effect of stress ratio (SR). The results show that the Young’s modulus in a given direction generally depends on the stress component in that direction. The Young’s modulus normalized by the related stress component remains nearly constant when SR is less than a threshold value $$SR_\mathrm{th}$$ . When SR is larger than $$SR_\mathrm{th}$$ , the normalized Young’s modulus decreases, particularly in the minor principle stress direction. Moreover, the Young’s modulus during unloading is always smaller than the one during loading at the same stress state, which indicates that the microstructure of the specimen has been modified by the historical shearing process. The shear modulus mainly depends on the mean effective stress and shows similar evolution trend as the Young’s modulus. This study finds that the macroscopic stiffness of the specimen is closely related to the evolutions of particle contact number and contact force during shearing. When SR is less than $$SR_\mathrm{th}$$ , the specimen only adjusts the distribution of contact forces to resist the external load, without any apparent change of contact number. When SR is larger than $$SR_\mathrm{th}$$ , however, the specimen has to adjust both contact number and contact forces to resist the external load. The study also illustrates that there is a good relationship between the macroscopic stiffness anisotropy and fabric anisotropy, and therefore the stiffness anisotropy may be used as an indicator of fabric anisotropy.

Full 3D investigation and characterisation of capillary collapse of a loose unsaturated sand using X-ray CT

Abstract: The aim of this paper is to characterise in 3D the capillary collapse phenomenon using X-ray Computed Tomography (X-ray CT) during water infiltration into a partially saturated soil To understand the mechanisms leading to capillary collapse, we progressivelly saturated a specimen of sand by controlling the water pressure using the negative water column technique During this imbibition process, we followed the granular structure using X-ray CT The microstructure was analysed to assess the volume of water filling the pores and deformation of the granular skeleton using Volumetric Digital Image Correlation tools Matheron’s granulometry was used in parallel to characterize the initial microstructure and its evolution during the imbibition We show that the collapse phenomenon can occur in a clean sand and can be controlled continuously with the negative water column technique The volume change of the specimen at local scale started at a particular water content which coincided with the coalescence of capillary bridges between grain clusters Gravity effects leading to a non-negligible gradient of the hydrostatic pressure along the specimen’s height were observed and induced a vertical gradient of strain Localisation of the vertical strain on conical surfaces and of the volumetric strain and water content at the bottom corner of the specimen appeared during the imbibition process These localisations are thought to be due to an inhomogeneity of the initial density or/and an effect of cell walls facilitating the sliding of grains and the provision of water along preferential paths However, in spite of those localisations, macroscopic measurements at the scale of the sample were representative of the local behaviour of the unsaturated sand

Force analysis of clogging arches in a silo

Abstract: In this work, we examine a quasi-2D silo that clogs due to the spontaneous formation of stable arches. We validate a numerical scheme comparing the morphology of clogging arches with previous experimental findings. Additionally, we inspect the forces that act on particles, both on those in the bulk of the silo as well as those belonging to the arches formed above the outlet. In the silo, we have found that normal forces are higher close to the wall, in contrast to the central part of the silo, where normal forces are notably lower. Besides, it is revealed that normal forces on particles belonging to the clogging arches are significantly larger than in their surroundings. In a particle of the arch, the magnitude of the force strongly depends on the angle subtended from its center to the contact points with its two neighbors in the arch. Indeed, for angles exceeding \(180^{\circ }\), the larger the angle, the lower the normal force and the higher the tangential one. On the contrary, for smaller angles the behavior is reversed, so the normal forces increase with the angle. Finally, we present a comparison of the normal and tangential force distributions for the particles within the arch and in the bulk. All this shows the special nature of the forces developed in clogging arches, which suggests that direct extrapolations of bulk properties should not be taken for granted.

