Computer simulation of model cohesive powders: influence of assembling procedure and contact laws on low consolidation states

Dynamic compaction of cohesive granular materials: scaling behavior and bonding structures

The compaction of cohesive granular materials is a common operation in powder-based manufacture of many products. However, the influence of particle-scale parameters such as bond strength on the packing structure and the general scaling of the compaction process are still poorly understood. We use particle dynamics simulations to analyze jammed configurations obtained by dynamic compaction of sticky particles under a fixed compressive pressure for a broad range of system parameter values. We show that relative porosity, representing the relative importance of porosity with respect to its minimum and maximum values, is a unique function of a modified cohesion number that combines adhesion force, confining pressure, and particle size, as well as contact stiffness, which is often assumed to be ineffective but is shown here to play an essential role in compaction. An asymmetric sigmoidal form based on two power laws provides an excellent fit to the data. The statistical properties of the bond network reveal self-balanced force structures and an exponential fall-off of the number of both tensile and compressive forces. Remarkably, the properties of the bond network depend on the cohesion number rather than the modified cohesion number, implying that similar bond network characteristics are compatible with a broad range of porosities mainly due to the effect of contact stiffness. We also discuss the origins of data points escaping the general scaling of porosity and show that they reflect either finite system size or rigid confining walls.

Parameter calibration of discrete element model for gluten densification molding

The densified powder material is convenient for storage and transportation, with broad market application prospects. In this study, the discrete element model parameters required for simulating gluten densification were calibrated using the Hertz-Mindlin with JKR contact model. Initially, physical testing techniques were utilized to assess the size distribution, density, and angle of repose (AoR) of gluten particles. Following this, the Plackett-Burman test, the steepest ascent test, and the Box-Behnken test were conducted, and the significant factors were obtained: The coefficient of rolling friction (P-P) was 1.038, the coefficient of static friction (P-P) was 0.071, and the surface energy (P-P) was 0.047. Finally, the AoR and densification simulations were performed under the optimal parameter combination, along with validation tests. The results showed that the relative error between the simulated and tested AoR was 0.52%. The compression ratio and compression force curves of simulated and actual were similar.

Study on the Powder-Spreading Process of Walnut Shell/Co-PES Biomass Composite Powder in Additive Manufacturing

Powder laying is a necessary procedure during powder bed additive manufacturing (PBAM), and the quality of powder bed has an important effect on the performance of products. Because the powder particle motion state during the powder laying process of biomass composites is difficult to observe, and the influence of the powder laying process parameters on the quality of the powder bed is still unclear, a simulation study of the biomass composite powder laying process during powder bed additive manufacturing was conducted using the discrete element method. A discrete element model of walnut shell/Co-PES composite powder was established using the multi-sphere unit method, and the powder-spreading process was numerically simulated using two different powder spreading methods (rollers/scrapers). The results showed that the quality of powder bed formed by roller laying was better than that formed by scrapers with the same powder laying speed and powder laying thickness. For both of the two different spreading methods, the uniformity and density of the powder bed decreased as spreading speed increased, although the spreading speed had a more important influence on scraper spreading compared to roller spreading. As powder laying thickness increased, the powder bed formed by the two different powder laying methods became more uniform and denser. When the powder laying thickness was less than 110μm, the particles were easily blocked at the powder laying gap and are pushed out of the forming platform, forming many voids, and decreasing the powder bed's quality. When the powder thickness was greater than 140 μm, the uniformity and density of the powder bed increased gradually, the number of voids decreased, and the quality of the powder bed improved.

Ultraslow Settling Kinetics of Frictional Cohesive Powders

Using discrete element method simulations, we show that the settling of frictional cohesive grains under ramped-pressure compression exhibits strong history dependence and slow dynamics that are not present for grains that lack either cohesion or friction. Systems prepared by beginning with a dilute state and then ramping the pressure to a small positive value P_{final} over a time τ_{ramp} settle at packing fractions given by an inverse-logarithmic rate law, ϕ_{settled}(τ_{ramp})=ϕ_{settled}(∞)+A/[1+Bln(1+τ_{ramp}/τ_{slow})]. This law is analogous to the one obtained from classical tapping experiments on noncohesive grains, but crucially different in that τ_{slow} is set by the slow dynamics of structural void stabilization rather than the faster dynamics of bulk densification. We formulate a kinetic free-void-volume theory that predicts this ϕ_{settled}(τ_{ramp}), with ϕ_{settled}(∞)=ϕ_{ALP} and A=ϕ_{settled}(0)-ϕ_{ALP}, where ϕ_{ALP}≡.135 is the "adhesive loose packing" fraction found by Liu et al. [Equation of state for random sphere packings with arbitrary adhesion and friction, Soft Matter 13, 421 (2017)SMOABF1744-683X10.1039/C6SM02216B].

