Stress-strain behavior and geometrical properties of packings of elongated particles

Packing of cohesive angular particles: Cohesive strength, structure, and effects of angularity

Employing extensive 2D contact dynamics simulations, we analyze the effects of grain shape angularity on the quasistatic shear strength properties of cohesive granular packings. We consider sticky irregular polygons ranging from disklike shapes to triangle. We find that the Mohr-Coulomb cohesion (i.e., the cohesive strength) is an increasing function of grain angularity. Meanwhile, the macroscopic friction angle increases with angularity and saturates for the most angular shapes, similar to dry cases. Using an effective stresslike approach, we show that the Mohr-Coulomb cohesion emerges from the cohesive force network for all shapes. From this, a micromechanical model reminiscent of the so-called "Rumpf" formula, is derived and reveals the increasing competition between the macroscopic friction, the anisotropy of the cohesive contacts network, and the grain shape parameter (i.e., the number of sides of the polygons) in the variation of Mohr-Coulomb cohesion with increasing angularity.

Contact networks and force transmission in aggregates of hexapod-shaped particles

Hexapods, consisting of three mutually orthogonal arms, have been utilized as a representative nonconvex shape to demonstrate the impact of interlocking on the strength properties of granular materials. Nevertheless, the microstructural characteristics of hexapod packings, which underlie their strength, have remained insufficiently characterized. We use particle dynamics simulations to build isotropically-packed aggregates of hexapods and we analyze the effects of aspect ratio and interparticle friction on the microstructure and force transmission. We find that the packing fraction is an unmonotonic function of aspect ratio due to competition between steric exclusions and interlocking. Interestingly, the contact coordination number declines considerably with friction coefficient, showing the stronger effect of friction on the stability of hexapod packings as compared with sphere packings. The pair distribution functions show that local ordering due to steric exclusions disappears beyond the aspect ratio 3 and the hexapods touch their second neighbors. Remarkably, hexapods of aspect ratio 3 tend to align with their neighbors and form locally ordered structures, implying a contact coordination number which is highly sensitive to the confining pressure. We also show that the probability density function of forces between hexapods is similar to that of sphere packings but with broadening exponential fall-off of strong forces as aspect ratio increases. Finally, the elastic bulk modulus of the aggregates is found to increase considerably with aspect ratio as a consequence of the rapid increase of contact density and the number of contacts with second neighbors.

Geometric cohesion in two-dimensional systems composed of star-shaped particles

Using a discrete element method, we investigate the phenomenon of geometric cohesion in granular systems composed of star-shaped particles with 3 to 13 arms. This was done by analyzing the stability of columns built with these particles and by studying the microstructure of these columns in terms of density and connectivity. We find that systems composed of star-shaped particles can exhibit geometric cohesion (i.e., a solidlike behavior, in the absence of adhesive forces between the grains), depending on the shape of the particles and the friction between them. This phenomenon is observed up to a given critical size of the system, from which a transition to a metastable behavior takes place. We also have evidence that geometric cohesion is closely linked to the systems' connectivity and especially to the capability of forming interlocked interactions (i.e., multicontact interactions that hinder the relative rotation of the grains). Our results contribute to the understanding of the interesting and potentially useful phenomenon of geometric cohesion. In addition, our work supplements an important set of experimental observations and sheds light on the complex behavior of real, three-dimensional, granular systems.

Force transmission during repose of flexible granular chains

We study the mechanics of standing columns formed during the repose of flexible granular chains. It is one of the many intriguing behaviours exhibited by granular materials when links capable of transmitting tension exist between particles. We develop and calibrate a discrete element method contact model to simulate the mechanics of the macroscopic flexible granular chains and conduct simulations of the angle of repose experiments of these chains by extracting a chain-filled cylinder and allowing the material to flow out under gravity and repose. We evaluate various micro-mechanical, topological and macroscopic parameters to elucidate the mechanics of the repose behaviour of chain ensembles. It is the ability of the links connecting the individual particles to transmit tensile forces along the chain backbone that provides lateral stability to the column, enabling them to stand. In particular, the contact force rearrangement inside the columns generates a self-confining radial stress near the base of the columns, which provides an important stabilizing stress.