Experimental and numerical determination of mechanical properties of polygonal wood particles and their flow analysis in silos

Abstract: Responding to a lack in the literature, mechanical properties of polygonal wood particles are determined for use in a discrete element model (DEM) for flow analysis in silos, and some methods are proposed for determining such parameters. The parameters arrived at here have also formed part of the input to the SPOLY software, developed in-house to compute the DEM model with spheropolyhedron elements. The model is validated using a 2D physical model, where “prismatic” particles with polygonal cross sections are placed inside a silo with variable aperture and hopper angle. Validation includes comparison of flow-rates computed by SPOLY, displacement profiles, and clogging thresholds with experimental results. The good agreement that emerges will encourage future use of miniature triaxial tests, grain-surface profilometry, inclined slope tests, and numerical analysis of the intragranular stresses—toward a direct construction of the contact-deformation relations required in realistic DEM modelling of particle flow with angular-shaped particles.

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

Abstract: 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.

The effect of liquids on radial segregation of granular mixtures in rotating drums

Abstract: The presence of liquids can significantly affect the dynamics of granular flow. This paper investigates the effect of liquids on radial segregation of granular mixture in a rotating drum using the discrete element method. The wet granular mixture, due to differences in particle size and density, segregates in a similar way to that of dry particles: lighter/larger particles move to the periphery of the bed while heavier/smaller particles stay in the centre. An index based on the variance of local concentration of one type of particles was proposed to measure the degree of segregation. While the liquid induced capillary force slows down the segregation process, its effect on the final state is more complicated: small cohesion shows no or even positive effect on segregation while high cohesion significantly reduces particle segregation. The effect can be explained by the change of flow regimes and the competing effects of mixing and segregation (un-mixing) in particle flow which are both reduced by the interparticle cohesion. A diagram is generated to describe the combined effect of particle size and density on segregation of wet particles. A theory is adopted to predict the segregation of particles under different density/size ratios.

Influence of the gravity on the discharge of a silo

Abstract: We performed a series of experiments to investigate the flow of an assembly of non-cohesive spherical grains in both high and low gravity conditions (i.e. above and under the Earth’s gravity). In high gravity conditions, we studied the flow of glass beads out of a cylindrical silo and the flow of metallic beads out of a vertical Hele-Shaw rectangular silo. Both silos were loaded in one of the gondolas of the large diameter centrifuge facility (located at ESTEC) in which an apparent gravity up to 20 times the Earth’s gravity can be established. To simulate low gravity conditions, we submitted a horizontal monolayer of metallic beads to the centrifuge force of a small rotation device (located at University of Liege). The influences of both gravity and aperture size on the mass flow were analysed in these various conditions. For the three systems (cylindrical silo, the Hele-shaw silo and the monolayer of beads), we demonstrated that (i) the square root scaling of the gravity found by Beverloo is relevant and (ii) the critical aperture size below which the flow is jammed does not significantly increase with the apparent gravity. Moreover, we studied in more details the Hele-Shaw silo in high gravity because this configuration allowed to determine local properties of the flow at the level of the aperture. We measured the velocity profiles and the packing fraction profiles for the various aperture sizes and apparent high gravities. We demonstrate the existence of a slip length for the flow at the level of the aperture. This later fact seems to result from the geometrical configuration of the silo.

A simple distinct element modeling of the mechanical behavior of methane hydrate-bearing sediments in deep seabed

Abstract: The study on the mechanical behavior of methane hydrate-bearing sediments (HBS) in deep seabed is of great significance for the safe exploitation of methane hydrate in the future. Recent studies have shown that the mechanical behavior of HBS is significantly influenced by methane hydrate since it leads to cementation among soil grains. For better understanding its microscopic mechanical mechanism, this paper presents a simple numerical model of HBS using the distinct element method (DEM). First, a set of tests on two bonded aluminum rods were performed under different loading paths with a specially designed apparatus. Then, a simple bond contact model was proposed based on the experimental data and implemented into our two-dimensional DEM code, NS2D. Finally, a series of drained biaxial compression tests under different confining stresses on HBS samples with different bond strengths, which are used to represent different methane hydrate saturations \((S_{\mathrm{MH}})\), were carried out with this code. By comparing the results of numerical simulations with the experimental data obtained from triaxial compression tests, the study shows that the DEM incorporating the new bond contact model is capable of capturing the main mechanical characteristics of HBS such as the strain softening and dilation. And it can also capture that (a) the peak shear strength increases as \(S_{\mathrm{MH}}\) or the confining stress increases, while the dilation increases as \(S_{\mathrm{MH}}\) increases or the confining stress decreases; (b) both the cohesion and friction angle increase with the increasing of \(S_{\mathrm{MH}}\), but the influence of \(S_{\mathrm{MH}}\) on the cohesion is much more significant than on the friction angle.