Characterizing Pure Polymers under High Speed Compression for the Micromechanical Prediction of Unidirectional Composites

The nonlinear behaviour of fibre-reinforced polymer composites (FRPC) in transverse loading is mainly induced by the constituent polymer matrix. The thermoset and thermoplastic matrices are typically rate- and temperature-dependent, complicating the dynamic material characterization process. Under dynamic compression, the microstructure of the FRPC develops local strains and local strain rates whose values can be much higher than those applied at macroscopic level. The correlation between the local (microscopic) values and the measurable (macroscopic) ones still present challenges when applying the strain rate in the range 10-3-103 s-1. This paper presents an in-house uniaxial compression test setup to provide robust stress-strain measurements applying strain rates up to 100 s-1. A semi-crystalline thermoplastic polyetheretherketone (PEEK) and a toughened thermoset epoxy PR520 are assessed and characterized. The thermomechanical response of the polymers is further modelled using an advanced glassy polymer model, naturally capturing the isothermal to adiabatic transition. A micromechanical model of a unidirectional composite undergoing dynamic compression is developed by using both validated polymers as matrices reinforced by carbon fibres (CF) using Representative Volume Element (RVE) models. These RVEs are used to analyse the correlation between the micro- and macroscopic thermomechanical response of the CF/PR520 and CF/PEEK systems investigated at intermediate to high strain rates. Both systems experience an excessive strain localization with local plastic strain about 19% when a macroscopic strain of 3.5% is applied. The comparison of using a thermoplastic and a thermoset as a matrix in composites is discussed with regard to the rate-dependence, the interface debonding and the self-heating effect.

Numerical Study on the Effect of Matrix Self-Heating on the Thermo-Visco-Plastic Response of Continuous Fiber-Reinforced Polymers under Transverse Tensile Loading

The recyclability and improved suitability for high-volume production make fiber-reinforced thermoplastic polymers (FRP) attractive alternatives for the current thermoset-based ones. However, while they are more ductile than their thermoset counterparts, their behavior is also more susceptible to environmental conditions such as humidity, temperature, and strain rate. The latter can trigger self-heating and thermal softening effects. The role of matrix self-heating in FRP subjected to transverse loading is investigated using micromechanical modeling. Particularly, the effect of self-heating, strain rate and conductivity of the fiber-matrix interface is illustrated. It is shown that local heating of the matrix is dominant for the homogenized behavior of the material. Although the global homogenized temperature increase is limited, local thermal softening can induce premature failure. It is shown that the effect of thermal softening can be more prominent with increasing volume fraction, increasing strain rate, and lower interface conductivity.

Numerical Simulation of EPB Shield Tunnelling with TBM Operational Condition Control Using Coupled DEM–FDM

This study demonstrates a three-dimensional numerical simulation of earth pressure balance (EPB) shield tunnelling using a coupled discrete element method (DEM) and a finite difference method (FDM). The analysis adopted the actual size of a spoke-type EPB shield tunnel boring machine (TBM) consisting of a cutter head with cutting tools, working chamber, screw conveyor, and shield. For the coupled model to reproduce the in situ ground condition, the ground formation was generated partially using the DEM (for the limited domain influenced by excavation), with the rest of the domain being composed of FDM grids. In the DEM domain, contact parameters of particles were calibrated via a series of large-scale triaxial test analyses. The model simulated tunnelling as the TBM operational conditions were controlled. The penetration rate and the rotational speed of the screw conveyor were automatically adjusted as the TBM advanced to prevent the generation of excessive or insufficient torque, thrust force, or chamber pressure. Accordingly, these parameters were maintained consistently around their set operational ranges during excavation. The simulation results show that the proposed numerical model based on DEM–FDM coupling could reasonably simulate EPB driving while considering the TBM operational conditions.

Quasistatic response of loose cohesive granular materials

DEM-simulated model cohesive assemblies of spherical grains of diameter d, with contact tensile strength F0, once prepared in loose states, are quasistatically subjected to growing isotropic pressure P, and then to triaxial compression, maintaining lateral stresses σ2 = σ3 = P while increasing axial stress σ1 = P + q and strain є1. Reduced pressure P* = d2P/F0 varies from 0.1 (cohesion dominated case, for which systems typically equilibrate with solid fraction Ф ≃ 0.35), to large values for which the cohesionless behavior is retrieved. In triaxial compression, while the moderate strain response (є1 ~ 0.1) is influenced by initial coordination numbers and mesoscale heterogeneities, the approach to the critical state, as both q (deviator) and Ф steadily increase, gets slower for smaller P*. Critical ratio q/P strongly increases for decreasing P*, as roughly predicted in an “effective stress” scheme. Anomalously small elastic moduli are observed in the gel-like structures. While extensive geometric rearrangements take place, no shear banding is observed. Loose cohesive granular assemblies are thus capable of large quasistatic stable plastic strains and ductile rupture.