Nonlinear effect of grain elongation on the flow rate in silo discharge

By means of two-dimensional numerical simulations based on contact dynamics, we present a systematic analysis of the joint effects of grain shape (i.e., grain elongation) and system size on silo discharge for increasing orifice sizes D. Grains are rounded-cap rectangles whose aspect ratio are varied from 1 (disks) to 7. In order to clearly isolate the effect of grain shape, the mass of the grains is keeping constant as well as the condition of the discharge by reintroducing the exiting grains at the top of the silo. In order to quantify the possible size effects, the thickness W of the silos is varied from 7 to 70 grains diameter, while keeping the silos aspect ratio always equal to 2. We find that, as long as size effects are negligible, the flow rate Q increases as a Beverloo-like function with D, also for the most elongated grains. In contrast, the effects of grain elongation on the flow rate depend on orifice size. For small normalized orifice sizes, the flow rate is nearly independent with grain elongation. For intermediate normalized orifice sizes the flow rate first increases with grain elongation up to a maximum value that depends on the normalized size of the orifice and saturates as the grains become more elongated. For larger normalized orifice size, the flow rate is an increasing function of grains' aspect ratio. Velocity profiles and packing fraction profiles close to the orifice turn out to be self-similar for all grain shapes and for the whole range of orifice and system sizes studied. Following the methodology introduced by Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.248001], we explain the nonlinear variation of Q with grain elongation, and for all orifice sizes, from compensation mechanisms between the velocity and packing fraction measured at the center of the orifice. Finally, an equation to predict the evolution of Q as a function of the aspect ratio of the grains is deduced.

Comparison of compression versus shearing near jamming, for a simple model of athermal frictionless disks in suspension

Using a simplified model for a non-Brownian suspension, we numerically study the response of athermal, overdamped, frictionless disks in two dimensions to isotropic and uniaxial compression, as well as to pure and simple shearing, all at finite constant strain rates ε[over ̇]. We show that isotropic and uniaxial compression result in the same jamming packing fraction ϕ_{J}, while pure-shear- and simple-shear-induced jamming occurs at a slightly higher ϕ_{J}^{*}, consistent with that found previously for simple shearing. A critical scaling analysis of pure shearing gives critical exponents consistent with those previously found for both isotropic compression and simple shearing. Using orientational order parameters for contact bond directions, we compare the anisotropy of the force and contact networks at both lowest nematic order, as well as higher 2n-fold order.

Colloidal Shear-Thickening Fluids Using Variable Functional Star-Shaped Particles: A Molecular Dynamics Study

Complex colloidal fluids, depending on constituent shapes and packing fractions, may have a wide range of shear-thinning and/or shear-thickening behaviors. An interesting way to transition between different types of such behavior is by infusing complex functional particles that can be manufactured using modern techniques such as 3D printing. In this paper, we perform 2D molecular dynamics simulations of such fluids with infused star-shaped functional particles, with a variable leg length and number of legs, as they are infused in a non-interacting fluid. We vary the packing fraction (ϕ) of the system, and for each different system, we apply shear at various strain rates, turning the fluid into a shear-thickened fluid and then, in jammed state, rising the apparent viscosity of the fluid and incipient stresses. We demonstrate the dependence of viscosity on the functional particles’ packing fraction and we show the role of shape and design dependence of the functional particles towards the transition to a shear-thickening fluid.

Testing mean-field theory for jamming of non-spherical particles: contact number, gap distribution, and vibrational density of states

We perform numerical simulations of the jamming transition of non-spherical particles in two dimensions. In particular, we systematically investigate how the physical quantities at the jamming transition point behave when the shapes of the particle deviate slightly from the perfect disks. For efficient numerical simulation, we first derive an analytical expression of the gap function, using the perturbation theory around the reference disks. Starting from disks, we observe the effects of the deformation of the shapes of particles by the n-th-order term of the Fourier series [Formula: see text]. We show that the several physical quantities, such as the number of contacts, gap distribution, and characteristic frequencies of the vibrational density of states, show the power-law behaviors with respect to the linear deviation from the reference disks. The power-law behaviors do not depend on n and are fully consistent with the mean-field theory of the jamming of non-spherical particles. This result suggests that the mean-field theory holds very generally for nearly spherical particles.