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

Abstract: 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 TeX scales inversely proportional to the inertial number TeX, for all shear rates. On the contrary, in the dry case, an intermediate scaling regime inversely quadratic in TeX is observed for moderate shear rates. In the simulations, both scaling regimes are found for dry and wet granular material as well.

Wave propagation in elasto-plastic granular systems

Abstract: 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.

Micro-scale modeling of anisotropy effects on undrained behavior of granular soils

Abstract: This paper presents a micro-scale modeling of fabric anisotropy effects on the mechanical behavior of granular assembly under undrained conditions using discrete element method. The initial fabrics of the numerical samples engendered from the deposition under gravity are measured, quantified and compared, where the gravitational field can be applied in different directions to generate varying anisotropy orientations. The samples are sheared under undrained biaxial compression, and identical testing conditions are applied, with samples having nearly the same anisotropy intensities, but with different anisotropy directions. The macroscopic behaviors are discussed for the samples, such as the dilatancy characteristics and responses at the critical state. And the associated microstructure changes are further examined, in terms of the variables in the particulate scale, with the focus on the fabric evolution up to a large deformation reaching the critical state. The numerical analysis results compare reasonably well with available experimental data. It is also observed that at critical state, in addition to the requirements by classical critical state theory, a unique fabric structure has also been developed, and might be independent of its initial fabric. This observation is coincided with the recent theoretical achievement of anisotropic critical state theory. Finally, a general framework is introduced for quantifying and modeling the anisotropy effects.

Liquid migration in sheared unsaturated granular media

Abstract: We show how liquid migrates in sheared unsaturated granular media using a grain scale model for capillary bridges. Liquid is redistributed to neighboring contacts after rupture of individual capillary bridges leading to redistribution of liquid on large scales. The liquid profile evolution coincides with a recently developed continuum description for liquid migration in shear bands. The velocity profiles which are linked to the migration of liquid as well as the density profiles of wet and dry granular media are studied.

Stick-slip behaviour of model granular materials in drained triaxial compression

Abstract: Drained triaxial axisymmetric compression tests are performed on water-saturated short cylindrical samples of nearly monodisperse glass beads, initially assembled in a loose state by a moist tamping technique. Both deviator stress \(q\) and volumetric strain \(\epsilon _v\), measured as functions of axial strain \(\epsilon _a\), for different strain rates, are affected by stick-slip events of very large amplitude, while the classical behavior of loose, contractant granular assemblies, approaching the critical state for large \(\epsilon _a\), corresponds to the upper envelop of the stress-strain behaviour. Those events consist in \((i)\) a very fast (slip) part in which a drop of \(q\) coincides with a jump of \(\epsilon _v\) (contraction), while loss of control of \(\epsilon _a\) and generation of pore pressure signal a dynamic collapse of the material structure triggered by an instability; and then \((ii)\) a quasi-static (stick) part in which the sample regains its strength and, over a short strain interval, behaves similarly to a denser system that dilates before reaching its critical state. A unique stress-dilatancy relation applies to all stick-slip events. Apparent internal friction angles and effects of strain rate and confining pressure are discussed, and it is argued that stick-slip instabilities originate in physico-chemical aging phenomena coupled to contact mechanics.