Discrete Element Simulation of the Effect of Roller-Spreading Parameters on Powder-Bed Density in Additive Manufacturing

The powder-bed with uniform and high density that determined by the spreading process parameters is the key factor for fabricating high performance parts in Additive Manufacturing (AM) process. In this work, Discrete Element Method (DEM) was deployed in order to simulate Al₂O₃ ceramic powder roller-spreading. The effects of roller-spreading parameters include translational velocity V_s, roller’s rotational speed ω, roller’s diameter D, and powder layer thickness H on powder-bed density were analyzed. The results show that the increased translational velocity of roller leads to poor powder-bed density. However, the larger roller’s diameter will improve powder-bed density. Moreover, the roller’s rotational speed has little effect on powder-bed density. Layer thickness is the most significant influencing factor on powder-bed density. When layer thickness is 50 μm, most of particles are pushed out of the build platform forming a lot of voids. However, when the layer thickness is greater than 150 μm, the powder-bed becomes more uniform and denser. This work can provide a reliable basis for roller-spreading parameters optimization.

Insights into the rheology of cohesive granular media

An uninterrupted flow of powders is the key to smooth production operations of many industries. However, powders have more difficulty flowing than coarse, granular media like sand because of the interparticle cohesive interactions. What precisely controls the “flowability” of powders remains unclear. Here, we address this issue by performing numerical simulations of the flow of cohesive grains. We show that the cohesiveness during flow is not only controlled by the interparticle adhesion, but also by the stiffness and inelasticity of the grains. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow, i.e., higher “flowability.” This combined effect can be embedded in a single dimensionless number—a result that enriches our understanding of powder rheology.

Characterization and prediction of the “flowability” of powders are of paramount importance in many industries. However, our understanding of the flow of powders like cement or flour is sparse compared to the flow of coarse, granular media like sand. The main difficulty arises because of the presence of adhesive forces between the grains, preventing smooth and continuous flows. Several tests are used in industrial contexts to probe and quantify the “flowability” of powders. However, they remain empirical and would benefit from a detailed study of the physics controlling flow dynamics. Here, we attempt to fill the gap by performing intensive discrete numerical simulations of cohesive grains flowing down an inclined plane. We show that, contrary to what is commonly perceived, the cohesive nature of the flow is not entirely controlled by the interparticle adhesion, but that stiffness and inelasticity of the grains also play a significant role. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow. This observation is rationalized by introducing the concept of a dynamic, “effective” adhesive force, a single parameter, which combines the effects of adhesion, elasticity, and dissipation. Based on this concept, a rheological description of the flow is proposed for the cohesive grains. Our results elucidate the physics controlling the flow of cohesive granular materials, which may help in designing new approaches to characterize the “flowability” of powders.

Micro-mechanical theory of shear yield stress for strongly flocculated colloidal gel

Shear yield stress is an important parameter in the processing of colloidal suspensions as it characterizes the solid-to-fluid transition. Although shear rheology of colloidal gel is of widespread academic and industrial interest, first principles theory that connects the microscopic properties to the macroscopic mechanical response in a self-consistent manner is lacking. In this work, we derive a constitutive relation to predict the yield stress for a strongly attractive gel undergoing quasi-static shear deformation as a function of volume fraction, inter-particle potential, contact scale properties and the micro-structure of a strongly-aggregated colloidal gel. The model also predicts the strain at which the colloidal gel network will yield under shear load. To test the model, discrete element simulation is performed using a non-central potential with friction while accounting for the rolling resistance, which is important in real colloidal gel systems. The theoretical predictions are not only in good agreement with the simulation results, but also with previous experiments.

Constraint-Based Approach to Granular Dispersion Rheology

We present a phenomenological model for granular suspension rheology in which particle interactions enter as constraints to relative particle motion. By considering constraints that are formed and released by stress respectively, we derive a range of experimental flow curves in a single treatment and predict singularities in viscosity and yield stress consistent with literature data. Fundamentally, we offer a generic description of suspension flow that is independent of bespoke microphysics.

