Effect of size polydispersity versus particle shape in dense granular media

NVU view on energy polydisperse Lennard-Jones systems

When energy polydispersity is introduced into the Lennard-Jones (LJ) system, there is little effect on structure and dynamics [T. S. Ingebrigtsen and J. C. Dyre, J. Phys. Chem. B 127, 2837 (2023)10.1021/acs.jpcb.3c00346]. For instance, at a given state point both the radial distribution function and the mean-square displacement as a function of time are virtually unaffected by even large energy polydispersity, which is in stark contrast to what happens when size polydispersity is introduced. We here argue-and validate by simulations of up to 30% polydispersity-that this almost invariance of structure and dynamics reflects an approximate invariance of the constant-potential-energy surface. Because NVU dynamics defined as geodesic motion at constant potential energy is equivalent to Newtonian dynamics in the thermodynamic limit, the approximate invariance of the constant-potential-energy surface implies virtually the same physics of energy polydisperse LJ systems as of the standard single-component version. In contrast, the constant-potential-energy surface is significantly affected by introducing size polydispersity.

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.

An explicit granular-mechanics approach to marine sediment acoustics

Here, we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms, which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features.

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.

Effects of polydispersity on the plastic behaviors of dense two-dimensional granular systems under shear

We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied amorphous systems with low polydispersity. In particular, an analysis of the nonaffine motion of particles reveals qualitative differences between large and small particles: The smaller particles have dramatically more nonaffine motion, which is induced by the presence of the large particles. We characterize how the nonaffine motion changes from the low- to high-polydispersity regimes. We further demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes. A macroscopic consequence of the nonaffine motion is a decrease in the energy dissipation rate for highly polydisperse samples, which is due both to a geometric consequence of the changing jamming conditions for higher polydispersity and to the changing character of nonaffine motion.

Compacting an assembly of soft balls far beyond the jammed state: Insights from three-dimensional imaging

Very soft grain assemblies have unique shape-changing capabilities that allow them to be compressed far beyond the rigid jammed state by filling void spaces more effectively. However, accurately following the formation of these systems by monitoring the creation of new contacts, monitoring the changes in grain shape, and measuring grain-scale stresses is challenging. We developed an experimental method that overcomes these challenges and connects their microscale behavior to their macroscopic response. By tracking the local strain energy during compression, we reveal a transition from granular-like to continuous-like material. Mean contact geometry is shown to vary linearly with the packing fraction, which is supported by a mean field approximation. We also validate a theoretical framework which describes the compaction from a local view. Our experimental framework provides insights into the granular micromechanisms and opens perspectives for rheological analysis of highly deformable grain assemblies in various fields ranging from biology to engineering.

Even Strong Energy Polydispersity Does Not Affect the Average Structure and Dynamics of Simple Liquids

Size-polydisperse liquids have become standard models for avoiding crystallization, thereby enabling studies of supercooled liquids and glasses formed, e.g., by colloidal systems. Purely energy-polydisperse liquids have been studied much less, but provide an interesting alternative. We here study numerically the difference in structure and dynamics obtained by introducing these two kinds of polydispersity into systems of particles interacting via the Lennard-Jones and EXP pair potentials. To a very good approximation, the average pair structure and dynamics are unchanged even for strong energy polydispersity, which is not the case for size-polydisperse systems. When the system at extreme energy polydispersity undergoes a continuous phase separation into lower and higher particle-energy regions whose structure and dynamics are different from the average, the average structure and dynamics are still virtually the same as for the monodisperse system. Our findings are consistent with the fact that the distribution of forces on the individual particles do not change when energy polydispersity is introduced, while they do change in the case of size polydispersity. A theoretical explanation remains to be found, however.

