Protocol dependence of mechanical properties in granular systems

We study the protocol dependence of the mechanical properties of granular media by means of computer simulations. We control a protocol of realizing disk packings in a systematic manner. In 2D, by keeping material properties of the constituents identical, we carry out compaction with various strain rates. The disk packings exhibit the strain rate dependence of the critical packing fraction above which the pressure becomes non-zero. The observed behavior contrasts with the well-studied jamming transitions for frictionless disk packings. We also observe that the elastic moduli of the disk packings depend on the strain rate logarithmically. Our results suggest that there exists a time-dependent state variable to describe macroscopic material properties of disk packings, which depend on its protocol.     

Effect of the ratios of diameter of silo to bead on the pressure screening in granular columns

We present the apparent mass measurements at the bottom of granular packings for different bead and silo sizes. The redirection parameter K in Janssen theory is found to increase with the ratios of the diameter of the silo to the bead. We attribute this feature to the friction between the beads and the confining wall of silo; it is the role of friction that leads to variations in the shielding of vertical stresses as well as pressure screening.     

Packing of compressible granular materials

3D computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. In the rigid ball limit, we find a continuous transition in which the stress vanishes as (straight phi-straight phi(c))(beta), where straight phi is the (solid phase) volume density. The value of straight phi(c) depends on whether the grains interact via only normal forces (giving rise to random close packings) or by a combination of normal and friction generated transverse forces (producing random loose packings). In both cases, near the transition, the system's response is controlled by localized force chains.     

Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.     

准静态颗粒介质的弹性势能弛豫分析

颗粒体系是典型的多体相互作用体系, 具有多重的能量亚稳态. 对于准静态颗粒体系, 引入构型颗粒温度T_c描述弹性势能涨落. 本文认为平衡的体系具有一定的构型颗粒温度T_a, 其量值反映了其结构特征. 当外界扰动激发的构型颗粒温度超出T_a时, 产生不可逆过程. 通过对应力松弛过程的分析, 发现(T_c-T_a)激发了弹性弛豫, 且(T_c-T_a)越大则松弛过程中应力变化越大, 最终构型颗粒温度T_c→T_a时,宏观应力松弛结束,体系达到新的能量亚稳态.     

Stresses in isostatic granular systems and emergence of force chains

Progress is reported on several questions that bedevil understanding of granular systems: (i) Are the stress equations elliptic, parabolic, or hyperbolic? (ii) How can the often-observed force chains be predicted from a first-principles continuous theory? (iii) How do we relate insight from isostatic systems to general packings? Explicit equations are derived for the stress components in two dimensions including the dependence on the local structure. The equations are shown to be hyperbolic and their general solutions, as well as the Green function, are found. It is shown that the solutions give rise to force chains, and the explicit dependence of the force chains trajectories and magnitudes on the local geometry is predicted. Direct experimental tests of the predictions are proposed. Finally, a framework is proposed to relate the analysis to nonisostatic and more realistic granular assemblies.     

Discrete element simulation of localized deformation in stochastic distributed granular materials

The deformation in granular material under loading conditions is a problem of great interest currently. In this paper, the micro-mechanism of the localized deformations in stochastically distributed granular materials is investigated based on the modified distinct element method under the plane strain conditions, and the influences of the confining pressure, the initial void ratio and the friction coefficient on the localized deformation and the stability of granular materials are also studied. It is concluded, based on the numerical simulation testing, that two crossed shear sliding planes may occur inside the granular assembly, and deformation patterns vary with the increasing of transverse strain. These conclusions are in good agreement with the present experimental results. By tangential velocity profiles along the direction normal to the two shear sliding planes, it can be found that there are two different shear deformation patterns: one is the fluid-like shear mode and the other is the solid-like shear mode. At last, the influences of various material parameters or factors on localized deformation features and patterns of granular materials are discussed in detail. Supported by the Key Project of the National Natural Science Foundation of China (Grant No. 10532040)     

Granular packing as model glass formers

Static granular packings are model hard-sphere glass formers. The nature of glass transition has remained a hotly debated issue. We review recent experimental progresses in using granular materials to study glass transitions. We focus on the growth of glass order with five-fold symmetry in granular packings and relate the findings to both geometric frustration and random first-order phase transition theories.     

不同卸围压速率下花岗岩的力学性质及声发射特征

为了研究不同卸围压速率下花岗岩的力学性质,利用RMT-150B岩石力学试验系统对花岗岩试样进行恒轴压卸围压应力路径试验。试验结果表明:相同的初始围压下,随着卸围压速率增大,岩样的延性减小,表现为脆性破坏。卸围压速率越大,卸围压阶段的应变率越高,但总变形量小;当卸围压的速率相同时,初始围压越高,卸围压阶段岩样的应变率和总变形量越大。采用Mogi-Coulomb强度准则对试验结果进行拟合,结果显示:卸围压速率对花岗岩的黏聚力有劣化作用,对岩石的内摩擦角有强化作用;卸围压速率越小,振铃计数的活跃期越长,表明在低卸围压速率下,花岗岩岩样内部损伤发展缓慢且完全。     

Shocks near jamming

Nonlinear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed and demonstrate that the elementary excitations are strongly nonlinear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.     

