Behavior Of Granular Materials Research Articles

Elasticity and rheology of auxetic granular metamaterials

The flowing, jamming, and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: A granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular metamaterials made from particles with a negative Poisson's ratio yield more easily and flow more smoothly than ordinary granular materials. We first create a collection of auxetic grains based on a re-entrant mechanism and show that each grain exhibits a negative Poisson's ratio regardless of the direction of compression. Interestingly, we find that the elastic and yielding properties are governed by the high compressibility of granular metamaterials: At a given confinement, they exhibit lower shear modulus, lower yield stress, and more frequent, smaller avalanches than materials made from ordinary grains. We further demonstrate that granular metamaterials promote flow in more complex confined geometries, such as intruder and hopper geometries, even when the packing contains only a fraction of auxetic grains. Moreover, auxetic granular metamaterials exhibit enhanced impact absorption. Our findings blur the boundary between complex fluids and metamaterials and could help in scenarios that involve process, transport, and reconfiguration of granular materials.

Viscoelastic material properties determine the contact mechanics of hydrogel spheres

Granular materials are ubiquitous in nature and industry; their mechanical behavior has been a subject of academic and engineering interest for centuries. One of the reasons for their rather complex mechanical behavior is that stresses exerted on a granular material propagate only through contacts between the grains. These contacts can change as the packing evolves. This makes any deformation and mechanical response from a granular packing a function of the nature of contacts between the grains and the material response of the material the grains are made of. We present a study in which we isolate the role of the grain material in the contact forces acting between two particles sliding past each other. By using hydrogel particles, we find that a viscoelastic material model, in which the shear modulus decays with time, coupled with a simple Coulomb friction model, captures the experimental results. The results suggest that particle material evolution itself may play a role in the collective behavior of granular materials.

Effects of intermediate principal stress on the granular material behavior under partial drainage conditions

Effects of intermediate principal stress on the granular material behavior under partial drainage conditions

Cementor: A toolbox to generate bio-cemented soils with specific microstructures

Bio-cemented soils can exhibit various types of microstructure depending on the relative position of the carbonate crystals with respect to the host granular skeleton. Different microstructures can have different effects on the mechanical and hydraulic responses of the material, hence it is important to develop the capacity to model these microstructures. The discrete element method (DEM) is a powerful numerical method for studying the mechanical behaviour of granular materials considering grain-scale features. This paper presents a toolbox that can be used to generate 3D DEM samples of bio-cemented soils with specific microstructures. It provides the flexibility of modelling bio-cemented soils with precipitates in the form of contact cementing, grain bridging and coating, and combinations of these distribution patterns. The algorithm is described in detail in this paper, and the impact of the precipitated carbonates on the soil microstructure is evaluated. The results indicate that carbonates precipitated in different distribution patterns affect the soil microstructure differently, suggesting the importance of modelling the microstructure of bio-cemented soils.

Experimental study on dynamic angle of repose formation: Effect of granular type and water content

The experiment of granular in rotating cylinder is a common experiment to study granular material behaviour. In this study, we investigate the effect of granular type and water content on the dynamic angle of repose in a rotating cylinder. Rice seed, mung bean, and sand are used as samples. Experimental results show each sample has a different dynamic angle of repose that is related to the shape of the sample. We also study the effect of the water content on the sand sample. The addition of water content has no significant effect on the dynamic angle of repose. This occurs because the water content used has passed the critical point.

A micromechanical model for estimating the shear modulus and damping ratio of loose sands under low stresses. Application to a Mars regolith simulant

The dynamic properties of loose sands under low stresses have been poorly investigated because of the higher order of magnitude of stress levels in terrestrial geotechnical structures. However, low densities and low stresses prevail in the sandy surface deposits of some other rocky planets, making low stress conditions relevant for extra-terrestrial soil mechanics. This is the case of Mars, on the surface of which a seismometer has been placed during the InSight mission. In this context, a dynamic shear rheometer was used to measure the shear modulus and damping ratio of a Martian regolith simulant under very low stresses to improve the interpretation of the InSight dataset on surface materials. This paper also revisits the grain contact stiffness and the overall modulus of a random packing of identical spheres, based on the Hertz-Mindlin contact theory. A micromechanical model accounting for the effects of both grain roughness and slipping in the soil degradation curve is proposed. The results of the model show a good agreement with experimental data, capturing the non-linear transition from low to high-shear strains. The model hence provides a new framework for a better understanding of the behaviour of granular materials in low gravity (extra-terrestrial) conditions.