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number z_{c} of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of z_{c} and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ν_{c}=z_{c}ϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Compaction of noncohesive and cohesive granular materials under vibrations: Experiments and stochastic model

We study the time evolution of the compaction of a noncohesive or cohesive granular material submitted to shaking through experiments and a stochastic model. Beyond well-known empirical expressions, we show that the characteristic time scales depend on the number of objects in the assembly. For a noncohesive granular material, the compaction time scale is governed by the number of individual grains in the system. In the case of a cohesive granular material, a two-scale model (individual particles and clusters) allows one to mimic the time evolution of the compaction of an actual cohesive powder driven by horizontal vibrations. In this case, the two time scales are associated with the numbers of clusters and grains, respectively.

Universality in consolidation of colloidal gels

Consolidation of colloidal dispersions under external load is a complex process involving inter-particle interactions, thermal forces and hydrodynamics. Despite its importance in diverse industrial applications, past studies involving experiments, scaling approaches and simulations are yet to provide a comprehensive understanding of how the microstructure determines the mechanical response in three dimensional colloidal gels. Here, we develop a model that accounts for the microstructural details and predicts the mechanical response under slow, uniaxial compression of a strongly aggregated three dimensional colloidal gel. The particle network assumes a fractal structure that is independent of the strength of inter-particle interactions. While the yield strain changes negligibly during the entire process, the yield stress increases by several orders of magnitude. The predicted yield stress and strain are in close agreement with those observed in simulations and experiments with diverse colloidal systems, suggesting a universality in the consolidation process.

Athermal rheology of weakly attractive soft particles

We study the rheology of a soft particulate system where the interparticle interactions are weakly attractive. Using extensive molecular dynamics simulations, we scan across a wide range of packing fractions (ϕ), attraction strengths (u), and imposed shear rates (γ[over ̇]). In striking contrast to repulsive systems, we find that at small shear rates generically a fragile isostatic solid is formed even if we go to ϕ≪ϕ_{J}. Further, with increasing shear rates, even at these low ϕ, nonmonotonic flow curves occur which lead to the formation of persistent shear bands in large enough systems. By tuning the damping parameter, we also show that inertia plays an important role in this process. Furthermore, we observe enhanced particle dynamics in the attraction-dominated regime as well as a pronounced anisotropy of velocity and diffusion constant, which we take as precursors to the formation of shear bands. At low enough ϕ, we also observe structural changes via the interplay of low shear rates and attraction with the formation of microclusters and voids. Finally, we characterize the properties of the emergent shear bands, and thereby, we find surprisingly small mobility of these bands, leading to prohibitively long time scales and extensive history effects in ramping experiments.

Effect of long-range repulsive Coulomb interactions on packing structure of adhesive particles

The packing of charged micron-sized particles is investigated using discrete element simulations based on adhesive contact dynamic model. The formation process and the final obtained structures of ballistic packings are studied to show the effect of interparticle Coulomb force. It is found that increasing the charge on particles causes a remarkable decrease of the packing volume fraction ϕ and the average coordination number 〈Z〉, indicating a looser and chainlike structure. Force-scaling analysis shows that the long-range Coulomb interaction changes packing structures through its influence on particle inertia before they are bonded into the force networks. Once contact networks are formed, the expansion effect caused by repulsive Coulomb forces are dominated by short-range adhesion. Based on abundant results from simulations, a dimensionless adhesion parameter Ad*, which combines the effects of the particle inertia, the short-range adhesion and the long-range Coulomb interaction, is proposed and successfully scales the packing results for micron-sized particles within the latest derived adhesive loose packing (ALP) regime. The structural properties of our packings follow well the recent theoretical prediction which is described by an ensemble approach based on a coarse-grained volume function, indicating some kind of universality in the low packing density regime of the phase diagram regardless of adhesion or particle charge. Based on the comprehensive consideration of the complicated inter-particle interactions, our findings provide insight into the roles of short-range adhesion and repulsive Coulomb force during packing formation and should be useful for further design of packings.