Start-up shear of spherocylinder packings: Effect of friction

We study the response to shear deformations of packings of long spherocylindrical particles that interact via frictional forces with friction coefficient μ. The packings are produced and deformed with the help of molecular dynamics simulations combined with minimization techniques performed on a GPU. We calculate the linear shear modulus g_{∞}, which is orders of magnitude larger than the modulus g_{0} in the corresponding frictionless system. The motion of the particles responsible for these large frictional forces is governed by and increases with the length ℓ of the spherocylinders. One consequence of this motion is that the shear modulus g_{∞} approaches a finite value in the limit ℓ→∞, even though the density of the packings vanishes, ρ∝ℓ^{-2}. By way of contrast, the frictionless modulus decreases to zero, g_{0}∼ℓ^{-2}, in accordance with the behavior of density. Increasing the strain beyond a value γ_{c}∼μ, the packing strain weakens from the large frictional to the smaller frictionless modulus when contacts saturate at the Coulomb inequality and start to slide. In this regime, sliding friction contributes a "yield stress" σ_{y}=g_{∞}γ_{c} and the stress behaves as σ=σ_{y}+g_{0}γ. The interplay between static and sliding friction gives rise to hysteresis in oscillatory shear simulations.

Impact of sample scaling on shear strength: coupled effects of grains size and shape

Size limitations of geotechnical testing equipment often require that samples of coarse granular materials have to be scaled in order to be tested in the laboratory. Scaling implies a convenient modification of the particle size distribution (PSD) to reduce particle sizes. However, it is well known that particle size and shape may be correlated in nature, due to geological factors (as an example). By means of two-dimensional contact dynamics simulations, we analyzed the effect of altering the size span on the shear strength of granular materials when particle size and shape are correlated. Two different systems were considered: one made of only circular particles, and the second made of size-shape correlated particles. By varying systematically the size span we observed that the resulting alteration of material strength is not due to the change in particle sizes. It results instead from the variation of the particle shapes induced by the modification of the PSD, when particle size and particle shape are correlated. This finding suggests that particle shape distribution is a higher order factor than PSD for the shear strength of granular materials. It also highlights the importance of particle shape quantification in soil classification and the case for its consideration in activities such as sampling, subsampling, and scaling of coarse materials for geotechnical testing

Shape or friction? Which of these characteristics drives the shear strength in granular systems?

The shape of the particles and local friction, separately, are known to strongly affect the macroscopic properties of an assembly of grains. But the combined effects of these two parameters still remain poorly described. By means of extensive two dimensional contact dynamics simulations, we perform a systematic analysis of the interplay between friction and shape on strength properties of granular systems. The shape of the particles is varied from disks to triangles, while the friction is varied from 0 to 0.7. We find that the macroscopic friction first increases with angularity, but it may decline (for low friction values), saturate (for intermediates friction values), or continue to increase (for large friction values) for the most angular shapes. In other words, the effect of the particle’s angularity on the shear strength depends on the level of sliding friction. In contrast, the effect of local friction on the shear strength does not depend on the specific properties of shape. The results presented here highlight the subtle coupling existing between shape and friction effects.

Planar column collapse of elongated grains

The granular column collapse is a benchmark configuration for the study of granular flows in dry, saturated, and submerged conditions. The collapse sequence and resultant mobility is acknowledged to be controlled by the column aspect ratio, while grain properties define the relative transition of each stage. Grain shape effects are found to modify the global shear resistance of granular media, with a strong and coupled interaction when interacting with a fluid. In this work, we present the first steps towards the study of grain shape effects in a column collapse when interacting with an ambient fluid. For this purpose, we use a planar configuration and explore the collapse of a column consisting of rod-like grains and study the initial and after collapse grain orientations. On it, the mobilized grains deposit in a preferential horizontal orientation, but further experiments are required to confirm if a nematic configuration can be achieved.

Structural characteristics of ordered clusters in packs of ellipses

Structural characteristics of two-dimensional elliptic granular packs with various aspect ratios and intergranular friction coefficients were studied using the Discrete Element Method (DEM). Isotropic compaction from random unjammed state leads to a jammed state with polycrystals of orientationally ordered clusters (OOC). The OOCs were identified using a cluster labelling algorithm, based on the relative angle Δθ between the major axes of two contacting particles. The threshold value of Δθ was optimised to give the strongest correlation between OOCs and the force chain network. We found that the resulting OOC size distribution decays algebraically with an exponent of −2, independently of grain aspect ratio and material properties.