Micro computed tomography images of capillary actions in rough and irregular granular materials

The present work investigates the effect of both surface roughness and particle morphology on the retention behaviour of granular materials via X-ray micro-computed tomography (µCT) observations. X-ray µCT images were taken on two types of spherical glass beads (i.e. smooth and rough) and two different sands (i.e. natural and roughened). Each sample was subjected to drainage and soaking paths consisting in a multiphase ‘static’ flow of potassium iodine (KI) brine (wetting phase) and dry air (non-wetting phase). Tomograms were obtained at different saturation states ranging from fully brine saturated to air dry conditions with 6.2 μm voxel size resolution. The data acquisition and pre-processing are here described while all data, a total of 48 tomograms, are made publicly available. The combined dataset offers new opportunities to study the influence of surface roughness and particle morphology on capillary actions as well as supporting validation of pore-scale models of multiphase flow in granular materials.

Understanding the interplay between particle shape, grading and sample density on the behaviour of granular assemblies: A DEM approach

This study investigates the interplay between particle shape, grading and initial sample density, three of the most important factors influencing the mechanical behaviour of sheared granular assemblies. Using the discrete element method (DEM), two-dimensional assemblies of varying initial sample density, particle aspect ratio, AR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AR$$\\end{document}, and coefficients of uniformity, Cu\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${C}_{u}$$\\end{document}, were prepared and subjected to drained biaxial shearing until the critical state was reached. We assessed the interplay between each of these parameters by evaluating whether the effect of any given parameter on a mechanical quantity is influenced by any other parameter. Our analyses show that the effect of some of these key parameters on mechanical response, can indeed be influenced by other key parameters. The effect of the particle AR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AR$$\\end{document} on the peak shear strength for the initially dense assemblies differs when compared with the medium-dense assemblies. The mechanical coordination number of the assemblies at the initial state correlates with the peak strength thereby explaining the interplay between particle AR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AR$$\\end{document} and initial sample density on the peak shear strength. The linear relationship established between strength and dilatancy for a combination of all assemblies studied suggests that the strength-dilatancy relationship is a unique characteristic of granular assemblies. The dilatancy of the assemblies correlates strongly with the amount of contacts lost during shearing. The interplays found between particle shape, grading and initial sample density in this study show that to develop robust constitutive models for the prediction of granular material behaviour, the effects of multiple factors must be considered.Graphic abstract

Discrete modelling of the mechanical response of Cuxhaven sand under shear and oedometric conditions using the rolling resistance contact model

The Distinct element method (DEM) is a promising approach to model the microscopic behaviour of granular materials, but the capability of the simulations to reproduce the mechanical response of real granular materials depends strongly on the contact model parameters utilized. The present study focuses on the calibration and validation of the rolling resistance linear model parameters for Cuxhaven sand based on the experimental results from triaxial and oedometer tests. A sensitivity analysis was conducted to explore the influence of contact model parameters on the sample preparation and the shear stage of triaxial tests. The influence of parameters like rolling resistance friction coefficient, inter-particle friction coefficient, effective modulus, and normal-to-shear stiffness ratio were investigated. For calibration of the DEM model, the input parameters were selected such that the simulations reproduce the macro mechanical characteristics like dilation angle, peak stress, and stiffness. The calibrated parameters were then validated by simulating a one-dimensional compression test. The results are in good agreement with the experiments, which proves the suitability of the calibrated parameters. In addition, the validated parameters were applied to investigate the mechanical behaviour including the evolution of contact force chains, non-coaxiality of principal stress and strain rate, and sample inhomogeneity during a simple shear test.