Flow of wet granular materials: A numerical study

We simulate dense assemblies of frictional spherical grains in steady shear flow under controlled normal stress P in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci, assumed isolated (pendular regime), and attractive forces, which are hysteretic: Menisci form at contact, but do not break until grains are separated by a finite rupture distance. The system behavior depends on two dimensionless control parameters, inertial number I and reduced pressure P*=aP/(πΓ), comparing confining forces ∼a2P to meniscus tensile strength F0=πΓa, for grains of diameter a joined by menisci with surface tension Γ. We pay special attention to the quasistatic limit of slow flow and observe systematic, enduring strain localization in some of the cohesion-dominated (P*∼0.1) systems. Homogeneous steady flows are characterized by the dependence of internal friction coefficient μ* and solid fraction Φ on I and P*. We also record normal stress differences, fairly small but not negligible and increasing for decreasing P*. The system rheology is moderately sensitive to saturation within the pendular regime, but would be different in the absence of capillary hysteresis. Capillary forces have a significant effect on the macroscopic behavior of the system, up to P* values of several units, especially for longer force ranges associated with larger menisci. The concept of effective pressure may be used to predict an order of magnitude for the strong increase of μ* as P* decreases but such a crude approach is unable to account for the complex structural changes induced by capillary cohesion, with a significant decrease of Φ and different agglomeration states and anisotropic fabric. Likewise, the Mohr-Coulomb criterion for pressure-dependent critical states is, at best, an approximation valid within a restricted range of pressures, with P*≥1. At small enough P*, large clusters of interacting grains form in slow flows, in which liquid bonds survive shear strains of several units. This affects the anisotropies associated with different interactions and the shape of function μ*(I), which departs more slowly from its quasistatic limit than in cohesionless systems (possibly explaining the shear banding tendency).

Attractive particle interaction forces and packing density of fine glass powders

We study the packing of fine glass powders of mean particle diameter in the range (4-52) μm both experimentally and by numerical DEM simulations. We obtain quantitative agreement between the experimental and numerical results, if both types of attractive forces of particle interaction, adhesion and non-bonded van der Waals forces are taken into account. Our results suggest that considering only viscoelastic and adhesive forces in DEM simulations may lead to incorrect numerical predictions of the behavior of fine powders. Based on the results from simulations and experiments, we propose a mathematical expression to estimate the packing fraction of fine polydisperse powders as a function of the average particle size.

Armoring a droplet: soft jamming of a dense granular interface

Droplets and bubbles protected by armors of particles have found vast applications in encapsulation, stabilization of emulsions and foams, or flotation processes. The liquid phase stores capillary energy, while concurrently the solid contacts of the granular network induce friction and energy dissipation, leading to hybrid interfaces of combined properties. By means of nonintrusive tensiometric methods and structural measurements, we distinguish three surface phases of increasing rigidity during the evaporation of armored droplets. The emergence of surface rigidity is reminiscent of jamming of granular matter, but it occurs differently since it is marked by a step by step hardening under surface compression. These results show that the concept of the effective surface tension remains useful only below the first jamming transition. Beyond this point, the surface stresses become anisotropic.

Effect of cohesion on shear banding in quasistatic granular materials

Cohesive powders have widely different bulk behavior due to their peculiar interactions. We use discrete element simulations to investigate the effect of contact cohesion on the steady state flow of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the granular Bond number (Bo), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenomenon is almost independent of cohesion for Bond numbers Bo<1, however for Bo≥1 cohesive forces start to play an important role, as both width and center position of the band increase. Inside the shear band, the mean normal contact force is independent of cohesion and depends only on the confining stress. In contrast, when the behavior is analyzed focusing on the eigendirections of the local strain rate tensor, a dependence on cohesion shows up. Forces carried by contacts along the compressive and tensile directions are symmetric about the mean force (larger and smaller respectively), while the force along the third, neutral direction follows the mean force. This anisotropy of the force network increases with cohesion, just like the heterogeneity in all (compressive, tensile and neutral) directions.

Three-dimensional simulations of nanopowder compaction processes by granular dynamics method

In order to describe and to study the processes of cold compaction within the discrete element method a three-dimensional model of nanosized powder is developed. The elastic forces of repulsion, the tangential forces of "friction" (Cattaneo-Mindlin), and the dispersion forces of attraction (van der Waals-Hamaker), as well as the formation and destruction of hard bonds between the individual particles are taken into account. The monosized powders with the size of particles in the range 10-40 nm are simulated. The simulation results are compared to the experimental data of the alumina nanopowders compaction. It is shown that the model allows us to reproduce experimental data reliably and, in particular, describes the size effect in the compaction processes. A number of different external loading conditions is used in order to perform the theoretical and experimental researches. The uniaxial compaction (the closed-die compaction), the biaxial (radial) compaction, and the isotropic compaction (the cold isostatic pressing) are studied. The real and computed results are in a good agreement with each other. They reveal a weak sensitivity of the oxide nanopowders to the loading condition (compaction geometry). The application of the continuum theory of the plastically hardening porous body, which is usually used for the description of powders, is discussed.

Cohesive granular materials composed of nonconvex particles

The macroscopic cohesion of granular materials made up of sticky particles depends on the particle shapes. We address this issue by performing contact dynamics simulations of 2D packings of nonconvex aggregates. We find that the macroscopic cohesion is strongly dependent on the strain and stress inhomogeneities developing inside the material. The largest cohesion is obtained for nearly homogeneous deformation at the beginning of unconfined axial compression and it evolves linearly with nonconvexity. Interestingly, the aggregates in a sheared packing tend to form more contacts with fewer neighboring aggregates as the degree of nonconvexity increases. We also find that shearing leads either to an isotropic distribution of tensile contacts or to the same privileged direction as that of compressive contacts.

