Granular Packing Research Articles

Confinement controls the creep rate in soft granular packings.

Flow in soft materials encompasses a wide range of viscous, plastic and elastic phenomena which provide challenges to modelling at the microscopic level. To create a controlled flow, we perform falling ball viscometry tests on packings of soft, frictionless hydrogel spheres. Systematic creep flow is found when a controlled driving stress is applied to a sinking sphere embedded in a packing. Here, we take the novel approach of applying an additional global confinement stress to the packing using an external load. This has enabled us to identify two distinct creep regimes. When confinement stress is small, the creep rate is independent of the load imposed. For larger confinement stresses, we find that the creep rate is set by the mechanical load acting on the packing. In the latter regime, the creep rate depends exponentially on the imposed stress. We can combine the two regimes via a rescaling onto a master curve, capturing the creep rate over five orders of magnitude. Our results indicate that bulk creep phenomena in these soft materials can be subtly controlled using an external mechanical force.

Effects of cementing matrix characteristics and particle size on the adhesion rule and mechanical properties of cemented granular materials

The process of filling self-compacting cement grout (SCCG) into granular packing without disturbing the granular skeleton culminates in the formation of a well-defined cemented granular materials (CGMs). The inherent attributes of both the cementing matrix and granular packing critically dictate the adhesion behavior and mechanical performance of CGMs. A succession of cement grout flow tests was conducted to elucidate the influence of particle size and the SCCG flowability on SCCG adhesion mechanism within granular packing. Furthermore, the influence of particle size and the cementing matrix volume on the mechanical characteristics of CGMs was scrutinized via uniaxial compressive testing. The results illuminate that the adhesion behavior of SCCG within granular packing is predominantly dependent on the yield stress of SCCG and the average particle size. Additionally, it is established that the peak strength of CGMs is intimately intertwined with the cementing matrix volume and the average particle size, as corroborated by a substantial aggregate of 135 uniaxial compression tests.

Reversible-to-irreversible transition of colloidal polycrystals under cyclic athermal quasistatic deformation.

Cyclic loading on granular packings and amorphous media exhibits a transition from reversible elastic behavior to irreversible plasticity. The present study compares the irreversibility transition and microscopic details of colloidal polycrystals under oscillatory tensile-compressive and shear strain. Under both modes, the systems exhibit a reversible to irreversible transition. However, the strain amplitude at which the transition is observed is larger in the shear strain than in the tensile-compressive mode. The threshold strain amplitude is confirmed by analyzing the dynamical properties, such as mobility and atomic strain (von Mises shear strain and the volumetric strain). The structural changes are quantified using a hexatic order parameter. Under both modes of deformation, dislocations and grain boundaries in polycrystals disappear, and monocrystals are formed. We also recognize the dislocation motion through grains. The key difference is that strain accumulates diagonally in oscillatory tensile-compressive deformation, whereas in shear deformation, strain accumulation is along the x or y axis.

The force and dynamic response of low-velocity projectile impact into 3D dense wet granular media

The presence of liquid bridges between particles in a wet granular media gives rise to capillary forces at the microscopic scale that dramatically alters the material's microstructure and macroscopic responses. Previous experimental studies show significant differences in the penetration depth of the projectile into assemblies of dry or wet particles. Still, there is a lack of fundamental understanding of the difference induced by the presence of liquid bridges in dynamic regimes. In this study, the contact model parameters of wet glass beads are calibrated employing the angle of repose tests and cylinder lifting tests, and a series of three-dimensional discrete element method simulations of spheres impact into wet granular packings are conducted. The dynamic characteristics of the projectile are obtained numerically and found to be in good agreement with the experimental data. The analyses indicate that the final penetration depth in the wet granular media is linearly related to the initial velocity and has a power function relationship with the impact energy. The generalized Poncelet law is suitable for wet granular materials, but the presence of liquid significantly affects the values of the parameters. There is a velocity “stagnation zone” at the initial stage of the wet granular impact, and the final penetration depth and the duration interaction time are smaller than that of the dry case. The difference can be attributed to the resistance evolution of the projectile exerted by particles and gives the parameter scaling law of the peak impact force. Further, a macro-micro transition technique is employed to characterize the velocity field, pressure field, and stress field inside the wet granular media and the spatial distribution is quantified based on stress theory.