Combined effects of contact friction and particle shape on strength properties and microstructure of sheared granular media

We present a systematic numerical investigation concerning the combined effects of sliding friction and particle shape (i.e., angularity) parameters on the shear strength and microstructure of granular packings. Sliding friction at contacts varied from 0 (frictionless particles) to 0.7, and the particles were irregular polygons with an increasing number of sides, ranging from triangles to disks. We find that the effect of local friction on shear strength follows the same trend for all shapes. Strength first increases with local friction and then saturates at a shape-dependent value. In contrast, the effect of angularity varies, depending on the level of sliding friction. For low friction values (i.e., under 0.3), the strength first increases with angularity and then declines for the most angular shapes. For high friction values, strength systematically increases with angularity. At the microscale, we focus on the connectivity and texture of the contact and force networks. In general terms, increasing local friction causes these networks to be less connected and more anisotropic. In contrast, increasing particle angularity may change the network topology in different directions, directly affecting the macroscopic shear strength. These analyses and data constitute a first step toward understanding the joint effect of local variables such as friction and grain shape on the macroscopic rheology of granular systems.

Random sequential adsorption of partially ordered discorectangles onto a continuous plane

A computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane. The problem was analyzed for a wide range of discorectangle aspect ratios (ɛ∈[1;100]). We studied the anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing fraction found at different values of such the alignment are discussed. Partial ordering of the discorectangles significantly affected the packing fraction at the jamming state, φ_{j}, and shifted the cusps in the φ_{j}(ɛ) dependencies. The structure of the jammed state was analyzed using the adsorption of disks of different diameters into the porous space between the deposited discorectangles. The analysis of the connectivity between the discorectangles was performed assuming a core-shell structure of particles.

Yielding, rigidity, and tensile stress in sheared columns of hexapod granules

Granular packings of nonconvex or elongated particles can form freestanding structures like walls or arches. For some particle shapes, such as staples, the rigidity arises from interlocking of pairs of particles, but the origins of rigidity for noninterlocking particles remains unclear. We report on experiments and numerical simulations of sheared columns of "hexapods," particles consisting of three mutually orthogonal sphero-cylinders whose centers coincide. We vary the length-to-diameter aspect ratio, α, of the sphero-cylinders and subject the packings to quasistatic direct shear. For small α, we observe a finite yield stress. For large α, however, the column becomes rigid when sheared, supporting stresses that increase sharply with increasing strain. Analysis of x-ray microcomputed tomography (micro-CT) data collected during the shear reveals that the stiffening is associated with a tilted, oblate cluster of hexapods near the nominal shear plane in which particle deformation and average contact number both increase. Simulation results show that the particles are collectively under tension along one direction, even though they do not interlock pairwise. These tensions comes from contact forces carrying large torques, and they are perpendicular to the compressive stresses in the packing. They counteract the tendency to dilate, thus stabilizing the particle cluster.

Shear-driven flow of athermal, frictionless, spherocylinder suspensions in two dimensions: Particle rotations and orientational ordering

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate γ[over ̇]. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions ϕ and particle asphericities α at small γ[over ̇], we study the angular rotation θ[over ̇]_{i} and the nematic orientational ordering S_{2} of the particles induced by the shear flow, finding a nonmonotonic behavior as the packing ϕ is varied. We interpret this nonmonotonic behavior as a crossover from dilute systems at small ϕ, where single-particle-like behavior occurs, to dense systems at large ϕ, where the geometry of the dense packing dominates and a random Poisson-like process for particle rotations results. We also argue that the finite nematic ordering S_{2} is a consequence of the shearing serving as an ordering field, rather than a result of long-range cooperative behavior among the particles. We arrive at these conclusions by consideration of (i) the distribution of waiting times for a particle to rotate by π, (ii) the behavior of the system under pure, as compared to simple, shearing, (iii) the relaxation of the nematic order parameter S_{2} when perturbed away from the steady state, and (iv) by construction, a numerical mean-field model for the rotational motion of a particle. Our results also help to explain the singular behavior observed when taking the α→0 limit approaching circular disks.

Effects of particle shape mixture on strength and structure of sheared granular materials

Using bi-dimensional discrete element simulations, the shear strength and microstructure of granular mixtures composed of particles of different shapes are systematically analyzed as a function of the proportion of grains of a given number of sides and the combination of different shapes (species) in one sample. We varied the angularity of the particles by varying the number of sides of the polygons from 3 (triangles) up to 20 (icosagons) and disks. The samples analyzed were built keeping in mind the following cases: (1) increase of angularity and species starting from disks; (2) decrease of angularity and increase of species starting from triangles; (3) random angularity and increase of species starting from disks and from polygons. The results show that the shear strength vary monotonically with increasing numbers of species (it may increase or decrease), even in the random mixtures (case 3). At the micro-scale, the variation in shear strength as a function of the number of species is due to different mechanisms depending on the cases analyzed. It may result from the increase of both the geometrical and force anisotropies, from only a decrease of frictional anisotropy, or from compensation mechanisms involving geometrical and force anisotropies.