Restructuring of colloidal aggregates in shear flow: coupling interparticle contact models with Stokesian dynamics

A method to couple interparticle contact models with Stokesian dynamics (SD) is introduced to simulate colloidal aggregates under flow conditions. The contact model mimics both the elastic and plastic behavior of the cohesive connections between particles within clusters. Owing to this, clusters can maintain their structures under low stress while restructuring or even breakage may occur under sufficiently high stress conditions. SD is an efficient method to deal with the long-ranged and many-body nature of hydrodynamic interactions for low Reynolds number flows. By using such a coupled model, the restructuring of colloidal aggregates under shear flows with stepwise increasing shear rates was studied. Irreversible compaction occurs due to the increase of hydrodynamic stress on clusters. Results show that the greater part of the fractal clusters are compacted to rod-shaped packed structures, while the others show isotropic compaction.

Nonlinear effects of particle shape angularity in sheared granular media

We analyze the effects of particle shape angularity on the macroscopic shear behavior and texture of granular packings simulated by means of the contact dynamics method. The particles are regular polygons with an increasing number of sides ranging from 3 (triangles) to 60. The packings are analyzed in the steady shear state in terms of their shear strength, packing fraction, connectivity, and fabric and force anisotropies, as functions of the angularity. An interesting finding is that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below six sides). In contrast, the packing fraction declines towards a constant value, so that the packings of more angular particles are looser but have higher shear strength. We show that the increase of the shear strength at low angularity is due to an increase of both contact and force anisotropies and the saturation of the shear strength for higher angularities is a consequence of a rapid falloff of the contact and normal force anisotropies compensated for by an increase of the tangential force anisotropy. This transition reflects clearly the rather special geometrical properties of these highly angular shapes, implying that the stability of the packing relies strongly on the side-side contacts and the mobilization of friction forces.

Jamming in granular polymers

We examine the jamming transition in a two-dimensional granular polymer system using compressional simulations. The jamming density Φ(c) decreases with increasing length of the granular chain due to the formation of loop structures, in excellent agreement with recent experiments. The jamming density can be further reduced in mixtures of granular chains and granular rings, also as observed in experiment. We show that the nature of the jamming in granular polymer systems has pronounced differences from the jamming behavior observed for polydisperse two-dimensional disk systems at point J. This result provides further evidence that there is more than one type of jamming transition.

Heterogeneous structure of granular aggregates with capillary interactions

We investigate the spatial structure of cohesive granular matter with spheres floating at an air-liquid interface that form disordered close packings with pores in between. The interface is slowly lowered in a conical container to uniformly compress and study the system as a function of area fraction ϕ. We find that the free area distributions associated with Voronoi cells show significant exponential tails indicating greater heterogeneity compared with random distributions at low ϕ with a crossover towards a Γ distribution as ϕ is increased. Further, we find significant short range order as measured by the radial correlation function and the orientational order parameter even at low and intermediate ϕ, which is absent when particles interact only sterically.

Simulation of cemented granular materials. II. Micromechanical description and strength mobilization at the onset of macroscopic yielding

This is the second of two papers investigating the mechanical response of cemented granular materials by means of contact dynamics simulations. In this paper, a two-dimensional polydisperse sample with high void ratio is sheared in a load-controlled simple shear numerical device until the stress state of the sample reaches the yield stress. We first study the stress transmission properties of the granular material in terms of the fabric of different subsets of contacts characterized by the magnitude of their normal forces. This analysis highlights the existence of a peculiar force carrying structure in the cemented material, which is reminiscent of the bimodal stress transmission reported for cohesionless granular media. Then, the evolution of contact forces and torques is investigated trying to identify the micromechanical conditions that trigger macroscopic yielding. It is shown that global failure can be associated to the apparition of a group of particles whose contacts fulfill at least one of the local rupture conditions. In particular, these particles form a large region that percolates through the sample at the moment of failure, evidencing the relationship between macroscopic yielding and the emergence of large-scale correlations in the system.