Sedimentation path theory for mass-polydisperse colloidal systems

Both polydispersity and the presence of a gravitational field are inherent to essentially any colloidal experiment. While several theoretical works have focused on the effect of polydispersity on the bulk phase behavior of a colloidal system, little is known about the effect of a gravitational field on a polydisperse colloidal suspension. We extend here the sedimentation path theory to study sedimentation-diffusion-equilibrium of a mass-polydisperse colloidal system: the particles possess different buoyant masses but they are otherwise identical. The model helps to understand the interplay between gravity and polydispersity on sedimentation experiments. Since the theory can be applied to any parent distribution of buoyant masses, it can also be used to study the sedimentation of monodisperse colloidal systems. We find that mass-polydispersity has a strong influence in colloidal systems near density matching for which the bare density of the colloidal particles equals the solvent density. To illustrate the theory, we study crystallization in sedimentation-diffusion-equilibrium of a suspension of mass-polydisperse hard spheres.

Granular effects in sea ice rheology in the marginal ice zone

Sea ice in the marginal ice zone (MIZ) consists of relatively small floes with a wide size span. In response to oceanic and atmospheric forcing, it behaves as an approximately two-dimensional, highly polydisperse granular material. The established viscous-plastic rheologies used in continuum sea ice models are not suitable for the MIZ; the collisional rheology, in which sea ice is treated as a granular gas, captures only one aspect of the granular behaviour, typical for a narrow range of conditions when dynamics is dominated by binary floe collisions. This paper reviews rheology models and concepts from research on granular materials relevant for MIZ dynamics (average stress as a result of 'microscopic' interactions of grains; [Formula: see text] and collisional rheologies). Idealized discrete-element simulations are used to illustrate granular effects and strong influence of the floe size distribution on strain-stress relationships in sheared sea ice, demonstrating the need for an MIZ rheology model capturing the whole range of 'regimes', from quasi-static/dense flow in the inner MIZ to the inertial flow in the outer MIZ. This article is part of the theme issue 'Theory, modelling and observations of marginal ice zone dynamics: multidisciplinary perspectives and outlooks'.

Finding the grain size distribution that produces the densest arrangement in frictional sphere packings: Revisiting and rediscovering the century-old Fuller and Thompson distribution

By means of discrete-element methods, we investigate the joint effects of the grain size distribution (GSD) and contact friction on the structure of three-dimensional samples composed of spherical grains. Specifically, we compress these systems isotropically until jamming and then analyze their structure in terms of density, connectivity, coefficients of uniformity and curvature, and parameters of grading entropy. Our study focuses on power-law GSDs and particularly on the Fuller and Thompson distribution, proposed over a century ago. First, we show that, among the set of GSDs investigated, this particular distribution produces the densest and best-connected systems, falsifying a conjecture recently posed in the literature. Second, we find that the jamming packing fraction can be accurately predicted as a function of simple descriptors of the GSD, but among these descriptors the granular entropy concept proves to be the most useful. This allows for an alternative interpretation of both jamming and grading entropy concepts. Finally, we compare the Fuller and Thompson distribution with two well-known GSDs: that of the Apollonian sphere packing and that towards which granular systems evolve after intensive grain fracturing. Surprisingly, we find that these three GSDs are practically coincident in the limit of large size spans, despite having been introduced or discovered in different scientific contexts (i.e., engineering, mathematics, and earth sciences, respectively).

Three-dimensional compaction of soft granular packings

This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to 1, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increases, a transition is observed from a granular-like material with exponential tails of the shear stress distributions to a continuous-like material characterized by Gaussian-like distributions of the shear stresses. We develop an equation that describes the evolution of the packing fraction as a function of the applied pressure. This equation, based on the micromechanical expression of the granular stress tensor, the limit of the Hertz contact law for small deformation, and the power-law relation between the packing fraction and the coordination of the particles, provides good predictions from the jamming point up to very high densities without the need for tuning any parameters.

Rotational diffusion and rotational correlations in frictional amorphous disk packings under shear

We show here that rotations of round particles in amorphous disk packing reveal various nontrivial microscopic features when the packing is close to rigidification. We analyze experimental measurements on disk packing subjected to simple shear deformation with various inter-particle friction coefficients and across a range of volume fractions where the system is known to stiffen. The analysis of measurements indicates that shear induces diffusive microrotation, that can be both enhanced and suppressed depending upon the volume fraction as well as the inter-particle friction. Rotations also display persistent anticorrelated motion. Spatial correlations in microrotation are observed to be directly correlated with system pressure. These observations point towards the broader mechanical relevance of collective dynamics in the rotational degree of freedom of particles.