Shear-driven flow of athermal, frictionless, spherocylinder suspensions in two dimensions: Stress, jamming, and contacts

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state shear strain applied at a fixed finite rate. Energy dissipation occurs via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension and resulting in a Newtonian rheology. We study the resulting pressure p and deviatoric shear stress σ of the interacting spherocylinders as a function of packing fraction ϕ, strain rate γ[over ̇], and a parameter α that measures the asphericity of the particles; α is varied to consider the range from nearly circular disks to elongated rods. We consider the direction of anisotropy of the stress tensor, the macroscopic friction μ=σ/p, and the divergence of the transport coefficient η_{p}=p/γ[over ̇] as ϕ is increased to the jamming transition ϕ_{J}. From a phenomenological analysis of Herschel-Bulkley rheology above jamming, we estimate ϕ_{J} as a function of asphericity α and show that the variation of ϕ_{J} with α is the main cause for differences in rheology as α is varied; when plotted as ϕ/ϕ_{J}, rheological curves for different α qualitatively agree. However, a detailed scaling analysis of the divergence of η_{p} for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We also compute the number of contacts per particle Z in the system and show that the value at jamming Z_{J} is a nonmonotonic function of α that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length P(ϑ) at polar angle ϑ with respect to the spherocylinder spine and find that as α→0 this distribution seems to diverge at ϑ=π/2, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally, we consider the variation of the average contact force as a function of location on the particle surface.

Kinematic Model of Transient Shape-Induced Anisotropy in Dense Granular Flow

Nonspherical particles are ubiquitous in nature and industry, yet previous theoretical models of granular media are mostly limited to systems of spherical particles. The problem is that in systems of nonspherical anisotropic particles, dynamic particle alignment critically affects their mechanical response. To study the tendency of such particles to align, we propose a simple kinematic model that relates the flow to the evolution of particle alignment with respect to each other. The validity of the proposed model is supported by comparison with particle-based simulations for various particle shapes ranging from elongated rice-like (prolate) to flattened lentil-like (oblate) particles. The model shows good agreement with the simulations for both steady-state and transient responses, and advances the development of comprehensive constitutive models for shape-anisotropic particles.

Rheology of granular materials composed of crushable particles

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

Inertial shear flow of assemblies of frictionless polygons: Rheology and microstructure

Motivated by the understanding of shape effects in granular materials, we numerically investigate the macroscopic and microstructural properties of anisotropic dense assemblies of frictionless polydisperse rigid pentagons in shear flow, and compare them with similar systems of disks. Once subjected to large cumulative shear strains their rheology and microstructure are investigated in uniform steady states, depending on inertial number I, which ranges from the quasistatic limit ([Formula: see text]) to 0.2. In the quasistatic limit both systems are devoid of Reynolds dilatancy, i.e., flow at their random close packing density. Both macroscopic friction angle [Formula: see text], an increasing function of I , and solid fraction [Formula: see text], a decreasing function of I, are larger with pentagons than with disks at small I, but the differences decline for larger I and, remarkably, nearly vanish for [Formula: see text]. Under growing I , the depletion of contact networks is considerably slower with pentagons, in which increasingly anisotropic, but still well-connected force-transmitting structures are maintained throughout the studied range. Whereas contact anisotropy and force anisotropy contribute nearly equally to the shear strength in disk assemblies, the latter effect dominates with pentagons at small I, while the former takes over for I of the order of 10^-2. The size of clusters of grains in side-to-side contact, typically comprising more than 10 pentagons in the quasistatic limit, very gradually decreases for growing I.