Identifying microscopic factors that influence ductility in disordered solids

There are empirical strategies for tuning the degree of strain localization in disordered solids, but they are system-specific and no theoretical framework explains their effectiveness or limitations. Here, we study three model disordered solids: a simulated atomic glass, an experimental granular packing, and a simulated polymer glass. We tune each system using a different strategy to exhibit two different degrees of strain localization. In tandem, we construct structuro-elastoplastic (StEP) models, which reduce descriptions of the systems to a few microscopic features that control strain localization, using a machine learning-based descriptor, softness, to represent the stability of the disordered local structure. The models are based on calculated correlations of softness and rearrangements. Without additional parameters, the models exhibit semiquantitative agreement with observed stress-strain curves and softness statistics for all systems studied. Moreover, the StEP models reveal that initial structure, the near-field effect of rearrangements on local structure, and rearrangement size, respectively, are responsible for the changes in ductility observed in the three systems. Thus, StEP models provide microscopic understanding of how strain localization depends on the interplay of structure, plasticity, and elasticity.

Analysis of the influence of excess cement paste content on the compression strength of UHPC

This research aimed to propose a rational method for dosing ultra-high performance concretes based on the association of three approaches: the definition of the ideal silica content, the use of the minimum paste volume, and the incorporation of fine basalt artificial sand. Through the combination of experimental methods and granular packing models, a robust experimental program consisting of eight steps was developed, aiming to obtain different compositions of ultra-high performance concretes, with self-compacting characteristics and compressive strength greater than 150 MPa at 28 days, after heat water treatment at 90°C. In addition, the influence of silica content, additional paste volume, different types of cure, test ages, and the addition of metallic fibers on the fluidity and strength of the composites were evaluated. Through the proposed method, the average strength of 186 MPa was achieved in the mix containing the minimum volume of paste, 484 kg∕m³ of cement, and 25% silica fume. The results obtained indicate that the proposed method tends to have the best proportion among the component materials, giving rise to traits that fit the international parameters that define the UHPC, but with reduced paste volumes and consumption of binders lower than those identified in the related literature. Through a rational, economic, and sustainable approach, which aims to optimize the use of higher-cost materials and minimize the use of scarce natural resources, the method contributes positively to the technological development of the sector.

Influence of the acrylamide-based monomer on the sintering of ceramics shaped by gelcasting

Alumina ceramics were prepared by gelcasting, based on an in-situ polymerization that promotes the formation of homogeneous green ceramic parts and allows the preparation of complex shapes and/or large-size ceramics. The influence of the monomer on the sintering behaviour of alumina pellets has been studied by considering three acrylamide-based monomers, i.e. acrylamide (AM), methacrylamide (MAM) and dimethylacrylamide (DMAA). Slurries with an alumina solid content of 50 vol% have been cast and pre-sintered pellets (1000 °C) with relative densities around 55% were obtained. These presintered pellets exhibit different granular packing, depending on the initial monomer used, as demonstrated by X-ray tomography, SEM and Hg porosimetry analyses. This results in significant differences in sintering behaviour, giving rise to very different final densities after 1 h sintering at 1530 °C: from 88% to 98%. This behaviour is described in terms of shrinkage rate, linked to the granular packing induced by the gelation process.

Physicochemical properties of starch in sodium chloride solutions and sucrose solutions: Importance of starch structure.

The influences of sodium chloride (NaCl)/sucrose on starch properties as affected by starch structural characteristics are little understood. In this study, the effects were observed in relation to the chain length distribution (from size exclusion chromatography) and granular packing (inferred through morphological observation and determination of swelling factor and paste transmittance) of starches. Adding NaCl/sucrose dramatically delayed the gelatinization of starch that had a high ratio of short-to-long amylopectin chains and had loose granular packing. The effects of NaCl on the viscoelasticity of gelatinizing starch were related to the flexibility of amylopectin internal structure. Effects of NaCl/sucrose on starch retrogradation varied with starch structure, co-solute concentration, and analytical method. The co-solute-induced changes in retrogradation were highly associated with amylose chain length distribution. Sucrose strengthened the weak network formed by short amylose chains, while the effect was not significant on amylose chains that were capable of forming strong networks.

Granular convergence as an iterated local map.

Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations encountered converges to a periodic sequence after sufficient shear cycles. Prior work modeled this evolution as the iteration of a pre-determined, random map from a set of discrete configurations into itself. Iterating such a map from a random starting point leads to similar periodic repetition. This work explores the effect of restricting the randomness of such maps in order to account for the local nature of the discrete events. The number of cycles needed for convergence shows similar statistical behavior to that of numerical granular experiments. The number of cycles in a repeating period behaves only qualitatively like these granular studies.

Anchoring Effect of an Obstacle in the Silo Unclogging Process.

Contrary to the proven beneficial role that placing an obstacle above a silo exit has in clogging prevention, we demonstrate that, when the system is gently shaken, this passive element has a twofold effect in the clogging destruction process. On one side, the obstacle eases the destruction of weak arches, a phenomenon that can be explained by the pressure screening that it causes in the outlet proximities. But on the other side, we discover that the obstacle presence leads to the development of a few very strong arches. These arches, which dominate in the heavy tailed distributions of unclogging times, correlate with configurations where the number of particles contacting the obstacle from below are higher than the average; hence suggesting that the obstacle acts as an anchoring point for the granular packing. This finding may help one to understand the ambiguous effect of obstacles in the bottleneck flow of other systems, such as pedestrians evacuating a room or active matter in general.

Grain-scale modeling of shear responses of dilative granular packings under stress path pertinent to rainfall-induced slope failures

Slope failures frequently occur under storm rainfall, for which the constant shear drained (CSD) stress path is more pertinent to the soil element underneath the slope surface. Soil mass in man-made slopes or other compacted slopes is often at medium-dense or even dense state. Evaluating the stability of such slopes entails a comprehensive understanding of the behavior of dilative granular packings under the CSD stress path. Here we use a robust grain-scale model to simulate responses of dilative granular packings along the CSD, constant-volume (CDCV), and conventional drained (CD) stress paths. We show that the behavior under the CSD stress path complies with the critical state theory at both macro- and micro-scale. When the second-order work becomes nonpositive, a substantial plastic strain starts to develop under the CSD loading, while a significant drop of shear strength happens along the CDCV stress path for medium-dense packing and along the CD stress path for dense packings. In these conditions, the second-order work vanishes at an almost identical stress ratio which marks the onset of strength reduction or large deformation, and such stress ratio is well correlated with the initial state parameter of the granular packing. Furthermore, we show that the CSD stress path drives an intensified fabric anisotropy and there exists a quantitative correlation between anisotropy parameters and mobilized shear strength.

Tessellated granular metamaterials with tunable elastic moduli

Most granular packings possess shear moduli (G) that increase with the applied external pressure, and bulk moduli (B) that increase or remain constant with pressure. This paper presents “tessellated” granular metamaterials for which both G and the ratio G/B decrease with increasing pressure. The granular metamaterials are made from flexible tessellations forming a ring of closed cells, each containing a small number of solid particles. For under-constrained tessellations, the dominant contributions to G and B are the particle–particle and particle–cell interactions. With specific particle configurations in the cells, we limit the number of possible particle rearrangements to achieve decreasing G as we increase the pressure difference between the inside and outside of the tessellation, leading to G/B≪1 at large pressures. We further study tessellated granular metamaterials with cells containing a single particle and many particles to determine the variables that control the mechanical response of particle-filled tessellations as a function of pressure.

Shear-induced anisotropy of effective thermal conductivity in granular packings

This work explores shear-induced anisotropy of the effective thermal conductivity (ETC) in granular packings when subjected to quasistatic shear deformation. The discrete element method is adopted to track the position, force, and contact condition of every particle in the packing during the shear process. The ETC of the packing at different shear strains is evaluated using the particle-resolved finite element method. The simulation results show that the anisotropy ratio of the ETC can reach 40% as the shear strain increases to 0.11. The increase of the anisotropy mainly results from the variation of the network formed by the contacts that exist in two consecutive shear steps. It is also proved that contacts with large contact radius and strong thermal conductance are preferentially aligned with the direction of the applied deformation. The non-uniform distribution of the contact radius and the preferential orientation of the contacts contribute to the anisotropy of the thermal conductivity. Finally, by grouping the contacts in a packing into sub-networks with either weak or strong contact, it is shown that the thermal conductivity anisotropy of a packing is mainly caused by strong contacts.

X-ray 3D imaging–based microunderstanding of granular mixtures: Stiffness enhancement by adding small fractions of soft particles

This research focuses on performing ultrasound propagation measurements and micro-X-ray computed tomography (µXRCT) imaging on prestressed granular packings prepared with biphasic mixtures of monodisperse glass and rubber particles at different compositions/fractions. Ultrasound experiments employing piezoelectric transducers, mounted in an oedometric cell (complementing earlier triaxial cell experiments), are used to excite and detect longitudinal ultrasound waves through randomly prepared mixtures of monodisperse stiff/soft particles. While the fraction of the soft particles is increasing linearly from zero, the effective macroscopic stiffness of the granular packings transits nonlinearly and nonmonotonically toward the soft limit, remarkably via an interesting stiffer regime for small rubber fractions between 0.1 ≲ ν ≲ 0.2. The contact network of dense packings, as accessed from µXRCT, plays a key role in understanding this phenomenon, considering the structure of the network, the chain length, the grain contacts, and the particle coordination. While the maximum stiffness is due to surprisingly shortened chains, the sudden drop in elastic stiffness of the mixture packings, at ν ≈ 0.4, is associated with chains of particles that include both glass and rubber particles (soft chains); for ν ≲ 0.3, the dominant chains include only glass particles (hard chains). At the drop, ν ≈ 0.4, the coordination number of glass and rubber networks is approximately four and three, respectively, i.e., neither of the networks are jammed, and the chains need to include particles from another species to propagate information.

Rainfall-induced flowslides of granular soil slopes: Insights from grain-scale modeling

Rainfall-induced flowslides in soil slopes remain one of the most destructive natural hazards. To prevent and mitigate the hazard requires a good understanding of soil behavior under the constant shear drained (CSD) stress path. This stress path differs from typical triaxial compression stress paths that have been extensively studied in soil laboratories. Here we present an attempt to explore various behaviors of loose granular packings along different stress paths and the associated micromechanical mechanisms using a robust grain-scale modeling technique. Through systematic simulations of the CSD, constant-volume (CDCV), and conventional drained (CD) shearing stress paths, we show that the behavior under the CSD stress path conforms to critical state concepts at both macro- and micro-scale. The evolutions of the stress ratio (q/p'), coordination number (Z), and fabric anisotropy (ac) along the CSD stress path are highly similar to those along the CD stress path. A substantial plastic strain tends to develop once the second-order work becomes nonpositive along the CSD stress path, while a dramatic drop of shear strength will occur at the vanishing of second-order work along the CDCV stress path. In both cases, the second-order work vanishes at an almost identical stress ratio, which demarcates the lower boundary of the potential instability zone in the stress space. We establish an explicit relationship between this stress ratio and the initial state parameter of the packing. The significance of this relationship lies in its applicability for both CSD and CDCV loading paths and its root in the critical state theory.

A combined SPH-DEM approach for extremely deformed granular packings: validation and compression tests

We present a novel smoothed particle hydrodynamics-discrete element method (SPH-DEM) approach for the simulation of deformable granular media. First, we show how the method converges to the analytical solution in a simple contact mechanics problem, namely the Hertz contact law for elastic spherical grains. Second, we analyze the evolution of a 2D packing of disks under uniaxial compression, displaying the evolution of key metrics of the packing such as the coordination number and the vertical stress. We show that the code produces data in quantitative agreement with what is known from literature. Finally, we demonstrate that our SPH-DEM coupling can be used to study packings of deformable grains from the onset of jamming to extremely compacted states, reaching packing fractions of ϕ≃0.995\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi \\simeq 0.995$$\\end{document}.

Sound characteristics of disordered granular disks: effects of contact damping

We investigate numerically the sound properties of disordered dense granular packings in two dimensions. Employing linear equations of motion and excluding contact changes from our simulations, we demonstrate time evolution of sinusoidal standing waves of granular disks. We varied the strength of normal and tangential viscous forces between the disks in contact to explore the dependence of sound characteristics such as dispersion relations, attenuation coefficients, and sound speeds on the contact damping. For small wave numbers, the dispersion relations and sound speeds of acoustic modes are quite insensitive to the damping. However, a small dip in the phase speed of the transverse mode decreases as the viscous force in normal direction increases. In addition, the dispersion relation of the rotational mode differs qualitatively from the theoretical prediction for granular crystals. Therefore, disordered configurations with energy dissipation play a prominent role in sound properties of granular materials. Furthermore, we report how attenuation coefficients depend on the contact damping and quantify how they differ from the prediction of lattice theory. These improved relations, based on our numerical results, can in future be compared to advanced theories and experiments.

Mix design method of granular packing for high performance concrete with natural pozzolans

This study presents an enhanced mix design method for High performance concrete (HPC) with Natural Pozzolans (NP) content that considers material packing theory. Seven HPC mixes with different NP replacement levels of 0, 5, 10, 15, 20, 25, 30% by volume were conducted to investigate the effect of NP on the rheological and mechanical properties of HPC. A basic water demand experiment was designed to obtain the granular packing and packing density of mortar. Furthermore, the equivalent packing density was defined and calibrated to represent the effect of NP, And the bilinear interpolation method was used to analyses the HPC properties. The results show that the relative accuracies of the improved method are higher than 15% to the initial method. The HPC mixtures with NP was also assessed and shown to be within the optimum area.

Structural transitions in jammed asymmetric bidisperse granular packings

We study the local structural changes along the jamming transitions in asymmetric bidisperse granular packings. The local structure of the packing is assessed by the contact orientational order, tilde{Q}_{ell }, that quantifies the contribution of each contact configuration (Large–Large, Small–Small, Large–Small, Small–Large) in the jammed structure. The partial values of tilde{Q}_{ell } are calculated with respect to known ordered lattices that are fixed by the size ratio, delta , of the particles. We find that the packing undergoes a structural transition at phi _J, manifested by a sudden jump in the partial tilde{Q}_{ell }. Each contact configuration contributes to the jammed structure in a different way, changing with delta and concentration of small particles, X_{textrm{S}}. The results show not only that the packing undergoes a structural change upon jamming, but also that bidisperse packings exhibit local HCP and FCC structures also found in monodisperse packings. This suggests that the jammed structure of bidisperse systems is inherently endowed with local structural order. These results are relevant in understanding how the arrangement of particles determines the strength of bidisperse granular packings.Graphic abstract

Roles of packing fraction, microscopic friction, and projectile spin in cratering by impact.

From small seeds falling from trees to asteroids colliding with planets and moons, the impact of projectiles onto granular targets occurs in nature at different scales. In this paper, we investigate open questions in the mechanics of granular cratering, in particular, the forces acting on the projectile and the roles of granular packing, grain-grain friction, and projectile spin. For that, we carried out discrete element method computations of the impact of solid projectiles on a cohesionless granular medium, where we varied the projectile and grain properties (diameter, density, friction, and packing fraction) for different available energies (within relatively small values). We found that a denser region forms below the projectile, pushing it back and causing its rebound by the end of its motion, and that solid friction affects considerably the crater morphology. Besides, we show that the penetration length increases with the initial spin of the projectile, and that differences in initial packing fractions can engender the diversity of scaling laws found in the literature. Finally, we propose an ad hoc scaling that collapsed our data for the penetration length and can perhaps unify existing correlations. Our results provide new insights into the formation of craters in granular matter.