Simulation of cemented granular materials. I. Macroscopic stress-strain response and strain localization

This is the first of two papers investigating the mechanical response of cemented granular materials by means of contact dynamics simulations. In this paper, a two-dimensional polydisperse sample with high-void ratio is constructed and then sheared in a simple shear numerical device at different confinement levels. We study the macroscopic response of the material in terms of mean and deviatoric stresses and strains. We show that the introduction of a local force scale, i.e., the tensile strength of the cemented bonds, causes the material to behave in a rigid-plastic fashion, so that a yield surface can be easily determined. This yield surface has a concave-down shape in the mean:deviatoric stress plane and it approaches a straight line, i.e., a Coulomb strength envelope, in the limit of a very dense granular material. Beyond yielding, the cemented structure gradually degrades until the material eventually behaves as a cohesionless granular material. Strain localization is also investigated, showing that the strains concentrate in a shear band whose thickness increases with the confining stress. The void ratio inside the shear band at the steady state is shown to be a material property that depends only on contact parameters.

Bond anisotropy and cohesion of wet granular materials

We analyse the Coulomb cohesion of wet granular materials and its relationship with the distribution of capillary bonds between particles. We show that, within a harmonic representation of the bond and force states, the shear strength can be expressed as a state equation in terms of internal anisotropy parameters. This formulation involves a dependence of the shear strength on loading direction and leads to the fragile behaviour of granular materials. The contact dynamics simulations of a wet material, in which a capillary force law is prescribed, are in excellent agreement with the predictions of this model. We find that the fragile character decreases as the local adhesion is increased or the mean stress is decreased.

Characterization of interparticle forces in the packing of cohesive fine particles

We numerically investigate force structures in the packing of fine cohesive particles using the discrete element method. By changing the particle size and therefore the van der Waals force, the effect of cohesion on the normal contact force and the total normal force, which is the sum of the normal contact forces and the van der Waals forces, is analyzed. It is shown that, with decreasing particle size, the normal contact forces become more uniform and have a narrower and more symmetric distribution, while the distributions of the total normal forces widen. Spatial correlation between the interparticle forces exists for the packing of coarse noncohesive particles. As the particle size decreases, this correlation becomes weaker for the contact forces but stronger for the total normal forces. A comparison between the effective weight of particles and the internal force structure suggests that there are differences between the particle-particle and particle-wall forces. The bimodal distribution of the effective weight indicates that there may exist two phases in the packings when cohesion is present, governed by the compressive and tensile stresses.

Computer simulation of model cohesive powders: plastic consolidation, structural changes, and elasticity under isotropic loads

The quasistatic behavior of a simple two-dimensional model of a cohesive powder under isotropic loads is investigated by discrete element simulations. We ignore contact plasticity and focus on the effect of geometry and collective rearrangements on the material behavior. The loose packing states, as assembled and characterized in a previous numerical study [Gilabert, Roux, and Castellanos, Phys. Rev. E 75, 011303 (2007)], are observed, under growing confining pressure P , to undergo important structural changes, while solid fraction Phi irreversibly increases (typically, from 0.4-0.5 to 0.75-0.8). The system state goes through three stages, with different forms of the plastic consolidation curve, i.e., Phi as a function of the growing reduced pressure P;{*}=PaF_{0} , defined with adhesion force F0 and grain diameter a . In the low-confinement regime (I), the system undergoes negligible plastic compaction, and its structure is influenced by the assembling process. In regime II the material state is independent of initial conditions, and the void ratio varies linearly with lnP [i.e., Delta(1Phi)=lambdaDelta(lnP;{*}) ], as described in the engineering literature. Plasticity index lambda is reduced in the presence of a small rolling resistance (RR). In the last stage of compaction (III), Phi approaches an asymptotic, maximum solid fraction Phi_{max} , as a power law Phi_{max}-Phi proportional, variant(P;{*});{-alpha} , with alpha approximately 1 , and properties of cohesionless granular packs are gradually retrieved. Under consolidation, while the range xi of fractal density correlations decreases, force patterns reorganize from self-balanced clusters to force chains, with correlative evolutions of force distributions, and elastic moduli increase by a large amount. Plastic deformation events correspond to very small changes in the network topology, while the denser regions tend to move like rigid bodies. Elastic properties are dominated by the bending of thin junctions in loose systems. For growing RR those tend to form particle chains, the folding of which, rather than tensile ruptures, controls plastic compaction.

Shear strength and force transmission in granular media with rolling resistance

We investigate a class of granular materials characterized by the possibility of interlocking between the particles. The interlocking is modeled by its effect through rolling resistance depending on relative rotation and normal force at the contact points and involving a single parameter analogous to the sliding friction coefficient. The model, which is introduced in the framework of the contact dynamics method, is applied to simulate the simple shear of a large granular sample. We present a detailed analysis regarding the influence of rolling and sliding friction parameters on the macroscopic response in terms of shear strength, fabric properties, and force transmission. Interestingly, two distinct regimes can be distinguished in which the steady-state shear strength is controlled by either rolling resistance or sliding friction. The relative contributions of rolling and sliding contacts to the shear strength are consistent with the same two regimes. Interlocking strongly affects the force network by enhancing the arching effect and thus increasing the relative importance of weak contact forces and torques, which is reflected in a decreasing power-law probability distribution of the contact forces and torques below the mean. Due to the combined effect of friction and interlocking, the force-carrying backbone takes an increasingly columnar aspect involving a low fraction of particles. Our data suggest that the nature of the weak contact network is strongly affected by the formation of these columns of particles which do not need to be propped laterally. In particular, in the limit of high rolling resistance and sliding friction, the role of the weak network of contacts is no longer to prop the force chains, but, like the strong contact network, to actively sustain the deviatoric load imposed on the system.