Elegance of disordered granular packings: a validation of Edward's hypothesis

We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming a constant coordination number. It obtains the most entropic density of single grain states, which predicts several observables including the distribution of contact forces. We compare these results against empirical data obtained in dynamic simulations of granular packings. The agreement is quite good, helping validate the use of statistical mechanics methods in granular physics. The differences between theory and empirics are mainly related to the coordination number, and when the empirical data are sorted by that number we obtain several insights that suggest an underlying elegance in the density of states.     

Force chain buckling,unjamming transitions and shear banding in dense granular assemblies

Force chain buckling, leading to unjamming and shear banding, is examined quantitatively via a discrete element analysis of a two-dimensional, densely-packed, cohesionless granular assembly subject to quasistatic, boundary-driven biaxial compression. A range of properties associated with the confined buckling of force chains has been established, including: degree of buckling, buckling modes, spatial and strain evolution distributions, and relative contributions to non-affine deformation, dilatation and decrease in macroscopic shear strength and potential energy. Consecutive cycles of unjamming–jamming events, akin to slip–stick events arising in other granular systems, characterize the strain-softening regime and the shear band evolution. Peaks in the dissipation rate, kinetic energy and local non-affine strain are strongly correlated: the largest peaks coincide with each unjamming event that is evident in the concurrent drops in the macroscopic shear stress and potential energy. Unjamming nucleates from the buckling of a few force chains within a small region inside the band. A specific mode of force chain buckling, prevalent in and confined to the shear band, leads to above-average levels of local non-affine strain and release of potential energy during unjamming. Ongoing studies of this and other buckling modes from a structural stability standpoint serve as the basis for the formulation of internal variables and associated evolution laws, central to the development of thermomicromechanical constitutive theory for granular materials.     

Precursors and triggering mechanisms of granular avalanches

The dynamics of inclined granular packings driven towards their stability limits are studied experimentally using imaging techniques as well as acoustic methods. The former allow one to study grain rearrangements during the tilting. The implementation of both passive and active acoustic methods for probing the granular packings, with capabilities for time-resolved measurements, provides information on various elastic properties of the layers along the destabilization process, including the transient precursors. Systematic experiments of granular layer destabilization for various granular media and external conditions are compared and allow one to better understand the mechanisms responsible for the appearance, periodicity, and intensity of precursors.     

Force Distributions near Jamming and Glass Transitions

We calculate the distribution of interparticle normal forces P(F) near the glass and jamming transitions in model supercooled liquids and foams, respectively. P(F) develops a peak that appears near the glass or jamming transitions, whose height increases with decreasing temperature, decreasing shear stress and increasing packing density. A similar shape of P(F) was observed in experiments on static granular packings. We propose that the appearance of this peak signals the development of a yield stress. The sensitivity of the peak to temperature, shear stress, and density lends credence to the recently proposed generalized jamming phase diagram.     

Codalike multiple scattering of elastic waves in dense granular media

We study the multiple scattering of short-wavelength ultrasound through the force networks in dry and wet glass bead packings under stress. Over long distance scales, the diffusion approximation is shown to describe adequately the transport of elastic waves dominated by shear waves. The recovered transport mean path reveals a short-range correlation of the force chains. Also we observe the drastic effect of wetting liquids on the energy dissipation in the granular medium. The relevance of these experimental findings for the seismological applications is discussed.     

MRI investigation of granular interface rheology using a new cylinder shear apparatus

The rheology of granular materials near an interface is investigated through proton magnetic resonance imaging. A new cylinder shear apparatus has been inserted in the magnetic resonance imaging device, which allows the control of the radial confining pressure exerted by the outer wall on the grains and the measurement of the torque on the inner shearing cylinder. A multi-layer velocimetry sequence has been developed for the simultaneous measurement of velocity profiles in different sample zones, while the measurement of the solid fraction profile is based on static imaging of the sample. This study describes the influence of the roughness of the shearing interface and of the transverse confining walls on the granular interface rheology.     

Apollonian networks: simultaneously scale-free, small world, euclidean, space filling, and with matching graphs

We introduce a new family of networks, the Apollonian networks, that are simultaneously scale-free, small-world, Euclidean, space filling, and with matching graphs. These networks describe force chains in polydisperse granular packings and could also be applied to the geometry of fully fragmented porous media, hierarchical road systems, and area-covering electrical supply networks. Some of the properties of these networks, namely, the connectivity exponent, the clustering coefficient, and the shortest path are calculated and found to be particularly rich. The percolation, the electrical conduction, and the Ising models on such networks are also studied and found to be quite peculiar. Consequences for applications are also discussed.     

Tapped granular packings described as complex networks

Abstract

We characterize the structure of simulated two-dimensional granular packings using concepts from complex networks theory. The packings are generated by a simulated tapping protocol, which allows us to obtain states in mechanical equilibrium in a wide range of densities. We show that our characterization method is able to discriminate non-equivalent states that have the same density. We do this by examining differences in the topological structure of the contact network of the packings. In particular, we find that the polygons of the network are specially sensitive probes for the contact structure. Additionally, we compare the network properties obtained in two different scenarios: the tapped and a compressed system.     

Strain versus stress in a model granular material: A Devil's staircase

The series of equilibrium states reached by disordered packings of rigid, frictionless disks in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration space are found to be independent of specific assumptions ruling granular dynamics, and determined by geometry only. A monotonic increase in some macroscopic loading parameter causes a discrete sequence of rearrangements. For a biaxial compression, we show that, due to the statistical importance of such events of large magnitude, the dependence of the resulting strain on stress direction is a Levy flight in the thermodynamic limit.