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.     

Shear- and vibration-induced order-disorder transitions in granular media

By molecular dynamics simulations we investigate the order-disorder transitions induced in granular media by an applied drive combining vibrations and shear. As the steady state is attained, the pack is found in disordered configurations for comparatively high intensities of the drive; conversely, ordering and packing fractions exceeding the random close packing are found when vibrations and shear are weak. As forcing amplitudes get smaller, we find diverging time scales in the dynamics, as the system enters a jamming region. Under this perspective, our picture supports the intuition that externally applied forcing has, in driven granular media, a role similar to temperature in thermal systems.     

Kinetic Theory of Polydisperse Granular Mixtures: Influence of the Partial Temperatures on Transport Properties—A Review

It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures Ti (measuring the mean kinetic energy of each species) are different to the (total) granular temperature T. The goal of this paper is to provide an overview on the effect of different partial temperatures on the transport properties of the mixture. Our analysis addresses first the impact of energy nonequipartition on transport which is only due to the inelastic character of collisions. This effect (which is absent for elastic collisions) is shown to be significant in important problems in granular mixtures such as thermal diffusion segregation. Then, an independent source of energy nonequipartition due to the existence of a divergence of the flow velocity is studied. This effect (which was already analyzed in several pioneering works on dense hard-sphere molecular mixtures) affects to the bulk viscosity coefficient. Analytical (approximate) results are compared against Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory for describing granular flows.     

颗粒介质弹性的弛豫

颗粒介质是复杂的多体相互作用体系, 其弹性源自内部的力链结构, 弹性能量处在亚稳态, 具有复杂的弛豫行为. 在常规作用下, 颗粒介质往往呈现明显的弹性弛豫. 应力松弛是应变恒定时应力的衰减现象, 弹性弛豫是应力松弛的主要原因. 在前期工作基础上, 从弹性势能面和双颗粒温度热力学角度分析了弹性弛豫的机理, 量化了弹性应力演化不可逆过程; 基于双颗粒温度热力学计算得到了弹性能、颗粒温度和应力的演化, 其中应力松弛的计算结果与实验结果基本一致, 讨论了颗粒温度初值和输运系数的影响. 指出, 开展力链结构及其动力学研究是揭示宏观弹性弛豫机理的关键.     

Phase transition and bistable phenomenon of granular flows down a chute with successive turnings

This paper studies the granular flow down a chute with two successive turnings, which play the role of bottlenecks for the granular flow system and determine the granular flow state in main section between them. With the increase of main section width D, phase transition from dilute to dense granular flow is observed: When the main section width D is small (large), the granular flow at upper (lower) bottleneck is dense and the granular flow is dilute (dense) in the main section. More interestingly, a bistable region is exhibited, in which either dilute flow or dense flow may occur and continue for the entire run. In this region, the packing in the reservoir will affect initial flow rate and then affect the flow pattern. This study can be viewed as a paradigm for the jamming and unjamming transitions under shear due to gravity.     

Computing Particle Surface Areas and Contact Areas from Three‐Dimensional Tomography Data of Particulate Materials

Microtomography is an emerging technique for particle and particulate‐materials characterization. To use this technology effectively, robust and accurate computational algorithms are needed to compute relevant particle properties, including particle surface area and particle‐particle contact area. However, the most accurate algorithms that have been developed for computing the exposed (void/solid) surface area in a microtomography image cannot be used directly for computing surface areas or particle‐particle contact areas for individual particles in a dense packing. This paper presents an algorithm for extracting particle contact areas from a digitized, segmented image of a packed granular material, which in turn can be used to find individual particle surface areas (even if the complete surfaces are not exposed because of contacts in the packing). Results show that small errors in the binary surface‐area computations are magnified in the course of determining particle contact areas; the total error in the computation depends mainly on the size of the contact area in voxel units.     

颗粒-颗粒接触力的热力学模型

以颗粒二体接触力模型为基础和出发点的软球离散元模拟是当前颗粒物理和力学领域广泛应用的研究手段.但文献上经常使用的、包括著名的Hertz-Mindlin和Luding在内的力模型并没有完全明确弹性势能或耗散热的计算方法,故从热力学层面看它们还需要完善.考虑到机械能的耗散行为是这类材料的重要物理内容,本文借鉴近年来提出的颗粒固体流体动力学(GSH)思路,提出一种具有明确势能和热功率的接触力建模方法.该理论除明确给出了机械能和热能的计算公式外,还能具体描述能量守恒、热力学平衡态和熵增加等基本原理,解决了传统接触力模型在这些方面的欠缺问题.初步计算显示本文模型的恢复系数可以随碰撞速率的增加而减弱,这比现有的其他模型更符合实验观测.虽然为简单起见这些公式仅局限于二维和忽略颗粒转动运动情况,文中讨论了如何推广到三维含转动情形,以及所涉及的滚动和扭转接触力的热力学处理问题.鉴于是否在Onsager非平衡热力学基础上建模是本文给出的接触力公式有别于当前其他模型的关键所在,文中强调了这里的主要建模对象应该是热力学特征函数和Onsager迁移系数,而接触力是它们的推导结果.这是一个与目前直接针对接触力进行建模的不同思路.文中对颗粒物质特有的、反映样品几何变形与弹应变之间联络的一个非对角迁移系数做了详细介绍,并且认为它与打滑等复杂力学现象关系密切,无论宏观GSH尺度上,还是细观接触力尺度上都不可忽略.     