Influence of adhesion and friction on the geometry of packings of spherical particles

We study the effect of both adhesion and friction on the geometry of monosized packings of spheres by means of discrete element simulations. We use elastic properties that are characteristic of materials typically used for particulate processing (Young's modulus in the range 20-200 GPa). The geometrical features, both global and local, of the packings are studied using a variety of approaches in order to investigate their ability to quantify the effect of adhesion and/or friction. We show that both adhesion and friction interaction decrease the packing fraction. The very localized ordering that adhesion triggers is particularly investigated by use of the radial distribution function, the ordering parameter Q(6) , and four triclinic cells that allow a description of the microstructure at the local level. We show that the probability of occurrence of these triclinic cells is approximately proportional to their degree of freedom when neither adhesion nor friction plays a role. We find that the introduction of adhesive interactions increases the probability of occurrence of those cells that have the lowest degree of freedom.

Jamming transition and new percolation universality classes in particulate systems with attraction

We numerically study the jamming transition in particulate systems with attraction by investigating their mechanical response at zero temperature (T=0). We find three regimes of mechanical behavior separated by two critical transitions--connectivity and rigidity percolation. The transitions belong to different universality classes than their lattice counterparts, due to force balance constraints. We also find that these transitions are unchanged at low temperatures and resemble gelation transitions in experiments on colloidal and silica gels.

Internal states of model isotropic granular packings. II. Compression and pressure cycles

This is the second paper of a series of three investigating, by numerical means, the geometric and mechanical properties of spherical bead packings under isotropic stresses. We study the effects of varying the applied pressure P (from 1 or 10 kPa up to 100 MPa in the case of glass beads) on several types of configurations assembled by different procedures, as reported in the preceding paper [I. Agnolin and J.-N. Roux, Phys. Rev. E 76, 061302 (2007)]. As functions of P , we monitor changes in solid fraction Phi, coordination number z, proportion of rattlers (grains carrying no force) x_(0) , the distribution of normal forces, the level of friction mobilization, and the distribution of near neighbor distances. Assuming that the contact law does not involve material plasticity or damage, Phi is found to vary very nearly reversibly with P in an isotropic compression cycle, but all other quantities, due to the frictional hysteresis of contact forces, change irreversibly. In particular, initial low P states with high coordination numbers lose many contacts in a compression cycle and end up with values of z and x_(0) close to those of the most poorly coordinated initial configurations. Proportional load variations which do not entail notable configuration changes can therefore nevertheless significantly affect contact networks of granular packings in quasistatic conditions.

Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks

This is the first paper of a series of three, in which we report on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. The influence of various assembling processes on packing microstructures is investigated. It is accurately checked that frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, higher solid fractions corresponding to more ordered configurations with traces of crystallization. Specific properties directly related to isostaticity of the force-carrying structure in the rigid limit are discussed. With frictional grains, different preparation procedures result in quite different inner structures that cannot be classified by the sole density. If partly or completely lubricated they will assemble like frictionless ones, approaching the RCP solid fraction Phi_{RCP} approximately 0.639 with a high coordination number: z* approximately =6 on the force-carrying backbone. If compressed with a realistic coefficient of friction mu=0.3 packings stabilize in a loose state with Phi approximately 0.593 and z* approximately =4.5 . And, more surprisingly, an idealized "vibration" procedure, which maintains an agitated, collisional regime up to high densities results in equally small values of z* while Phi is close to the maximum value Phi_{RCP}. Low coordination packings have a large proportion (>10%) of rattlers--grains carrying no force--the effect of which should be accounted for on studying position correlations, and also contain a small proportion of localized "floppy modes" associated with divalent grains. Low-pressure states of frictional packings retain a finite level of force indeterminacy even when assembled with the slowest compression rates simulated, except in the case when the friction coefficient tends to infinity. Different microstructures are characterized in terms of near neighbor correlations on various scales, and some comparisons with available laboratory data are reported, although values of contact coordination numbers apparently remain experimentally inaccessible.