Evolution of ultrasonic velocity and dynamic elastic moduli with shear strain in granular layers

Abstract: Ultrasonic wave transmission has been used to investigate processes that influence frictional strength, strain localization, fabric development, porosity evolution, and friction constitutive properties in granular materials under a wide range of conditions. We present results from a novel technique using ultrasonic wave propagation to observe the evolution of elastic properties during shear in laboratory experiments conducted at stresses applicable to tectonic faults in Earth’s crust. Elastic properties were measured continuously during loading, compaction, and subsequent shear using piezoelectric transducers fixed within shear forcing blocks in the double-direct-shear configuration. We report high-fidelity measurements of elastic wave properties for normal stresses up to 20 MPa and shear strains up to 500 % in layers of granular quartz, smectite clay, and a quartz-clay mixture. Layers were 0.1–1 cm thick and had nominal contact area of \(5 \mathrm{cm} \!\times \! 5 \mathrm{cm}\). We investigate relationships among frictional strength, granular layer thickness, and ultrasonic wave velocity and amplitude as a function of shear strain and normal stress. For layers of granular quartz, P-wave velocity and amplitude decrease by 20–70 % after a shear strain of 0.5. We find that P-wave velocity increases upon application of shear load for layers of pure clay and for the quartz-clay mixture. The P-wave amplitude of pure clay and quart-clay mixtures first decreases by \(\sim \)50 and 30 %, respectively, and then increases with additional shear strain. Changes in P-wave speed and wave amplitude result from changes in grain contact stiffness, crack density and disruption of granular force chains. Our data indicate that sample dilation and shear localization influence acoustic velocity and amplitude during granular shear.

Energy dissipation from particulate systems undergoing a single particle crushing event

Abstract: The energy dissipation from particulate systems undergoing particle crushing is often assumed to scale solely with the increase in surface area, irrespective of the strain energy stored in the surrounding media. By analyzing idealized particulate systems undergoing a single particle crushing event, this assumption is questioned and proven invalid. Two analysis types are considered. One represents the particulate system as an idealized assembly and then represents particle contact forces as members belonging to a periodic lattice. The other treats the particulate system as an elastic continuum. Different sizes of two and three dimensional particulate systems are considered, as well as isotropic and anisotropic confining stress states. The overall dissipation is shown to depend strongly on the dimensionality of the system, the anisotropy of the confining stress state and the elastic properties of the system. The ratio between dissipation due to stored elastic energy redistribution from surrounding media and dissipation by fracture surface energy is calculated. The ratio is found to diminish with the increasing dimensionality of the system. It is also shown that this ratio is independent of the fracture surface energy of the material. The most relevant analysis of a three dimensional particulate system to accurately estimate this ratio seems to be a one dimensional analysis of the force chain containing the most heavily loaded particles.

Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction

Abstract: The three-dimensional X-ray diffraction (3DXRD) nondestructive technique was used to measure lattice strains within individual sand particles subjected to compressive loading. Three experiments were conducted on similar single columns of silica sand particles with particle sizes between 0.595 and 0.841 mm. In each experiment, three sand particles were placed inside an acrylic mold with an inner diameter of 1 mm. Multiple in situ 3DXRD scans were acquired for each sand column as compressive load was increased. The volume-averaged lattice strain tensor was calculated for each sand particle. In addition, particle orientation and volumetric strain were calculated for individual sand particles. The axial normal strain $$\upvarepsilon _\mathrm{zz}$$ exhibited a linear response in the range of 0 to $$10^{-3}$$ when the applied compressive axial load (F) increased from 0 to $$\sim $$ 30 N when one particle in the sand column fractured. Stress tensor of individual particles was calculated from the acquired lattice strain measurements and elastic constants of silica sand that were reported in the literature. To the best of our knowledge, there have been no reported experimental measurements of the lattice strain tensor measurements within individual silica sand particles. The quantitative measurements reported in this paper at the particle level are very valuable for developing, validating or calibrating micromechanics-based finite element and discrete element models to predict the constitutive behavior of granular materials. 3DXRD represents an exciting new non-destructive technique to directly measure constitutive behavior at the scale of individual particles.