Dynamics of a hard sphere granular impurity

An impurity particle coupling to its host fluid via inelastic hard sphere collisions is considered. It is shown that the exact equation for its distribution function can be mapped onto that for an impurity with elastic collisions and an effective mass. The application of this result to the Enskog-Lorentz kinetic equation leads to several conclusions: (1) every solution in the elastic case is equivalent to a class of solutions in the granular case; (2) for an equilibrium host fluid the granular impurity approaches equilibrium at a different temperature, with a dominant diffusive mode at long times; (3) for a granular host fluid in its scaling state, the granular impurity approaches the corresponding scaling solution.     

Random networks of fibres display maximal heterogeneity in the distribution of elastic energy

Above a small length scale, the distribution of local elastic energies in a material under an external load is typically Gaussian, and the dependence of the average elastic energy on strain defines the stiffness of the material. Some particular materials, such as granular packings, suspensions at the jamming transition, crumpled sheets and dense cellular aggregates, display under compression an exponential distribution of elastic energies, but also in this case the elastic properties are well defined. We demonstrate here that networks of fibres, which form uncorrelated non-fractal structures, have under external load a scale invariant distribution of elastic energy (epsilon) at the fibre-fibre contacts proportional to 1/epsilon. This distribution is much broader than any other distribution observed before for elastic energies in a material. We show that for small compressions it holds over 10 orders of magnitude in epsilon. In such a material a few 'hot spots' carry most of the elastic load. Consequently, these materials are highly susceptible to local irreversible deformations, and are thereby extremely efficient for damping vibrations.     

Unifying suspension and granular rheology

Using an original pressure-imposed shear cell, we study the rheology of dense suspensions. We show that they exhibit a viscoplastic behavior similarly to granular media successfully described by a frictional rheology and fully characterized by the evolution of the friction coefficient μ and the volume fraction ? with a dimensionless viscous number I(v). Dense suspension and granular media are thus unified under a common framework. These results are shown to be compatible with classical empirical models of suspension rheology and provide a clear determination of constitutive laws close to the jamming transition.     

基于超二次曲面的颗粒材料缓冲性能离散元分析

自然界或工业中普遍是由非球形颗粒组成的复杂体系,与球形颗粒相比,非球形颗粒间的高离散和咬合互锁可使冲击载荷引起的能量有效衰减实现缓冲作用.基于连续函数包络的超二次曲面单元能准确地描述非球形颗粒的几何形态,并可精确地计算单元间的接触碰撞作用.本文采用离散元方法对冲击载荷作用下非球形颗粒物质的缓冲性能进行数值分析,并与圆柱体冲击的理论结果和球体冲击的实验结果进行对比验证.在此基础之上,进一步研究了筒底作用力在不同颗粒层厚度和形状等因素影响下的变化规律.计算结果表明:不同颗粒形状都存在一个临界厚度H_c.当HH_c时,缓冲率随H的增加而增加;当HH_c时,缓冲率的变化不再显著并趋于稳定值.此外,减小颗粒表面尖锐度和增加或减小圆柱形和长方形颗粒的长宽比都会提高颗粒材料的缓冲效果.     

Equipartition of rotational and translational energy in a dense granular gas

Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees of freedom. This equipartition persists when the particle properties, confining pressure, packing density, or spatial ordering are changed. While the translational velocity distributions are the same for both large and small particles, the angular velocity distributions scale with the particle radius. The probability distributions of all particle velocities have approximately exponential tails. Additionally, we find that the system can be described with a granular Boyle's law with a van?der?Waals-like equation of state. These results demonstrate ways in which conventional statistical mechanics can unexpectedly apply to nonequilibrium systems.     

