Frictionless Particles Research Articles

Unified Understanding of Nonlinear Rheology near the Jamming Transition Point.

When slowly sheared, jammed packings respond elastically before yielding. This linear elastic regime becomes progressively narrower as the jamming transition point is approached, and rich nonlinear rheologies such as shear softening and hardening or melting emerge. However, the physical mechanism of these nonlinear rheologies remains elusive. To clarify this, we numerically study jammed packings of athermal frictionless soft particles under quasistatic shear γ. We find the universal scaling behavior for the ratio of the shear stress σ and the pressure P, independent of the preparation protocol of the initial configurations. In particular, we reveal shear softening σ/P∼γ^{1/2} over an unprecedentedly wide range of strain up to the yielding point, which a simple scaling argument can rationalize.

Shear zones in granular mixtures of hard and soft particles with high and low friction.

Granular materials show inhomogeneous flows characterized by strain localization. When strain is localized in a sheared granular material, rigid regions of a nearly undeformed state are separated by shear bands, where the material yields and flows. The characteristics of the shear bands are determined by the geometry of the system, the micromechanical material properties, and the kinematics at the particle level. For a split-bottom shear cell, recent experimental work has shown that mixtures of hard, frictional and soft, nearly frictionless particles exhibit wider shear zones than samples with only one of the two components. To explain this finding, we investigate the shear zone properties and the stress response of granular mixtures using discrete element simulations. We show that both interparticle friction and elastic modulus determine the shear-band properties and packing density of granular mixtures of various mixing ratios, but their stress response depends strongly on the interparticle friction. Our study provides a fundamental understanding of the micromechanics of shear band formation in granular mixtures.

Granular binary mixtures improve energy dissipation efficiency of granular dampers

Granular dampers are systems used to attenuate undesired vibrations produced by mechanical devices. They consist of cavities filled by granular particles. In this work, we consider a granular damper filled with a binary mixture of frictionless spherical particles of the same material but different size using numerical discrete element method simulations. We show that the damping efficiency is largely influenced by the composition of the binary mixture.

Discontinuous rigidity transition associated with shear jamming in granular simulations.

We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition under quasi-static shear is discontinuous, with an instantaneous emergence of a system spanning rigid clusters at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transition associated with shear jamming is discontinuous, as demonstrated in the past for isotropic jamming of frictionless particles, and therefore a unifying feature of the jamming transition in general.

Three-dimensional DEM-CFD simulation of a lab-scale fluidized bed to support the development of two-fluid model approach

The present work is dedicated to the numerical study of the hydrodynamics of a pressurized fluidized-bed using an Euler–Lagrange approach, with the goal to gain insight into the Two-Fluid Model (TFM) approach. The gas phase is modeled by filtered Navier–Stokes equations, and the solid particles are tracked using a Discrete Element Method (DEM). Collisions are handled using a soft-sphere model. Numerical predictions of the mean (time-averaged) vertical particle velocity are compared with experimental measurements available from the literature, obtained from a Positron Emission Particle Tracking (PEPT) technique. In addition, DEM-Computational Fluid Dynamics (CFD) results are extensively compared with predictions from TFM numerical simulations. Results accounting for inelastic frictionless particle–particle collisions show a very good agreement with the experimental data and TFM results in the central zone of the reactor. In the near wall region the numerical simulation overestimates the downward particle velocity with respect to the experimental measurements, especially when the particle–wall friction is neglected. The influence of the friction at the wall is therefore further investigated and a local analysis of the particle–wall interactions is carried out. It is demonstrated that the long sustained contacts of particle assemblies with the wall in such a dense regime play a crucial role on the overall bed behavior. Therefore, it is recommended that this effect is taken into account in the boundary conditions of a TFM approach when it is used to predict bubbling fluidized beds. • DEM-CFD 3D simulation of a lab-scale fluidized bed • Comparison with experiments and Two-Fluid Model predictions • Local statistical analysis to characterize particle–wall interactions • Dominant friction effect at wall due to sustained particle–wall contacts

