Two-dimensional Granular System Research Articles

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.

Deformation and Force Chain of Two-Dimensional Granular Systems under Continuous Loading.

A continuous loading experiment of a two-dimensional granular system was carried out and the experimental data were obtained by digital image correlation (DIC). The deformation field of the granular system and the changing laws of the deflection angle and coordination number of the granules on force chains with time were obtained. Based on the granule element method, the quantitative calculation of contact force was realized, and the internal force chains of the granular system were identified. The effects of contact force between granules and mechanical parameters on the evolution of force chains in a two-dimensional granular system under line loads were analyzed. The formation, evolution, and reconstruction of force chains in a granular system during loading, as well as the influence of the force chain network evolution on the macroscopic mechanical properties of granules were discussed. The experimental results indicated that the evolution of force chains was directly related to the number, geometric properties, and permutation distribution of granules in direct contact with the external load.

Steady states of two-dimensional granular systems are unique, stable, and sometimes satisfy detailed balance

Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse analytically and numerically the steady states of this theory in systems of arbitrary density and report the following. (1) We discover that all such dynamics almost certainly possess only one physical steady state, which may or may not satisfy detailed balance. (2) We show rigorously that, if a detailed balance solution is possible then it is unique. The above two results correct an erroneous conjecture in the literature. (3) We show rigorously that the detailed-balance solutions in very dense systems are globally stable, extending the local stability found for these solutions in the literature. (4) In view of recent experimental observations of robust detailed balance steady states in very dilute cyclically sheared systems, our results point to a self-organisation of process rates in dynamic granular systems.

Collaborative behavior of intruders moving amid grains

We investigate the motion of groups of intruders in a two-dimensional granular system by using discrete numerical simulations. By imposing either a constant velocity or a thrusting force on larger disks (intruders) that move within smaller ones (grains), we obtained instantaneous positions and components of forces for each intruder and grain. We found that (i) intruders cooperate even when at relatively large distances from each other; (ii) the cooperative dynamics is the result of contact chains linking the intruders as well as compaction and expansion of the granular medium in front and behind, respectively, each intruder; (iii) the collaborative behavior depends on the initial arrangement of intruders; and (iv) for some initial arrangements, the same spatial configuration is eventually reached. Finally, we show the existence of an optimal distance for minimum drag for a given set of intruders, which can prove useful for devices stirring the ground or other granular surfaces.

Contacts, motion, and chain breaking in a two-dimensional granular system displaced by an intruder

We investigate numerically how the motion of an intruder within a two-dimensional granular system affects its structure and produces drag on the intruder. We made use of discrete numerical simulations in which a larger disk (intruder) is driven at constant speed amid smaller disks confined in a rectangular cell. By varying the intruder's velocity and the basal friction, we obtained the resultant force on the intruder and the instantaneous network of contact forces, which we analyze at both the cell and grain scales. We found that there is a bearing network that percolates forces from the intruder toward the walls, being responsible for jammed regions and high values of the drag force, and a dissipative network that percolates small forces within the grains, in agreement with previous experiments on compressed granular systems. In addition, we found the anisotropy levels of the contact network for different force magnitudes and regions, that the force network can reach regions far downstream of the intruder by the end of the intruder's motion, that the extent of the force network decreases with decreasing the basal friction, and that the void region (cavity) that appears downstream of the intruder tends to disappear for lower values of the basal friction. Interestingly, our results show that grains within the bearing chains creep while the chains break, revealing the mechanism by which bearing chains collapse.

Disorder-induced vibrational anomalies from crystalline to amorphous solids

The origin of boson peak -- an excess of density of states over Debye's model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals, in which the van-Hove singularities gradually shift to higher frequency values while broadening their shapes and eventually disappear completely when the structural disorder $\eta$ becomes sufficiently high. By analyzing firstly the strongly disordered system ($\eta=1$) and the disordered granular crystals ($\eta=0$), and then systems of intermediate disorder with $\eta$ in between, we find that boson peak is associated with spatially uncorrelated random flucutations of shear modulus $\delta G/\langle G \rangle$ whereas the smearing of van-Hove singularities is associated with spatially correlated fluctuations of shear modulus $\delta G/\langle G \rangle$.

Crystallisation in a two-dimensional granular system at constant temperature

We study the crystallisation processes occurring in a nonvibrating two-dimensional magnetic granular system at various fixed values of the effective temperature. In this system, the energy loss due to dissipative effects is compensated by the continuous energy input coming into the system from a sinusoidal magnetic field. When this balance leads to high values of the effective temperature, no aggregates are formed, because particles’ kinetic energy prevents them from aggregating. For lower effective temperatures, formation of small aggregates is observed. The smaller the values of the applied field’s amplitude, the larger the number of these disordered aggregates. One also observes that when clusters form at a given effective temperature, the average effective diffusion coefficient decreases as time increases. For medium values of the effective temperature, formation of small crystals is observed. We find that the sixth bond-orientational order parameter and the number of bonds, when considering more than two, are very sensitive for exhibiting the order in the system, even when crystals are still very small.