Compression-driven jamming of athermal frictionless spherocylinders in two dimensions

We simulate numerically the compression-driven jamming of athermal, frictionless, soft-core spherocylinders in two dimensions, for a range of particle aspect ratios α. We find the critical packing fraction ϕ_{J}(α) for the jamming transition and the average number of contacts per particle z_{J}(α) at jamming. We find that both are nonmonotonic, with a peak at α≈1. We find that configurations at the compression-driven jamming point are always hypostatic for all α, with z_{J}<z_{iso}=2d_{f}=6 the isostatic value. We show that, for moderately elongated spherocylinders, there is no orientational ordering upon athermal compression through jamming. We analyze in detail the eigenmodes of the dynamical matrix close to the jamming point for a few different values of the aspect ratio, from nearly circular to moderately elongated. We find that there are low frequency bands containing N(z_{iso}-z_{J})/2 modes, such that the frequencies of these modes vanish as ϕ→ϕ_{J}. We consider the extended versus localized nature of these low frequency modes, and the extent to which they involve translational or rotational motion, and find many low frequency sliding modes where particles can move with little rotation. We highlight the importance of treating side-to-side contacts, along flat sides of the spherocylinder, properly for the correct determination of z_{J}. We note the singular nature of taking the α→0 limit. We discuss the similarities and differences with previous work on jammed ellipses and ellipsoids, to illustrate the effects that different particle shapes have on configurations at jamming.

Anisotropic particles strengthen granular pillars under compression

We probe the effects of particle shape on the global and local behavior of a two-dimensional granular pillar, acting as a proxy for a disordered solid, under uniaxial compression. This geometry allows for direct measurement of global material response, as well as tracking of all individual particle trajectories. In general, drawing connections between local structure and local dynamics can be challenging in amorphous materials due to lower precision of atomic positions, so this study aims to elucidate such connections. We vary local interactions by using three different particle shapes: discrete circular grains (monomers), pairs of grains bonded together (dimers), and groups of three bonded in a triangle (trimers). We find that dimers substantially strengthen the pillar and the degree of this effect is determined by orientational order in the initial condition. In addition, while the three particle shapes form void regions at distinct rates, we find that anisotropies in the local amorphous structure remain robust through the definition of a metric that quantifies packing anisotropy. Finally, we highlight connections between local deformation rates and local structure.

Rheology of dense granular flows for elongated particles

We study the rheology of dense granular flows for frictionless spherocylinders by means of 3D numerical simulations. As in the case of spherical particles, the effective friction μ is an increasing function of the inertial number I, and we systematically investigate the dependence of μ on the particle aspect ratio Q, as well as that of the normal stress differences, the volume fraction, and the coordination number. We show in particular that the quasistatic friction coefficient is nonmonotonic with Q: from the spherical case Q=1, it first sharply increases, reaches a maximum around Q≃1.05, and then gently decreases until Q=3, passing its initial value at Q≃2. We provide a microscopic interpretation for this unexpected behavior through the analysis of the distribution of dissipative contacts around the particles: as compared to spheres, slightly elongated grains enhance contacts in their central cylindrical band, whereas at larger aspect ratios particles tend to align and dissipate by preferential contacts at their hemispherical caps.

Shear strength and microstructure of polydisperse packings: The effect of size span and shape of particle size distribution

By means of extensive contact dynamics simulations, we analyzed the effect of particle size distribution (PSD) on the strength and microstructure of sheared granular materials composed of frictional disks. The PSDs are built by means of a normalized β function, which allows the systematic investigation of the effects of both, the size span (from almost monodisperse to highly polydisperse) and the shape of the PSD (from linear to pronouncedly curved). We show that the shear strength is independent of the size span, which substantiates previous results obtained for uniform distributions by packing fraction. Notably, the shear strength is also independent of the shape of the PSD, as shown previously for systems composed of frictionless disks. In contrast, the packing fraction increases with the size span, but decreases with more pronounced PSD curvature. At the microscale, we analyzed the connectivity and anisotropies of the contacts and forces networks. We show that the invariance of the shear strength with the PSD is due to a compensation mechanism which involves both geometrical sources of anisotropy. In particular, contact orientation anisotropy decreases with the size span and increases with PSD curvature, while the branch length anisotropy behaves inversely.

Revealing the frictional transition in shear-thickening suspensions

Shear thickening in dense particulate suspensions was recently proposed to be driven by the activation of friction above an onset stress needed to overcome repulsive forces between particles. Testing this scenario represents a major challenge because classical rheological approaches do not provide access to the frictional properties of suspensions. Here we adopt a different strategy inspired by pressure-imposed configurations in granular flows that specifically gives access to this information. By investigating the quasi-static avalanche angle, compaction, and dilatancy effects in different nonbuoyant suspensions flowing under gravity, we demonstrate that particles in shear-thickening suspensions are frictionless under low confining pressure. Moreover, we show that tuning the range of the repulsive force below the particle roughness suppresses the frictionless state and also the shear-thickening behavior of the suspension. These results, which link microscopic contact physics to the suspension macroscopic rheology, provide direct evidence that the recent frictional transition scenario applies in real suspensions.