DEM analysis of particle adhesion during powder mixing for dry powder inhaler formulation development

Abstract: Understanding the adhesive interactions between active pharmaceutical ingredient (API) particles and carrier particles in dry powder inhalers (DPIs) is critical for the development of formulations and process design. In the current study, a discrete element method, which accounts for particle adhesion, is employed to investigate the attachment processes in DPIs. A critical velocity criterion is proposed to determine the lowest impact velocity at which two elastic autoadhesive spherical particles will rebound from each other during impact. Furthermore, the process of fine API particles adhering to a large carrier in a vibrating container is investigated. It was found that there are optimal amplitude and frequency for the vibration velocity that can maximise the number of particles contacting with the carrier (i.e. the contact number). The impact number and detachment number during the vibration process both increase with increasing vibration amplitude and frequency while the sticking efficiency decreases as the amplitude and frequency are increased.

Characterization of fluctuations in granular hopper flow

Abstract: We present a 2D discrete modelling of sand flow through a hopper using realistic grain shapes. A post-processing method is used to assess the local fluctuations in terms of void ratio, coordination number, velocity magnitude, and mean stress. The characteristics of fluctuations associated with the four considered quantities along the vertical axis of the hopper and across the entire hopper are carefully examined. The flow fluctuations for coordination number, velocity magnitude and mean stress are all found to take the form of radial waves originating from the lower centre of the hopper and propagating in the opposite direction of the granular flow. Quantitative characteristics of these waves (shape, amplitude, frequency, velocity, etc.) are identified. The fluctuations in void ratio however are not supportive of the observation of density waves in the granular flow as mentioned in some experiments. The possible reasons for this apparent contradiction are discussed, as well as possible extensions of this work.

Contact forces of polyhedral particles in discrete element method

Abstract: A general contact force law for arbitrarily shaped bodies is presented. At first an advanced contact force law is derived from the well know Hertz contact law. The obtained formulation of the Hertz contact law can be applied to the contact of arbitrarily shaped bodies. In a second step this contact model is applied to the contacts among polyhedral particles. The results are compared to finite element simulations. The model is extended by terms for damping and friction. The behaviour of the damping and friction model are demonstrated with simple examples. The force law is then implemented in the discrete element method (DEM). The application of this DEM is demonstrated by a simulation of the particle movement in a mixer.

Study of capillary interaction between two grains: a new experimental device with suction control

Abstract: We investigated the behavior of a water liquid bridge formed between two grains. We mainly focused on tensile tests with suction control (capillary pressure). Theoretical and experimental studies are compared. A new experimental device involving suction control of the liquid bridge was developed specifically for this kind of test. Most of the liquid bridge variables and characteristics were measured by image analysis (gorge radius, volume, contact angles, filling angles). Capillary force was measured by differential weighting. Experimental conditions allows us to avoid viscous effects. Our experimental results were close to Young-Laplace equation solutions. The “gorge method”, commonly used for calculating the capillary force, was also validated by our experiments. Liquid bridge rupture was studied and a new rupture criterion is proposed. This criterion depends on the grain radius, contact angle, surface tension and suction and was in agreement with the experimental results.

Radial segregation of multi-component granular media in a rotating tumbler

Abstract: Segregation and mixing of granular mixtures are important to the minerals, food processing and pharmaceuticals industry to name just a few. It has recently been demonstrated that a rotating tumbler is a suitable device for separating out binary granular mixtures, i.e. mixtures composed of only two different particle types. However, most practical granular mixtures are composed of multi-component particle types. We therefore study the capability of this rotating tumbler to segregate mixtures composed of more than two components where the particles differ either in size or density. The general pattern of segregation involves the formation of an inner core of smallest or densest particles followed, at larger radii, by the next largest or densest particle type and so-on in an onion-like pattern. In the mixtures where particles differ in size we always get relatively pure inner cores of the smallest particles, while the other regions are less segregated. On the other hand for mixtures whose particles differ in density we get a relatively pure outer region (adjacent to cylinder wall) consisting of the least dense particles while the other regions are less segregated. We attempt to relate the simulation results to phenomenological theory and find that size segregation in a specific multi-component mixture can be suitably described by a recent theoretical model.