Disordered packings of binary mixtures of dimer particles

Disordered packings of non-spherical particles and their mixtures are abundant in nature, but have so far attracted only few systematic studies. Previous investigations of binary mixtures of specific convex shapes have established two generic properties: (i) the existence of a unique density maximum when shape or mixture composition of the two species are varied; (ii) the validity of an ideal mixing law indicating that the packing density is independent of the segregation state. These findings were so far only observed for mixtures of convex particles such as spherocylinders, ellipsoids, and spheres. Here, we investigate the packing properties of binary mixtures of frictionless dimer particles simulated by a gravitational pouring protocol in LAMMPS. Our results demonstrate the validity of (i, ii) also for such packings of non-convex particles. Moreover, we investigate the contact statistics of these packings to elucidate the microstructural features that underlie (i, ii). Our results show that the contact number per species also satisfies a simple mixing law and that similar microscopic rearrangements of contacts as in monodisperse dimer packings accompany the formation of the density peak in binary mixtures largely independent of the mixture composition.

Flow of lubricated granular material on an inclined plane

We have studied the gravity driven flow of spherical shaped, millimetric sized granular material coated with aspherical, micron-sized, near frictionless lubricant particles. Experiments were performed on an inclined plane using two different sized particles for varying concentrations of the lubricant. The particle volumetric flow rate exhibits a non-monotonic behavior with increasing lubricant concentration. It shows an increase at lower lubricant concentration followed by a decrease at higher lubricant concentration. The lubricant particles adhere to the granular particle surface thereby reducing the inter-particle friction. However, presence of lubricant particles at higher concentration damps out inter-particle collision thereby reducing the interparticle momentum transfer. Non-monotonicity in the observed behavior is then conjectured to arise due to competing effects of inter-particle friction and inter-particle collision. The present work and the overall observed behavior therein provides a simple experimental system to characterize the effects of added lubricant material in pharmaceutical and other relevant industrial applications.

Using good vibrations: Melting and controlled shear jamming of dense granular suspensions

Flows of suspensions can be blocked when the suspended particles are densely packed. This makes their formulation and their transport challenging in the industry. In this paper, we study the impact of vibrations on the behavior of dense granular suspensions prepared at a volume fraction above their jamming volume fraction but below the particle assembly random close packing. Vibrations are shown to have a strong effect on their rheological properties and to tune their transition from solidlike to liquidlike behavior. We study suspensions of rough silica particles in a Newtonian fluid. In the absence of vibrations, they have a solidlike behavior: they flow only above a yield stress. Particles are confined by the liquid interface, and the yield stress is of the frictional origin. When vibrations are applied, the yield stress vanishes to give rise to a liquidlike pseudo-Newtonian behavior at a low shear rate. Using shear-reversal experiments, we show that these liquidlike vibrated suspensions of frictional particles behave like nonvibrated suspensions of frictionless particles. As the shear rate is increased, we observe a shear thickening of the vibrated suspensions, eventually leading to shear-jamming. The yield stress behavior is recovered, and vibrations have no more impact. We show that this shear thickening can be tuned by changing the vibration energy injected into the system. We, finally, propose a physical picture based on the competition between contact opening by vibration and contact formation by shear to account for these behaviors. In the framework of the Wyart and Cates [Phys. Rev. Lett. 112, 098302 (2014)] model, vibrations can be seen as introducing a thermal-like repulsive force, yielding a critical stress proportional to the vibration stress introduced by Hanotin et al. [J. Rheol. 59, 253–273 (2015)].

Role of shape on the forces on an intruder moving through a dense granular medium

We use numerical simulation to investigate the effect an intruder’s shape has on the drag and lift forces that it experiences while moving through a granular medium composed of polydisperse disks of mean diameter d. The intruder velocity, v, was varied from 0.1 to 20 For frictionless particles (), there is a gradual increase in drag force with increasing v, whereas, for frictional systems (), a constant drag regime appears at low velocities. The drag force depends weakly on the object’s shape provided that its cross-section is constant. The drag force depends linearly on the immersion depth, while the lift force varies weakly with depth for certain shapes. The lift experienced by the object is a strong function of its shape at a given velocity. The shape has an effect on the distribution of contacts around the surface of the intruder, which may result in a strong lift for certain shapes. We also present and discuss the force profiles around the intruder surface.