Binary mixtures of disks and elongated particles: Texture and mechanical properties

We analyze the shear strength and microstructure of binary granular mixtures consisting of disks and elongated particles by varying systematically both the mixture ratio and degree of homogeneity (from homogeneous to fully segregated). The contact dynamics method is used for numerical simulations with rigid particles interacting by frictional contacts. A counterintuitive finding of this work is that the shear strength, packing fraction, and, at the microscopic scale, the fabric, force, and friction anisotropies of the contact network are all nearly independent of the degree of homogeneity. In other words, homogeneous mixtures have the same strength properties as segregated packings of the two particle shapes. In contrast, the shear strength increases with the proportion of elongated particles correlatively with the increase of the corresponding force and fabric anisotropies. By a detailed analysis of the contact network topology, we show that various contact types contribute differently to force transmission and friction mobilization.

Phase diagram for inertial granular flows

Flows of hard granular materials depend strongly on the interparticle friction coefficient μ_{p} and on the inertial number I, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for 10^{-4}≲I≲10^{-1}: frictionless, frictional sliding, and rolling. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as μ_{p} increases from zero at constant I. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display nonmonotonic behavior with μ_{p}, corresponding to transitions between the three regimes of flow. We rationalize the phase boundaries between these regimes, show that energy balance yields scaling relations between microscopic properties in each of them, and derive the strain scale at which particles lose memory of their velocity. For the frictional sliding regime most relevant experimentally, we find for I≥10^{-2.5} that the growth of the macroscopic friction μ(I) with I is induced by an increase of collisional dissipation. This implies in that range that μ(I)-μ(0)∼I^{1-2b}, where b≈0.2 is an exponent that characterizes both the dimensionless velocity fluctuations L∼I^{-b} and the density of sliding contacts χ∼I^{b}.

Effects of shape and size polydispersity on strength properties of granular materials

By means of extensive contact dynamics simulations, we analyze the combined effects of polydispersity both in particle size and in particle shape, defined as the degree of shape irregularity, on the shear strength and microstructure of sheared granular materials composed of pentagonal particles. We find that the shear strength is independent of the size span, but unexpectedly, it declines with increasing shape polydispersity. At the same time, the solid fraction is an increasing function of both the size span and the shape polydispersity. Hence, the densest and loosest packings have the same shear strength. At the scale of the particles and their contacts, we analyze the connectivity of particles, force transmission, and friction mobilization as well as their anisotropies. We show that stronger forces are carried by larger particles and propped by an increasing number of small particles. The independence of shear strength with regard to size span is shown to be a consequence of contact network self-organization, with the falloff of contact anisotropy compensated by increasing force anisotropy.

Bonded-cell model for particle fracture

Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.

Internal friction and absence of dilatancy of packings of frictionless polygons

By means of numerical simulations, we show that assemblies of frictionless rigid pentagons in slow shear flow possess an internal friction coefficient (equal to 0.183±0.008 with our choice of moderately polydisperse grains) but no macroscopic dilatancy. In other words, despite side-side contacts tending to hinder relative particle rotations, the solid fraction under quasistatic shear coincides with that of isotropic random close packings of pentagonal particles. Properties of polygonal grains are thus similar to those of disks in that respect. We argue that continuous reshuffling of the force-bearing network leads to frequent collapsing events at the microscale, thereby causing the macroscopic dilatancy to vanish. Despite such rearrangements, the shear flow favors an anisotropic structure that is at the origin of the ability of the system to sustain shear stress.

Particle alignment and clustering in sheared granular materials composed of platy particles

By means of molecular dynamics simulations, we investigate the texture and local ordering in sheared packings composed of cohesionless platy particles. The morphology of large packings of platy particles in quasistatic equilibrium is complex due to the combined effects of local nematic ordering of the particles and anisotropic orientations of contacts between particles. We find that particle alignment is strongly enhanced by the degree of platyness and leads to the formation of face-connected clusters of exponentially decaying size. Interestingly, due to dynamics in continuous shearing, this ordering phenomenon emerges even in systems composed of particles of very low platyness differing only slightly from spherical shape. The number of clusters is an increasing function of platyness. However, at high platyness the proportion of face-face interactions is too low to allow for their percolation throughout the system.