Impact-induced splash and spill in a quasi-confined granular medium

The splash and spill effects caused by the impact of a ball dropped from a height into a granular medium held in a small open container are examined. Different granular media, namely rice, mustard seeds, cream of wheat and plastic beads are used. The quantity of spilled-over granular matter (W, grams) is measured as a function of the ball-drop height and compared for different cases. Digital pictures of the splash process are also recorded. The quantity W is seen to vary approximately linearly with the energy of impact. Interestingly, a distinct upward jump is seen in the spilled quantity at specific impact energy in the case of mustard seeds, which have spherical shape and also exhibit some charging effects. Similar jump was also confirmed for the case of plastic beads with broadly similar properties. Although the parameters such as mass per grain and packing density for the case of mustard seeds are intermediate between those for rice and cream of wheat, the spill quantity for comparable impact energy is considerably higher in the former case. The possible reasons for this non-monotonicity of behavior are discussed in terms of the differences in grain shapes and properties. Experiments are also performed using plastic beads of the same type but with four different sizes to explore the dependence of spilled quantity on bead size. The container size dependence is also examined for various bead types. Interesting systematics are seen, which are discussed qualitatively.     

A first-order phase transition defines the random close packing of hard spheres

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ∼64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit. Here we show that RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the “freezing point” in a first-order phase transition between ordered and disordered packing phases. Despite the athermal nature of granular matter, we show the thermodynamic character of the transition in that it is accompanied by sharp discontinuities in volume and entropy. This occurs at a critical compactivity, which is the intensive variable that plays the role of temperature in granular matter. Our results predict the experimental conditions necessary for the formation of a jammed crystal by calculating an analogue of the “entropy of fusion”. This approach is useful since it maps out-of-equilibrium problems in complex systems onto simpler established frameworks in statistical mechanics.     

Kinetic theory for sheared granular flows

Rapid granular flows are far-from-equilibrium-driven dissipative systems where the interaction between the particles dissipates energy, and so a continuous supply of energy is required to agitate the particles and facilitate the rearrangement required for the flow. This is in contrast to flows of molecular fluids, which are usually close to equilibrium, where the molecules are agitated by thermal fluctuations. Sheared granular flows form a class of flows where the energy required for agitating the particles in the flowing state is provided by the mean shear. These flows have been studied using the methods of kinetic theory of gases, where the particles are treated in a manner similar to molecules in a molecular gas, and the interactions between particles are treated as instantaneous energy-dissipating binary collisions. The validity of the assumptions underlying kinetic theory, and their applicability to the idealistic case of dilute sheared granular flows are first discussed. The successes and challenges for applying kinetic theory for realistic dense sheared granular flows are then summarised.     

Upward penetration of grains through a granular medium

We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing, we use Voronoï tessellation and a certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like polydispersity and the initial packing fraction of the host granular system. It is found that the anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of the packing fraction of the host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into the host granular medium, we observe size segregation patterns.     

Evidence of rayleigh-hertz surface waves and shear stiffness anomaly in granular media

Using the nonlinear dependence of sound propagation speed with pressure, we evidence the anomalous elastic softness of a granular packing in the vicinity of the jamming transition. Under gravity and close to a free surface, the acoustic propagation is only possible through surface modes guided by the stiffness gradient. These Rayleigh-Hertz modes are evidenced in a controlled laboratory experiment. The shape and the dispersion relation of both transverse and sagittal modes are compared to the prediction of nonlinear elasticity including finite size effects. These results allow one to access the elastic properties of the packing under vanishing confining pressure.     

Experimental compaction of anisotropic granular media

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic and weakly confined granular material, using high-resolution -ray adsorption. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical solicitations evolve to a dense state. We find that the packing fraction evolution is slowed by the grain anisotropy but, as for spherically shaped grains, can be well fitted by a stretched exponential. For a given type of grains, the characteristic times of relaxation and of convection are found to be of the same order of magnitude. On the contrary, compaction mechanisms in the media strongly depend on the grain anisotropy.     

双分散颗粒体系在临界堵塞态的结构特征

堵塞行为是颗粒体系中一种常见的现象,其力学性质与堆积结构的关联非常复杂.本文采用离散元法研究了由两种不同半径颗粒组成的二维双分散无摩擦球形颗粒体系在临界堵塞态所呈现的结构特征,讨论了大小颗粒粒径比与大颗粒百分比对临界堵塞态的影响.数值模拟结果表明,当粒径比小于1.4时,临界平均接触数与大颗粒百分比关系不大,当粒径比大于1.4时随着大颗粒百分比的增大临界平均接触数先减小再增大.而临界体积分数在粒径比小于1.8时随着大颗粒百分比的增加先减小后增大,大于1.8时又基本不随大颗粒百分比而变化.大颗粒百分比在接近0或1时,系统近似为单分散体系,临界平均接触数与体积分数基本不随半径比的增大而变化;在接近0.5时,临界平均接触数随着半径比的增大逐渐减小,而临界体积分数则是先减小后增大.文中对大-小颗粒这一接触类型的百分比也进行了探讨,其值随着大颗粒百分比的增大呈二次函数的变化趋势,粒径比对这一变化趋势只有较小的影响.     

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