Dilatancy of frictional granular materials under oscillatory shear with constant pressure

We perform numerical simulations of a two-dimensional frictional granular system under oscillatory shear confined by constant pressure. We found that the system undergoes dilatancy as the strain increases. We confirmed that compaction also takes place at an intermediate strain amplitude for a small mutual friction coefficient between particles. We also found that compaction depends on the confinement pressure while dilatancy little depends on the pressure.

Intruder in a two-dimensional granular system: Effects of dynamic and static basal friction on stick-slip and clogging dynamics.

We present simulation results for an intruder pulled through a two-dimensional granular system by a spring using a model designed to mimic the experiments described by Kozlowski et al. [Phys. Rev. E 100, 032905 (2019)2470-004510.1103/PhysRevE.100.032905]. In that previous study the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick-slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions of particles with each other and with boundaries. We then use simulations to explore a broader range of parameter space, focusing on the friction between the particles and the base. We consider both static and dynamic basal friction coefficients, which are difficult to vary smoothly in experiments. The simulations show that dynamic friction strongly affects the stick-slip behavior when the coefficient is decreased below 0.1, while static friction plays only a marginal role.

Using Mechanoluminescent Materials to Visualize Interparticle Contact Intensity in Granular Media

Mechanoluminescent materials have the property of emitting light when they are mechanically deformed. The paper deals with the potential use of these active substances to reveal interparticle contact force networks in granular media under mechanical loading. Preliminary uniaxial tensile tests were first performed on two types of longitudinal specimens for comparison purposes: pure epoxy resin and epoxy resin containing mechanoluminescent powders. Stress-strain curves showed that the powder acted as a reinforcement, but fractographic analysis by SEM revealed that debonding occurred between the epoxy matrix and powder grains during mechanical loading. Various two-dimensional cohesionless granular systems were then studied, using mechanoluminescent cylinders subjected to compression. Whereas uniaxial tensile tests featured homogeneous light emission, localized mechanoluminescence intensities were revealed in the contact zones between cylinders. The study shows that mechanoluminescent materials open perspectives for the identification of interparticle contact intensities in granular media.

Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions.

We experimentally investigate the statistical behavior of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in a liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states: though heterogeneous, the packing fraction of the system can be tuned from fully dispersed to crystallized as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a thermal-like behavior, where the granular pressure and the packing fraction are related through an equation of state. We obtain an expression of the equation of state allowing us to probe the nature of the hydrodynamic interactions between the particles. This description is valid in the whole range of the physical parameters we investigated and reveals a buoyant energy scale that we interpret as an effective temperature. We finally discuss the behavior of our system at high packing fractions and the relevance of the equation of state to the liquid-solid phase transition.

Influence of particle packing structure on sound velocity**Project supported by the National Natural Science Foundation of China (Grant No. 11547009), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11602062), the Natural Science Foundation of Guizhou Province, China (Grant No. 2012/2166), and the Research Foundation of Guizhou University for Talent Introduction, China (Grant No. 2011/02).

The anisotropy in the particle systems of different packing structures affects the sound velocity. The acoustic propagation process in four kinds of packing structures (denoted as S45, H60, S90, and D) of two-dimensional granular system is simulated by the discrete element method. The velocity vtof obtained by the time of flight method and the velocity vc obtained from the stiffness tensor of the system are compared. Different sound velocities reflect various packing structures and force distributions within the system. The compression wave velocities of H60 and S90 are nearly the same, and transmit faster than that of D packing structure, while the sound velocity of S45 is the smallest. The shear wave velocities of S45 and H60 are nearly the same, and transmit faster than that of D packing structure. The compression wave velocity is sensitive to the volume fraction of the structure, however, the shear wave velocity is more sensitive to the geometrical structure itself. As the normal stress p is larger than 1 MPa, vtof and vc are almost equal, and the stiffness tensors of various structures explain the difference of sound velocities. When the normal stress is less than 1 MPa, with the coordination number unchanged, the law vtof ∝ p1/4 still exists. This demonstrates that apart from different power laws between force and deformation as well as the change of the coordination number under different stresses, there are other complicated causes of vtof ∝ p1/4, and an explanation of the deviation from vtof ∝ p1/6 is given from the perspective of dissipation.

Brownian motion in non-equilibrium systems and the Ornstein-Uhlenbeck stochastic process

The Ornstein-Uhlenbeck stochastic process is an exact mathematical model providing accurate representations of many real dynamic processes in systems in a stationary state. When applied to the description of random motion of particles such as that of Brownian particles, it provides exact predictions coinciding with those of the Langevin equation but not restricted to systems in thermal equilibrium but only conditioned to be stationary. Here, we investigate experimentally single particle motion in a two-dimensional granular system in a stationary state, consisting of 1 mm stainless balls on a plane circular surface. The motion of the particles is produced by an alternating magnetic field applied perpendicular to the surface of the container. The mean square displacement of the particles is measured for a range of low concentrations and it is found that following an appropriate scaling of length and time, the short-time experimental curves conform a master curve covering the range of particle motion from ballistic to diffusive in accordance with the description of the Ornstein-Uhlenbeck model.