Effect of size polydispersity versus particle shape in dense granular media

We present a detailed analysis of the morphology of granular systems composed of frictionless pentagonal particles by varying systematically both the size span and particle shape irregularity, which represent two polydispersity parameters of the system. The microstructure is characterized in terms of various statistical descriptors such as global and local packing fractions, radial distribution functions, coordination number, and fraction of floating particles. We find that the packing fraction increases with the two parameters of polydispersity, but the effect of shape polydispersity for all the investigated structural properties is significant only at low size polydispersity where the positional and/or orientational ordering of the particles prevail. We focus in more detail on the class of side/side contacts, which is the interesting feature of our system as compared to a packing of disks. We show that the proportion of such contacts has weak dependence on the polydispersity parameters. The side- side contacts do not percolate but they define clusters of increasing size as a function of size polydispersity and decreasing size as a function of shape polydispersity. The clusters have anisotropic shapes but with a decreasing aspect ratio as polydispersity increases. This feature is argued to be a consequence of strong force chains (forces above the mean), which are mainly captured by side-side contacts. Finally, the force transmission is intrinsically multiscale, with a mean force increasing linearly with particle size.

Micro-macro correlations and anisotropy in granular assemblies under uniaxial loading and unloading

The influence of contact friction on the behavior of dense, polydisperse granular assemblies under uniaxial (oedometric) loading and unloading deformation is studied using discrete element simulations. Even though the uniaxial deformation protocol is one of the "simplest" element tests possible, the evolution of the structural anisotropy necessitates its careful analysis and understanding, since it is the source of interesting and unexpected observations. On the macroscopic, homogenized, continuum scale, the deviatoric stress ratio and the deviatoric fabric, i.e., the microstructure behave in a different fashion during uniaxial loading and unloading. The maximal stress ratio and strain increase with increasing contact friction. In contrast, the deviatoric fabric reaches its maximum at a unique strain level independent of friction, with the maximal value decreasing with friction. For unloading, both stress and fabric respond to unloading strain with a friction-dependent delay but at different strains. On the micro-level, a friction-dependent non-symmetry of the proportion of weak (strong) and sliding (sticking) contacts with respect to the total contacts during loading and unloading is observed. Coupled to this, from the directional probability distribution, the "memory" and history-dependent behavior of granular systems is confirmed. Surprisingly, while a rank-2 tensor is sufficient to describe the evolution of the normal force directions, a sixth order harmonic approximation is necessary to describe the probability distribution of contacts, tangential force, and mobilized friction. We conclude that the simple uniaxial deformation activates microscopic phenomena not only in the active Cartesian directions, but also at intermediate orientations, with the tilt angle being dependent on friction, so that this microstructural features cause the interesting, nontrivial macroscopic behavior.

Packings of irregular polyhedral particles: strength, structure, and effects of angularity

We present a systematic numerical investigation of the shear strength and structure of granular packings composed of irregular polyhedral particles. The angularity of the particles is varied by increasing the number of faces from 8 (octahedronlike shape) to 596. We find that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below 46 faces). At the same time, the packing fraction increases to a peak value but declines for more angular particles. We analyze the connectivity and anisotropy of the microstructure by considering both the contacts and branch vectors joining particle centers. The increase of the shear strength with angularity is shown to be due to a net increase of the fabric and force anisotropies but at higher particle angularity a rapid falloff of the fabric anisotropy is compensated by an increase of force anisotropy, leading thus to the saturation of shear strength.

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.

Rheology of three-dimensional packings of aggregates: microstructure and effects of nonconvexity

We use three-dimensional contact dynamics simulations to analyze the rheological properties of granular materials composed of rigid aggregates. The aggregates are made from four overlapping spheres and described by a nonconvexity parameter depending on the relative positions of the spheres. The macroscopic and microstructural properties of several sheared packings are analyzed as a function of the degree of nonconvexity of the aggregates. We find that the internal angle of friction increases with the nonconvexity. In contrast, the packing fraction first increases to a maximum value but declines as the nonconvexity increases further. At a high level of nonconvexity, the packings are looser but show a higher shear strength. At the microscopic scale, the fabric and force anisotropy, as well as the friction mobilization, are enhanced by multiple contacts between aggregates and interlocking, thus revealings the mechanical and geometrical origins of shear strength.

Influence of the feeding mechanism on deposits of square particles

In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ.