Fluctuations in granular media

Dense slowly evolving or static granular materials exhibit strong force fluctuations even though the spatial disorder of the grains is relatively weak. Typically, forces are carried preferentially along a network of "force chains." These consist of linearly aligned grains with larger-than-average force. A growing body of work has explored the nature of these fluctuations. We first briefly review recent work concerning stress fluctuations. We then focus on a series of experiments in both two- and three-dimension [(2D) and (3D)] to characterize force fluctuations in slowly sheared systems. Both sets of experiments show strong temporal fluctuations in the local stress/force; the length scales of these fluctuations extend up to 10(2) grains. In 2D, we use photoelastic disks that permit visualization of the internal force structure. From this we can make comparisons to recent models and calculations that predict the distributions of forces. Typically, these models indicate that the distributions should fall off exponentially at large force. We find in the experiments that the force distributions change systematically as we change the mean packing fraction, gamma. For gamma's typical of dense packings of nondeformable grains, we see distributions that are consistent with an exponential decrease at large forces. For both lower and higher gamma, the observed force distributions appear to differ from this prediction, with a more Gaussian distribution at larger gamma and perhaps a power law at lower gamma. For high gamma, the distributions differ from this prediction because the grains begin to deform, allowing more grains to carry the applied force, and causing the distributions to have a local maximum at nonzero force. It is less clear why the distributions differ from the models at lower gamma. An exploration in gamma has led to the discovery of an interesting continuous or "critical" transition (the strengthening/softening transition) in which the mean stress is the order parameter, and the mean packing fraction, gamma, must be adjusted to a value gamma(c) to reach the "critical point." We also follow the motion of individual disks and obtain detailed statistical information on the kinematics, including velocities and particle rotations or spin. Distributions for the azimuthal velocity, V(theta), and spin, S, of the particles are nearly rate invariant, which is consistent with conventional wisdom. Near gamma(c), the grain motion becomes intermittent causing the mean velocity of grains to slow down. Also, the length of stress chains grows as gamma-->gamma(c). The 3D experiments show statistical rate invariance for the stress in the sense that when the power spectra and spectral frequencies of the stress time series are appropriately scaled by the shear rate, Omega, all spectra collapse onto a single curve for given particle and sample sizes. The frequency dependence of the spectra can be characterized by two different power laws, P proportional, variant omega(-alpha), in the high and low frequency regimes: alpha approximately 2 at high omega; alpha<2 at low omega. The force distributions computed from the 3D stress time series are at least qualitatively consistent with exponential fall-off at large stresses. (c) 1999 American Institute of Physics.     

Arch generated shear bands in granular systems

We propose an arch based model, on cubic and square lattices, to simulate the internal mobility of grains, in a dense granular system under shear. In this model, the role of the arches in granular transport presents a non-linear dependence on the local values of the stress components that can be modeled geometrically. This non-linearity is very important since a linear dependence on the stress will make the models behave similarly to viscous fluids, which will not reproduce highly interesting properties of the sheared systems such as shear bands. In particular, we study a modified Couette flow and find the appearance of shear bands in accordance with the literature.     

Contact forces in a granular packing

We present the results of a systematic numerical investigation of force distributions in granular packings. We find that all the main features of force transmission previously established for two-dimensional systems of hard particles hold in three-dimensional systems and for soft particles, too. In particular, the probability distribution of normal forces falls off exponentially for forces above the mean force. For forces below the mean, this distribution is either a decreasing power law when the system is far from static equilibrium, or nearly uniform at static equilibrium, in agreement with recent experiments. Moreover, we show that the forces below the mean do not contribute to the shear stress. The subnetwork of the contacts carrying a force below the mean thus plays a role similar to a fluid surrounding the solid backbone composed of the contacts carrying a force above the mean. We address the issue of the computation of contact forces in a packing at static equilibrium. We introduce a model with no local simplifying force rules, that allows for an exact computation of contact forces for given granular texture and boundary conditions. (c) 1999 American Institute of Physics.     

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.     

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.     

The dynamics of multiparticle collisions in motion of a granular material

We consider the complex problem of how to calculate particle motions taking into account multiparticle collisions. Multiparticle contacts occur when a particle collides with neighbouring particles, so that those contacts have a direct influence on each other. We will focus on the molecular dynamics method. Particularly, we will analyse what happens in cohesive materials during multiparticle contacts. We investigated the expression of repulsive force formulated under fractional calculus which is able to control dynamically the transfer and dissipation of energy in granular media. Such approach allows to perform simulations of arbitrary multiparticle collisions and also granular cohesion dynamics.     

双轴压缩下颗粒物质剪切带的形成与发展

本文采用离散元方法,研究了双轴压缩的颗粒体系在刚性边界约束下,局部剪切带的形成和发展过程,注重分析了细观的体积分数、配位数、颗粒旋转角度等参数以及力链结构形态的演变.并从颗粒体系jamming 相图中J点附近的边壁压强和配位数随体积分数的标度规律出发,分析了剪切带内外的体积分数和配位数的变化.结果表明:剪切带形成于颗粒体系的塑性变形开始阶段,此时体系发生剪胀,颗粒体积分数减小,颗粒体系抵抗旋转的能力降低,开始出现细小剪切带,随着轴向应变的继续,细小剪切带发生连接,最终导致贯穿性优势剪切带形成 关键词： 颗粒物质 力链 双轴压缩 剪切带     

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.     