Micromechanical description of the compaction of soft pentagon assemblies

We analyze the isotropic compaction of assemblies composed of soft pentagons interacting through classical Coulomb friction via numerical simulations. The effect of the initial particle shape is discussed by comparing packings of pentagons with packings of soft circular particles. We characterize the evolution of the packing fraction, the elastic modulus, and the microstructure (particle rearrangement, connectivity, contact force, and particle stress distributions) as a function of the applied stresses. Both systems behave similarly: the packing fraction increases and tends asymptotically to a maximum value ϕ_{max}, where the bulk modulus diverges. At the microscopic scale we show that particle rearrangements occur even beyond the jammed state, the mean coordination increases as a square root of the packing fraction, and the force and stress distributions become more homogeneous as the packing fraction increases. Soft pentagons experience larger particle rearrangements than circular particles, and such behavior decreases proportionally to the friction. Interestingly, the friction between particles also contributes to a better homogenization of the contact force network in both systems. From the expression of the granular stress tensor we develop a model that describes the compaction behavior as a function of the applied pressure, the Young modulus, and the initial shape of the particles. This model, settled on the joint evolution of the particle connectivity and the contact stress, provides outstanding predictions from the jamming point up to very high densities.

Optimal packing in 2D and 3D granular systems: Density, connectivity, and force distributions

In this work, we explore the influence of the grain size distribution (GSD) on density, connectivity and internal forces distributions, for both 2D and 3D granular packings built mechanically. For power law GSDs, we show that there is an exponent for which density and connectivity are optimized, and this exponent is close to those that characterize other well known GSDs such as the Fuller and Thompson distribution and the Appollonian packing. In addition, we studied the distributions of normal forces, finding that these can be well described by a power-law tail, specially for the GSDs with large size span. These results highlight the role of the GSD on internal structure and suggest important consequences on macroscopic properties.

Compression-Induced Tensile Mechanical Behaviors of the Crystalline Rock under Dynamic Loads

Characterization of the tensile mechanical behaviors of rocks under dynamic loads is of great significance for the practical engineering. However, thus far, its micromechanics have rarely been studied. This paper micromechanically investigated the compression-induced tensile mechanical behaviors of the crystalline rock using the grain-based model (GBM) by universal distinct element code (UDEC). Results showed that the crystalline rock has the rate- and heterogeneity-dependency of tensile behaviors. Essentially, dynamic Brazilian tensile strength increased in a linear manner as the loading rate increased. With the size distribution and morphology of grain-scale heterogeneity weakened, it increased, and this trend was obviously enhanced as the loading rate increased. Additionally, the rate-dependent characteristic became strong with the grain heterogeneity weakened. The grain heterogeneity prominently affected the stress distribution inside the synthetic crystalline rock, especially in the mixed compression and tension zone. Due to heterogeneity, there were tensile stress concentrations (TSCs) in the sample which could favor microcracking and strength weakening of the sample. As the grain heterogeneity weakened or the loading rate increased, the magnitude of the TSC had a decreasing trend and there was a transition from the sharp TSC to the smooth tensile stress distribution zone. The progressive failure of the crystalline rock was notably influenced by the loading rate, which mainly represented the formation of the crushing zone adjacent to two loading points. Our results are meaningful for the practical engineering such as underground protection works from stress waves.

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.

Scaling behavior of particle breakage in granular flows inside rotating drums

We perform systematic particle dynamics simulations of granular flows composed of breakable particles in a 2D rotating drum to investigate the evolution of the mean particle size and specific surface as a function of system parameters such as drum size, rotation speed, filling degree, and particle shape and size. The specific surface increases at a nearly constant rate up to a point where particle breakage begins to slow down. The rates of particle breakage for all values of system parameters are found to collapse on a master curve when the times are scaled by the characteristic time defined in the linear regime. We determine the characteristic time as a function of all system parameters, and we show that the rate of particle breakage can be expressed as a linear function of a general scaling parameter that incorporates all our system parameters. This scaling behavior provides a general framework for the upscaling of drum grinding process from laboratory to industrial scale.