Steering coefficient in ordered lattice pile of two-dimensional granular systems

Interparticle forces in granular system form an inhomogeneous distribution of filamentary force chains. For the granular system with an established packed structure, the normal pressure is steered through the force chains among the particles and the value of horizontal pressure is various at the different positions. In this paper, the steering coefficient in two-dimensional horizontal and vertical granular system is studied experimentally. The results show that, in the process of slowly increasing compression, the normal force increases slowly at first and gradually transforms into a nonlinear form, and changes into the linear growth finally. This phenomenon corresponds to the dynamic processes of friction-slip-extrusion. Through theoretical analysis, we revealed that how friction among particles, friction between particles and glass plate and stacking angle affect the steering coefficient. The saturated value of steering coefficient decreases with the stacking angle in experiment, which is agreed well with theoretical result. In addition, our experiment shows that the steering coefficient is independent of the width of container.

Numerical study on acoustic behavior of two-dimensional granular system

Numerical study on acoustic behavior of two-dimensional granular system

Jamming transition evinced by Voronoi Tesselation

We calculated the Voronoi tessellation (VT) of simulations of two-dimensional granular system disturbed by an intruder. The intruder is kept fixed within a rectangular box containing certain amount of grains. Making the box to move against the intruder we calculated the VT for several instants of this movement, analyzing geometrical properties of the Voronoi polygons in function of time. The dependence of stationary values of the polygon areas and number of sides in function of the packing fraction (ϕ ) of the granular media has shown that the system displays a possible jamming transition at critical point ϕc ≈ 80:5%.

Vibrational density of states and boson peak in two-dimensional frictional granular assemblies

In this paper, the two-dimensional granular assemblies composed of 2048 mono-dispersed frictional disks are simulated by the discrete element method. A set of eigenvalues and corresponding eigenvectors is obtained by diagonalizing the Hessian matrix for each stable configuration. The effects of the friction coefficient of disk on mechanical and geometrical properties of these systems under isotropic confining are studied. Results show that at a fixed pressure, with increasing from 0.001 to 1.0, the crossover frequency *, which separates the Debye scale region from the platform of vibrational density of states, and the boson peak BP gradually shift towards lower frequency, and the intensity of the boson peak D(BP) / BP increases. These results are mainly attributed to the fact that the system becomes more and more disordered with the increase of (i.e., the decrease of the average coordination number), resulting in more excess modes at *. For a better understanding of the different vibration modes of the two-dimensional frictional granular systems, we plot the polarization vector diagrams for different frequencies ( 1 = 0.15, 2 = 1.5 and 3 = 6.0) for configurations with = 0.001 and = 1.0, respectively. Mode analysis results show that the mode at low ( 1.0) has a mixed translational-rotational but translational-dominated character; the mode at intermediate frequency (1.0 4.0) is localized and has a mixed translational-rotational but translational-dominated character; and the mode at high frequency ( 4.0) have a strongly rotational in character. It is worth noting that the low-frequency modes become more localized and the rotational participation fraction also increases as increases, implying that the rotational modes play more important role in the system with higher friction coefficient.

Quantitatively mimicking wet colloidal suspensions with dry granular media.

Athermal two-dimensional granular systems are exposed to external mechanical noise leading to Brownian-like motion. Using tunable repulsive interparticle interaction, it is shown that the same microstructure as that observed in colloidal suspensions can be quantitatively recovered at a macroscopic scale. To that end, experiments on granular and colloidal systems made up of magnetized particles as well as computer simulations are performed and compared. Excellent agreement throughout the range of the magnetic coupling parameter is found for the pair distribution as well as the bond-orientational correlation functions. This finding opens new ways to efficiently and very conveniently explore phase transitions, crystallization, nucleation, etc in confined geometries.

Energy equipartition in two-dimensional granular systems with spherical intruders

We study the effects of a line of spherical interstitial particles (or intruders) placed between two adjacent uncompressed chains of larger particles in a square packing of spheres, using experiments and numerical simulations. We excite one of the chains of particles adjacent to the intruders with an impact and show how energy is transmitted across the system until equipartition is reached from the excited (or impacted) chain to the absorbing (or adjacent) chain. The coupling of the two chains, although a purely two-dimensional effect, is modeled by a simplified one-and-a-half-dimensional system in which transverse motions of the particles are neglected.

Normal force distribution in two-dimensional granular system of compositional disorder

Point defects are implanted in an ordered granular system by randomly selecting granules and changing their stiffness coefficients. The discrete element method is used to research the normal force probability distribution. Simulation result shows that force network is almost homogeneous without defects whereas force network will become inhomogeneous with defects. The concepts of primary normal force and secondary normal force are proposed and their statistics are analyzed separately. As the rate of defects increases, the changing process of primary normal force distribution is complex, whereas the secondary normal force distribution is always exponential distribution. Our simulation shows that normal force distributions are different between randomly packing system and compositional disordered system of low defect rate. But when defect rate is large, the distributions are similar. These results are beneficial to the understanding of the relationship between inhomogeneous force network and disordered system.