Effects of friction on stress on a plate penetrating into granular media

The penetration of a plate into granular media was analyzed, and the effects of particle–plate and particle–particle frictions, penetration direction, and initial plate orientation were examined. Results showed that stress was directly proportional to immersion depth for frictionless particles but jumped at the bed surface and then increased linearly for frictional particles. Moreover, stress was mostly independent of the penetration direction when the plate was frictionless. However, initial orientation always had an effect regardless of whether the plate was frictional or frictionless. Furthermore, a theoretical model was developed for stress analysis. This model revealed that friction on the plate essentially affected stress via changing the push angle of the particles that were in contact with the plate.

Nonaffine displacements below jamming under athermal quasistatic compression.

Critical properties of frictionless spherical particles below jamming are studied using extensive numerical simulations, paying particular attention to the nonaffine part of the displacements during the athermal quasistatic compression. It is shown that the squared norm of the nonaffine displacement exhibits a power-law divergence toward the jamming transition point. A possible connection between this critical exponent and that of the shear viscosity is discussed. The participation ratio of the displacements vanishes in the thermodynamic limit at the transition point, meaning that the nonaffine displacements are localized marginally with a fractal dimension. Furthermore, the distribution of the displacement is shown to have a power-law tail, the exponent of which is related to the fractal dimension.

Shear response of granular packings compressed above jamming onset.

We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power law in the interparticle overlap with exponent α, have found that the ensemble-averaged shear modulus 〈G(P)〉 increases with pressure P as ∼P^{(α-3/2)/(α-1)} at large pressures. 〈G〉 has two key contributions: (1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and (2) discontinuous jumps during compression that arise from changes in the contact network. Using numerical simulations, we show that the form of the shear modulus G^{f} for jammed packings within near-isostatic geometrical families is largely determined by the affine response G^{f}∼G_{a}^{f}, where G_{a}^{f}/G_{a0}=(P/P_{0})^{(α-2)/(α-1)}-P/P_{0},P_{0}∼N^{-2(α-1)} is the characteristic pressure at which G_{a}^{f}=0,G_{a0} is a constant that sets the scale of the shear modulus, and N is the number of particles. For near-isostatic geometrical families that persist to large pressures, deviations from this form are caused by significant nonaffine particle motion. We further show that the ensemble-averaged shear modulus 〈G(P)〉 is not simply a sum of two power laws, but 〈G(P)〉∼(P/P_{c})^{a}, where a≈(α-2)/(α-1) in the P→0 limit and 〈G(P)〉∼(P/P_{c})^{b}, where b≳(α-3/2)/(α-1), above a characteristic pressure that scales as P_{c}∼N^{-2(α-1)}.

Effects of particle compressibility on structural and mechanical properties of compressed soft granular materials

Changes in the mechanical properties of granular materials, induced by variations in the intrinsic compressibility of the particles, are investigated by means of numerical simulations based on the combination of the Finite Element and Contact Dynamics methods. Assemblies of athermal 2D particles are subjected to quasi-static uni-axial compactions up to packing fractions close to 1. We show that the effect of the compressibility of the particles both on the global and the local stresses, can be described by considering only the packing fraction of the system. This result, demonstrated in the whole range of accessible packing fractions in case of frictionless particles, remains relevant for moderate inter-particles coefficients of friction. The small discrepancies observed with frictional particles originate from irreversible local reorganizations in the system, the later being facilitated by the compressibility of the particles.

Packings of frictionless spherocylinders.

We present simulation results on the properties of packings of frictionless spherocylindrical particles. Starting from a random distribution of particles in space, a packing is produced by minimizing the potential energy of interparticle contacts until a force-equilibrated state is reached. For different particle aspect ratios α=10⋯40, we calculate contacts z, pressure as well as bulk and shear modulus. Most important is the fraction f_{0}(α) of spherocylinders with contacts at both ends, as it governs the jamming threshold z_{c}(α)=8+2f_{0}(α). These results highlight the important role of the axial "sliding" degree of freedom of a spherocylinder, which is a zero-energy mode but only if no end contacts are present.

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.