Additive rheology of complex granular flows

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows.

Granular materials are abundant in nature, but we haven’t fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

Effects of size polydispersity on random close-packed configurations of spherical particles

We analyze the packing properties of simulated three-dimensional polydisperse samples of spherical particles assembled by mechanical compaction with zero interparticle friction, leading to random close-packed configurations of the highest packing fraction. The particle size distributions are generated from the incomplete beta distribution with three parameters: A size span and two shape parameters that control the curvature of the distribution function. For each size distribution, the number of particles is determined by accounting for the statistical representativity of all particle size classes in terms of both the numbers and volumes of particles. Remarkably, the packing fraction increases, up to a small variability, with an effective size span, known as the coefficient of uniformity, that combines the three control parameters of the distribution. The local particle environments are characterized by the particle connectivities and anisotropies, which unveil the class of particles with four contact neighbors as the largest class with an increasing population as a function of size span, indicating the higher stability of particles trapped by four larger particles. As a result of increasing topological inhomogeneity of the packings, the force distributions get increasingly broader with increasing effective size span. Finally, we find that larger particles do not always carry stronger average stresses, in particular when the particle size distribution allows for a sufficiently large number of small 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.

Microstructure as a function of the grain size distribution for packings of frictionless disks: Effects of the size span and the shape of the distribution

This article presents a numerical study of the effects of grain size distribution (GSD) on the microstructure of two-dimensional packings of frictionless disks. The GSD is described by a power law with two parameters controlling the size span and the shape of the distribution. First, several samples are built for each combination of these parameters. Then, by means of contact dynamics simulations, the samples are densified in oedometric conditions and sheared in a simple shear configuration. The microstructure is analyzed in terms of packing fraction, local ordering, connectivity, and force transmission properties. It is shown that the microstructure is notoriously affected by both the size span and the shape of the GSD. These findings confirm recent observations regarding the size span of the GSD and extend previous works by describing the effects of the GSD shape. Specifically, we find that if the GSD shape is varied by increasing the proportion of small grains by a certain amount, it is possible to increase the packing fraction, increase coordination, and decrease the proportion of floating particles. Thus, by carefully controlling the GSD shape, it is possible to obtain systems that are denser and better connected, probably increasing the system's robustness and optimizing important strength properties such as stiffness, cohesion, and fragmentation susceptibility.

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.

Role of length polydispersity in the phase behavior of freely rotating hard-rectangle fluids

We use the density-functional formalism, in particular the scaled-particle theory, applied to a length-polydisperse hard-rectangle fluid to study its phase behavior as a function of the mean particle aspect ratio κ_{0} and polydispersity Δ_{0}. The numerical solutions of the coexistence equations are calculated by transforming the original problem with infinite degrees of freedoms to a finite set of equations for the amplitudes of the Fourier expansion of the moments of the density profiles. We divide the study into two parts. The first one is devoted to the calculation of the phase diagrams in the packing fraction η_{0}-κ_{0} plane for a fixed Δ_{0} and selecting parent distribution functions with exponential (the Schulz distribution) or Gaussian decays. In the second part we study the phase behavior in the η_{0}-Δ_{0} plane for fixed κ_{0} while Δ_{0} is changed. We characterize in detail the orientational ordering of particles and the fractionation of different species between the coexisting phases. Also we study the character (second vs first order) of the isotropic-nematic phase transition as a function of polydispersity. We particularly focus on the stability of the tetratic phase as a function of κ_{0} and Δ_{0}. The isotropic-nematic transition becomes strongly of first order when polydispersity is increased: The coexistence gap widens and the location of the tricritical point moves to higher values of κ_{0} while the tetratic phase is slightly destabilized with respect to the nematic one. The results obtained here can be tested in experiments on shaken monolayers of granular rods.

Effects of grain size distribution on the packing fraction and shear strength of frictionless disk packings

Using discrete element methods, the effects of the grain size distribution on the density and the shear strength of frictionless disk packings are analyzed. Specifically, two recent findings on the relationship between the system's grain size distribution and its rheology are revisited, and their validity is tested across a broader range of distributions than what has been used in previous studies. First, the effects of the distribution on the solid fraction are explored. It is found that the distribution that produces the densest packing is not the uniform distribution by volume fractions as suggested in a recent publication. In fact, the maximal packing fraction is obtained when the grading curve follows a power law with an exponent close to 0.5 as suggested by Fuller and Thompson in 1907 and 1919 [Trans Am. Soc. Civ. Eng. 59, 1 (1907) and A Treatise on Concrete, Plain and Reinforced (1919), respectively] while studying mixtures of cement and stone aggregates. Second, the effects of the distribution on the shear strength are analyzed. It is confirmed that these systems exhibit a small shear strength, even if composed of frictionless particles as has been shown recently in several works. It is also found that this shear strength is independent of the grain size distribution. This counterintuitive result has previously been shown for the uniform distribution by volume fractions. In this paper, it is shown that this observation keeps true for different shapes of the grain size distribution.

Structure of force networks in tapped particulate systems of disks and pentagons. I. Clusters and loops

The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this and the companion paper [Kondic et al., Phys. Rev. E 93, 062903 (2016)10.1103/PhysRevE.93.062903], we consider two-dimensional simulations of tapped systems built from frictional disks and pentagons, and study the structure of the force networks of granular packings by considering network's topology as force thresholds are varied. We show that the number of clusters and loops observed in the force networks as a function of the force threshold are markedly different for disks and pentagons if the tangential contact forces are considered, whereas they are surprisingly similar for the network defined by the normal forces. In particular, the results indicate that, overall, the force network is more heterogeneous for disks than for pentagons. Such differences in network properties are expected to lead to different macroscale response of the considered systems, despite the fact that averaged measures (such as force probability density function) do not show any obvious differences. Additionally, we show that the states obtained by tapping with different intensities that display similar packing fraction are difficult to distinguish based on simple topological invariants.

Identification of the fragmentation of brittle particles during compaction process by the acoustic emission technique

Some nuclear fuels are currently manufactured by a powder metallurgy process that consists of three main steps, namely preparation of the powders, powder compaction, and sintering of the compact. An optimum between size, shape and cohesion of the particles of the nuclear fuels must be sought in order to obtain a compact with a sufficient mechanical strength, and to facilitate the release of helium and fission gases during irradiation through pores connected to the outside of the pellet after sintering. Being simple to adapt to nuclear-oriented purposes, the Acoustic Emission (AE) technique is used to control the microstructure of the compact by monitoring the compaction of brittle Uranium Dioxide (UO2) particles of a few hundred micrometers. The objective is to identify in situ the mechanisms that occur during the UO2 compaction, and more specifically the particle fragmentation that is linked to the open porosity of the nuclear matter. Three zones of acoustic activity, strongly related to the applied stress, can be clearly defined from analysis of the continuous signals recorded during the compaction process. They correspond to particle rearrangement and/or fragmentation. The end of the noteworthy fragmentation process is clearly defined as the end of the significant process that increases the compactness of the material. Despite the fact that the wave propagation strongly evolves during the compaction process, the acoustic signature of the fragmentation of a single UO2 particle and a bed of UO2 particles under compaction is well identified. The waveform, with a short rise time and an exponential-like decay of the signal envelope, is the most reliable descriptor. The impact of the particle size and cohesion on the AE activity, and then on the fragmentation domain, is analyzed through the discrete AE signals. The maximum amplitude of the burst signals, as well as the mean stress corresponding to the end of the recorded AE, increase with increasing mean diameter of the particles. Moreover, the maximum burst amplitude increases with increasing particle cohesion.

Confined disordered strictly jammed binary sphere packings

Disordered jammed packings under confinement have received considerably less attention than their bulk counterparts and yet arise in a variety of practical situations. In this work, we study binary sphere packings that are confined between two parallel hard planes and generalize the Torquato-Jiao (TJ) sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)] to obtain putative maximally random jammed (MRJ) packings that are exactly isostatic with high fidelity over a large range of plane separation distances H, small to large sphere radius ratio α, and small sphere relative concentration x. We find that packing characteristics can be substantially different from their bulk analogs, which is due to what we term "confinement frustration." Rattlers in confined packings are generally more prevalent than those in their bulk counterparts. We observe that packing fraction, rattler fraction, and degree of disorder of MRJ packings generally increase with H, though exceptions exist. Discontinuities in the packing characteristics as H varies in the vicinity of certain values of H are due to associated discontinuous transitions between different jammed states. When the plane separation distance is on the order of two large-sphere diameters or less, the packings exhibit salient two-dimensional features; when the plane separation distance exceeds about 30 large-sphere diameters, the packings approach three-dimensional bulk packings. As the size contrast increases (as α decreases), the rattler fraction dramatically increases due to what we call "size-disparity" frustration. We find that at intermediate α and when x is about 0.5 (50-50 mixture), the disorder of packings is maximized, as measured by an order metric ψ that is based on the number density fluctuations in the direction perpendicular to the hard walls. We also apply the local volume-fraction variance σ(τ)(2)(R) to characterize confined packings and find that these packings possess essentially the same level of hyperuniformity as their bulk counterparts. Our findings are generally relevant to confined packings that arise in biology (e.g., structural color in birds and insects) and may have implications for the creation of high-density powders and improved battery designs.

Structural characterization of the packings of granular regular polygons

By using a recently developed method for discrete modeling of nonspherical particles, we simulate the random packings of granular regular polygons with three to 11 edges under gravity. The effects of shape and friction on the packing structures are investigated by various structural parameters, including packing fraction, the radial distribution function, coordination number, Voronoi tessellation, and bond-orientational order. We find that packing fraction is generally higher for geometrically nonfrustrated regular polygons, and can be increased by the increase of edge number and decrease of friction. The changes of packing fraction are linked with those of the microstructures, such as the variations of the translational and orientational orders and local configurations. In particular, the free areas of Voronoi tessellations (which are related to local packing fractions) can be described by log-normal distributions for all polygons. The quantitative analyses establish a clearer picture for the packings of regular polygons.

Effect of Size Polydispersity on the Nature of Lennard-Jones Liquids

Polydisperse fluids are encountered everywhere in biological and industrial processes. These fluids naturally show a rich phenomenology exhibiting fractionation and shifts in critical point and freezing temperatures. We study here the effect of size polydispersity on the basic nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, via two- and three-dimensional molecular dynamics computer simulations. A single-component liquid constituting spherical particles and interacting via the LJ potential is known to exhibit strong correlations between virial and potential energy equilibrium fluctuations at constant volume. This correlation significantly simplifies the physical description of the liquid, and these liquids are now known as Roskilde-simple (RS) liquids. We show that this simple nature of the single-component LJ liquid is preserved even for very high polydispersities (above 40% polydispersity for the studied uniform distribution). We also investigate isomorphs of moderately polydisperse LJ liquids. Isomorphs are curves in the phase diagram of RS liquids along which structure, dynamics, and some thermodynamic quantities are invariant in dimensionless units. We find that isomorphs are a good approximation even for polydisperse LJ liquids. The theory of isomorphs thus extends readily to size polydisperse fluids and can be used to improve even further the understanding of these intriguing systems.

Ultrasonic evaluation of the morphological characteristics of metallic powders in the context of mechanical alloying

An ultrasonic method is proposed to characterize the morphological (geometrical) aspects of powders through the elastic modulus dependence of their packing on the factors of polydispersity, coordination number and particle shape. During the mechanical alloying process, the variation in geometrical characteristics of powders provides critical information. Ultrasonic parameters are shown to be sensitive not only to the average contact number per bead (i.e. the coordination number) but also to characteristics of the bead size distribution, when given the same sample preparation and confining pressure. These parameters, in turn, are sensitive to both the granular medium polydispersity and particle shapes. A non-monotonic behavior of the ultrasonic velocity (and of the derived compressional wave modulus) is observed throughout the alloying process, which thus offers possibilities for powder structure monitoring.

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.