Exploring the role of fabric anisotropy in cyclic liquefaction resistance under non-hydrostatic consolidation: Insights from DEM analysis

This study investigates the cyclic liquefaction resistance of granular materials under non-hydrostatic consolidation using 3D discrete element method (DEM) simulations. The study specifically examines how various sample preparation techniques affect the cyclic liquefaction resistance of polydisperse spherical particle samples with a Kc value of 0.5, where Kc represents the ratio of initial horizontal to vertical normal stresses. The results reveal that the choice of sample preparation technique significantly affects the cyclic liquefaction resistance of the samples. Furthermore, this study explores the inherent fabric of the samples using coordination number and contact-normal fabric anisotropy, and demonstrates that it plays a critical role in controlling the cyclic liquefaction resistance of granular materials under nonhydrostatic consolidation. The study emphasizes the significance of considering the inherent fabric in understanding the behavior of granular materials under non-hydrostatic consolidation. This can inform the design of experiments and the development of constitutive models to explore the interplay between sample preparation techniques, fabric anisotropy, and cyclic liquefaction resistance.

Rheological behavior of granular materials under different relative densities

Granular materials typically exhibit complex behaviour especially during shearing under different states. The material behaviour transitions from fluid-like to unfluid-like primarily due to various fundamental mechanisms involved during the shearing process such as momentum transport, compaction, and jamming. Describing this transition is particularly relevant in a variety of natural phenomena like landslides, debris flow, mudflow, and liquefaction. The mechanism involved in the transitional response is predominantly governed by the initial packing of granular medium, shear rate and boundary stresses. In this study, the influence of relative densities (20% to 74%) on the rheological behaviour of sand is studied using a vane-shear apparatus. The variation of critical shear strength (during jamming), yield strength, apparent viscosity, and the maximum shear rate with relative density is determined from this experimental program. Further, the characterization of the flow behaviour of sand revealed the existence of pre-jamming and post-jamming regimes. The post-jamming response is evaluated by using slope parameters (m and ξ) which predicted an increasing trend with increase in relative density and overburden pressure.

An Improved Contact Force Model of Polyhedral Elements for the Discrete Element Method

The discrete element method (DEM) serves as a robust tool for simulating the mechanical behavior of granular materials. The accuracy of the DEM simulation is determined by the calculation of contact forces between elements. Compared to spherical elements, the contact modes of polyhedral elements are more complex. In this work, the contact force between polyhedral elements under different contact modes was investigated by experiment. Based on the experimental results, the normal stiffness coefficient in the Cundall’s contact model was modified. The improved contact force model was then applied in the DEM simulation and validated by means of comparison with the results of packing experiments. The research results demonstrate that the improved contact force model can be effectively applied to the simulation of different contact modes between polyhedral elements. The results of the packing experiment highly coincide with the results of the DEM simulation, which confirms the accuracy and reliability of the improved contact force model.

Force-chain finder: A software tool for the recursive detection of force-chains in granular materials via minor principal stress

Force transmission in granular media occurs through an inhomogeneous network of inter-particle contacts referred to as force-chains. A thorough understanding of the structure of these chains is indispensable for a better comprehension of the macroscopic signatures they generate. This paper introduces Force-Chain Finder (FCF), an open-source software tool designed for detecting force-chains in granular materials. Leveraging the stress tensor computed for each particle based on its interactions with neighbouring particles, the tool effectively identifies the magnitude and direction of the most compressive principal stress. Through a recursive traversal of particles and their neighbours, force-chains are robustly detected based on the alignment of the principal stress directions, which is decided by a parameter α (an angle in radians). The software provides a comprehensive suite of post-processing features, including the exportation of results in different formats, enabling detailed analysis of specific regions and dynamic phenomena. Additionally, the software facilitates the computation of statistical measures pertaining to chain size and population. By streamlining the identification and characterization of force-chains within discrete element method (DEM) simulations, this tool significantly enhances the efficiency and accuracy of force-chain analysis. Thus, the software promotes deeper insights into the behaviour of granular materials by enabling researchers to effortlessly detect and analyse force-chains. PROGRAM SUMMARYProgram Title: Force Chain Finder (FCF)CPC Library link to program files:https://doi.org/10.17632/33pkc4f63t.1Developer's repository link:https://github.com/Particles-Research/Force_Chain_Finder_Public/tree/mainLicensing provisions: GNU General Public License 3Programming Language: C++, PythonSupplementary material: Illustrative examplesNature of the Problem: FCF has been developed with the primary objective of efficiently and comprehensively detecting force networks that arise in Discrete Element Modelling (DEM) simulations of granular flow.Solution Method: The method is based on the work of “J. Peters, M. Muthuswamy, J. Wibowo, and A. Tordesillas, Characterization of force chains in granular material, Physical Review E 72, 041307 (2005)”. It utilizes the concept of minor principal stress to identify quasilinear chains, each consisting of at least three particles. However, significant algorithmic modifications have been implemented to enhance the accuracy of the procedure, enabling the detection of chain branching and merging.

Modeling the single particle crushing behavior by random discrete element method

Microscopic properties of granular materials typically exhibit significant heterogeneity. Realistic particle crushing simulation in granular materials requires the use of model that incorporate the spatial heterogeneity of its microscopic properties. This study introduces a novel approach, the Random Field Theory-Discrete Element Method (RFT-DEM) model, to simulate the single-particle crushing behavior of granular materials, considering the spatial heterogeneity of microscopic properties within particles. The material heterogeneity was characterized through Random Field Theory, demonstrating reasonable consistency between simulated and experimental results. The size-dependent characteristics of crushing strength and Weibull modulus were confirmed through a series of single-particle crushing simulations, emphasizing the model's capability to capture such features. Systematic analyses explored the impact of coefficient of variation (COV) and scale of fluctuation (SOF) on single-particle crushing behavior. Increasing COV resulted in reduced characteristic crushing strength and Weibull modulus, with larger particles exhibiting greater sensitivity. Furthermore, increasing SOF initially increased these parameters until a threshold SOF value of 0.0005 m, beyond which they stabilized. Reduced COV or increased SOF diminished the size effect in characteristic crushing strength, and once COV exceeded a threshold of 0.03, the size effect became independent of its variations. These findings contribute to a comprehensive understanding of the intricate interplay between microscopic properties and crushing behavior in granular materials.

From flow to jamming: Lattice Gas Automaton simulations in granular materials

We introduce the first extension of a Lattice Gas Automaton (LGA) model to accurately replicate observed emergent phenomena in granular materials with a special focus on previously unexplored jamming transitions by incorporating gravitational effects, energy dissipation in particle collisions, and wall friction. We successfully reproduce flow rate evolution, density wave formation, and jamming transition observed in experiments. We also explore the critical density at which jamming becomes probable. This research advances our understanding of granular dynamics and offers insights into the jamming behavior of granular materials.

Numerical investigation of multi‐particle interactions using the discrete element method

AbstractThe numerical simulation of particles that can be used as crash absorbers, for example, in ship collisions, is of high interest, as experimental investigation is often associated with high costs. After extensive studies on the breakage of single‐particles, the focus is now on the investigation of multi‐particle simulation. Although many parameter studies have been carried out for single‐particle compression tests, their results cannot be transferred to multi‐particle compression tests. The influence of various simulation parameters differs greatly between single and multiple particles due to the interaction between individual granules. Therefore, it is necessary to repeat the parameter studies with respect to these interactions in order to gain a better insight into the bulk behaviour of granular materials, which can then be used for the simulation of particle‐enhanced collisions.

Discrete Element Modelling of a Bulk Cohesive Material Discharging from a Conveyor Belt onto an Impact Plate

The discrete element method (DEM) has become the numerical method of choice for analysing and predicting the behaviour of granular materials in bulk handling systems. Wet-and-sticky materials (WSM) are especially problematic, resulting in build-up and blockages. Furthermore, due to the large number of particles in industrial-scale applications, it is essential to decrease the number of particles in the model by increasing their size (upscaling or coarse graining). In this study, the accuracy with which upscaled DEM particles can model the discharge of a cohesive material from a belt conveyor onto an inclined impact plate was investigated. Experimentally, three sand grades (particle size distributions, PSDs) were used, each in a dry (non-cohesive) state and with three levels of moisture-induced cohesion. The effects of the modelled PSDs on the material flow, build-up on the plate, the peak impact force and the residual weight were investigated. Although a linear cohesion contact model was mostly used, the results were also compared to that of the Johnson–Kendall–Roberts (JKR) and simplified JKR (SJKR) models. It was found that the general profile of the pile (build-up) could be accurately modelled, but using a more accurate (but still upscaled) PSD improved the results. The impact force and the residual weight on the plate could be accurately modelled (error <15%) if the particle size was not excessively scaled. The maximum acceptable scaling factor was found to be a geometric factor of the bulk measure of interest, and not a factor of the physical particle size. Furthermore, with an increase in cohesion, the bulk measures such as the thickness of the discharge stream and the height of the material build-up increased, which meant that the maximum acceptable scale factor also increased. The results are valuable for future accurate and efficient modelling of large industrial scale applications of WSMs.

Influence of particle shape on creep and stress relaxation behaviors of granular materials based on DEM

The creep and stress relaxation behaviors stem from time-dependent changes in the microstructure of granular materials. As a non-negligible inherent granular material characteristic, particle shape plays a significant role on the formation and evolution of microstructure. However, the effects of particle shape on creep and stress relaxation behaviors of granular materials are still open questions. In this study, 3D DEM models based on the rate process theory and superellipsoids are incorporated to simulate the creep and stress relaxation of granular samples with different aspect ratios and blockiness. The results show that the aspect ratio and blockiness of particle have a great effect on creep and stress relaxation. However, the effects of aspect ratio and blockiness on creep and stress relaxation are coupled. Further analysis on contact forces shows the influences of aspect ratio and blockiness on creep mainly come from the contact force ratio. The influences of the aspect ratio and blockiness on stress relaxation mainly arise from the variation of the normal contact force anisotropy of the granular assemblies. The above results provide the tendency and mechanism on the effects of particle shape on creep and stress relaxation of granular assemblies.

Application of EDEM Simulation for Calculating and Optimizing a Closed Coal Fly Ash Screw Conveyor

In contemporary bulk material transportation systems, closed screw conveyors have become prevalent. These conveyors, enclosed within troughs or cylindrical bodies, effectively mitigate environmental contamination and material toxicity during transit. Their hermetic design prevents material dispersion by wind, thereby minimizing losses and preserving the integrity of raw materials, particularly those with potential health implications such as urea and cement. Consequently, employing a screw conveyor constitutes a prudent safety measure. Despite the widespread use of screw conveyors, a comprehensive understanding of the behavior of material particles within these systems remains elusive and subject to discrepancies across various methodologies. Presently, a multitude of calculation methods and applications exist, resulting in disparities between theoretical computations and practical implementation. Drawing upon Alan W. Roberts’ meticulously devised calculation methodology, renowned for its precision, the authors have developed a swift computational tool utilizing VBA Excel software 2023. Additionally, EDEM simulation software was employed to model granular material behavior. The ensuing calculations guided the selection of optimized technical dimensions for the screw conveyor, which were then fabricated and subjected to real-world testing at the Vinh Tan thermal power plant. Remarkably, the achieved output capacity demonstrated a mere 7% deviation from calculations performed with the VBA program and a 2% variation from those conducted via EDEM simulation. Furthermore, a comprehensive graph depicting the relationship between screw conveyor speed and capacity has been provided, affording a means to finely tune throughput with exceptional accuracy along the production line. The results obtained provide the basis for the development of a device that meets the required capacity specifications accurately and precisely on the first attempt. This accomplishment satisfies stringent capacity standards without the need for any adjustments or modifications, all while ensuring minimal cost and time efficiency.

Effects of pre-shearing and pre-consolidation histories on liquefaction behaviour of saturated loose sand: DEM investigation

PurposeThe study aims to investigate the effects of pre-loading histories (pre-shearing and pre-consolidation) on the liquefaction behaviour of saturated loose sand via discrete element method (DEM) simulations.Design/methodology/approachThe pre-shearing history is mimicked under drained conditions (triaxial compression) with different pre-shearing strain levels ranging from 0% to 2%. The pre-consolidation history is mimicked by increasing the isotropic compression to different levels ranging from 100 kPa to 300 kPa. The macroscopic and microscopic behaviours are analysed and compared.FindingsTemporary liquefaction, or quasi-steady state (QSS), is observed in most samples. A higher pre-shearing or pre-consolidation level can provide higher liquefaction resistance. The ultimate state line is found to be unique and independent of the pre-loading histories in stress space. The Lade instability line prematurely predicts the onset of liquefaction for all samples, both with and without pre-loading histories. The redundancy index is an effective microscopic indicator to monitor liquefaction, and the onset of the liquefaction corresponds to the phase transition state where the value of redundancy index is one, which is true for all cases irrespective of the proportions of sliding contacts.Originality/valueThe liquefaction behaviour of granular materials still remains elusive, especially concerning the effects of pre-loading histories on soils. Furthermore, the investigation of the effects of pre-consolidation histories on undrained behaviour and its comparison to pre-sheared samples is rarely reported in the DEM literature.