Inter-particle friction and particle sphericity effects on isotropic compression behavior in real-shaped sand assemblies

A numerical investigation on the effects of inter-particle friction and particle sphericity on isotropic compression in real-shaped sand assemblies is carried out using the discrete element method. Real-shaped sand assemblies are generated in terms of the cumulative distribution of the shape descriptor (sphericity) of real sand particles. The mechanical behaviors of compression are quantified in terms of the volumetric deformation, coordination number, probability distribution of the contact forces, and fabric. The results show that the compression deformation becomes larger with decreasing inter-particle friction, especially for an assembly with frictionless particles. The probability distribution of the coordination number is almost described by a Gaussian distribution, which is somewhat different from that of the monodisperse particles reported in previous studies. Moreover, the inter-particle friction and sphericity have an insignificant effect on the probability distribution of the normalized contact forces, which exhibit a clear exponential decay. Assemblies with lower inter-particle friction and lower sphericity experience greater friction mobilization during compression. The results of the anisotropy of the contact normal force show that all the samples are strongly homogeneous and isotropic, and inter-particle friction and sphericity have substantial effects on the magnitude of the normal contact force.

Jamming Below Upper Critical Dimension.

Extensive numerical simulations in the past decades proved that the critical exponents of the jamming of frictionless spherical particles are the same in two and three dimensions. This implies that the upper critical dimension is d_{u}=2 or lower. In this Letter, we study the jamming transition below the upper critical dimension. We investigate a quasi-one-dimensional system: disks confined in a narrow channel. We show that the system is isostatic at the jamming transition point as in the case of standard jamming transition of the bulk systems in two and three dimensions. Nevertheless, the scaling of the excess contact number shows the linear scaling. Furthermore, the gap distribution remains finite even at the jamming transition point. These results are qualitatively different from those of the bulk systems in two and three dimensions.

Two-Scale Scenario of Rigidity Percolation of Sticky Particles

In the presence of attraction, the jamming transition of packings of frictionless particles corresponds to the rigidity percolation. When the range of attraction is long, the distribution of the size of rigid clusters, P(s), is continuous and shows a power-law decay. For systems with short-range attractions, however, P(s) appears discontinuous. There is a power-law decay for small cluster sizes, followed by a low probability gap and a peak near the system size. We find that this appearing "discontinuity" does not mean that the transition is discontinuous. In fact, it signifies the coexistence of two distinct length scales, associated with the largest cluster and smaller ones, respectively. The comparison between the largest and second largest clusters indicates that their growth rates with system size are rather different. However, both cluster sizes tend to diverge in the large system size limit, suggesting that the jamming transition of systems with short-range attractions is still continuous. In the framework of the two-scale scenario, we also derive a generalized hyperscaling relation. With robust evidence, our work challenges the former single-scale view of the rigidity percolation.

Force balance controls the relaxation time of the gradient descent algorithm in the satisfiable phase.

We numerically study the relaxation dynamics of the single-layer perceptron with the spherical constraint. This is the simplest model of neural networks and serves a prototypical mean-field model of both convex and nonconvex optimization problems. The relaxation time of the gradient descent algorithm rapidly increases near the SAT-UNSAT (satisfiable-unsatisfiable) transition point. We numerically confirm that the first nonzero eigenvalue of the Hessian controls the relaxation time. This first eigenvalue vanishes much faster upon approaching the SAT-UNSAT transition point than the prediction of the Marchenko-Pastur law in random matrix theory derived under the assumption that the set of unsatisfied constraints are uncorrelated. This leads to a nontrivial critical exponent of the relaxation time in the SAT phase. Using a simple scaling analysis, we show that the isolation of this first eigenvalue from the bulk of spectrum is attributed to the force balance at the SAT-UNSAT transition point. Finally, we show that the estimated critical exponent of the relaxation time in the nonconvex region agrees very well with that of frictionless spherical particles, which have been studied in the context of the jamming transition of granular materials.

Rheology in dense assemblies of spherocylinders: Frictional vs. frictionless.

Using molecular dynamics simulations, we study the steady shear flow of dense assemblies of anisotropic spherocylindrical particles of varying aspect ratios. Comparing frictionless and frictional particles we discuss the specific role of frictional inter-particle forces for the rheological properties of the system. In the frictional system we evidence a shear-thickening regime, similar to that for spherical particles. Furthermore, friction suppresses the alignment of the spherocylinders along the flow direction. Finally, the jamming density in frictional systems is rather insensitive to variations in aspect ratio, quite contrary to what is known from frictionless systems.