Effect of particle shape on the stress dip under a sandpile

The results of an experimental investigation into the effects of particle shape on the stress dip formed under a 2D sandpile is reported. We find good agreement with previous results of a small dip for mixtures of disks poured from a localized source. The new finding is that the dip is significantly enhanced when elliptical particles are used. We attribute the amplification of the effect to orientational ordering induced by the shape of the grains which removes the degeneracy of circular particles.     

Segregation in arch formation

We report new segregation phenomena in the clogging arches formed during the discharge of granular piles. Results from molecular dynamics simulations show segregation effects with respect to both size and density ratios used in piles built with bidisperse mixtures of grains. The clogging arch is preferentially constituted of large grains when size bidisperse piles were discharged, whereas for density bidisperse mixtures there is a predominance of light grains in the arch for large orifice widths but, for small widths, an inversion in the preference is observed, with a slightly higher incidence of heavy grains forming the arches. We present arguments based on the reverse buoyancy effect and the statistics collected for the avalanche size distributions to explain how these effects can be understood as a crossover between two different segregation mechanisms acting independently at small and large orifice width limits.     

Modelling of nanometer scale dust grains in tokamak

Dust poses a serious threat to tokamak operation and safety. It is important to study the behaviour of dust grains under tokamak's discharge conditions, which depends heavily on their size and charge. Existing simulations mainly address issues on dust grains with radii larger than 1 μm, in which case, the drift effect due to electromagnetic fields can be safely ignored. For nanometer scale dust grains, however, the drift effect becomes significant and a new model based on guiding-centre system needs to be established. In this work, the NDS has been done under BOUT++ framework. The simulation contains two parts. Part one, NDS evaluates the charging and ablation processes of the dust grains. In the second part, the guiding-centre orbits of dust particles are tracked in tokamak plasmas, whose parameters are obtained from BOUT++, a highly desirable C++ code package for performing parallel plasma fluid simulations with an arbitrary number of equations in 3D curvilinear coordinates. The orbit of nanodust dynamics is described by guiding centre equations for simplicity, and these equations are numerically solved by conventional fourth-order Runge Kutta method. Simulations provide results such as trajectories and evolutions of dust particles with different sizes and velocities for different tokamak geometries. Results show tungsten dust grains with a radius of a few nanometers launched from outer midplane will oscillate before totally ablated in C-Mod. The oscillation in this case is driven by the ion drag force. Larger Nanodust with a radius of 100 nm, on the contrary, cannot be completely constrained by the electromagnetic field. The high plasma temperature and density in the seperatrix region causes severe dust ablation, resulting in total ablation within several ms.     

Study of atomic force microscopy nanoindentation for the development of nanostructures

We have studied the fabrication of atomic force microscope (AFM) based nanotemplates using electrically controlled indentation (ECI) and a composite barrier (photoresist/alumina) that is resistant to the lithography process and presents good mechanical properties for indentation. The indentation process is affected by several factors such as the indentation speed, the trigger voltage and the barrier type. We have used the nanotemplate technique to fabricate small gold–gold nanocontacts (1–10 nm). In this limit, the size of the contacts that is obtained through the indentation process seems to be stochastic. However, low dimension, clean metallic contacts were achieved with high temporal stability and compatible with low temperature measurements. The fabricated nanotemplates are versatile and can be used in a wide range of applications, from nanojunctions to connecting a single nano-object. Small area metallic contacts can be used to study spin injection or ballistic transport.     

Stress field in granular systems: loop forces and potential formulation

The transmission of stress through a marginally stable granular pile in two dimensions is exactly formulated in terms of a vector field of loop forces, and thence in terms of a single scalar potential. This leads to a local constitutive equation coupling the stress tensor to fluctuations in the local geometry. For a disordered pile of rough grains this means the stress tensor components are coupled in a frustrated manner. In piles of rough grains with long range staggered order, frustration is avoided and a simple linear theory follows. We show that piles of smooth grains can be mapped onto a pile of unfrustrated rough grains, indicating that the problems of rough and smooth grains may be fundamentally distinct.     

Increasing magnetoplasticity in polycrystalline Ni-Mn-Ga by reducing internal constraints through porosity

Foams with 55% and 76% open porosity were produced from a Ni-Mn-Ga magnetic shape-memory alloy by replication casting. These polycrystalline martensitic foams display a fully reversible magnetic-field-induced strain of up to 0.115% without bias stress, which is about 50 times larger than nonporous, fine-grained Ni-Mn-Ga. This very large improvement is attributed to the bamboolike structure of grains in the foam struts which, due to reduced internal constraints, deform by magnetic-field-induced twinning more easily than equiaxed grains in nonporous Ni-Mn-Ga.     

玻璃-橡胶混合颗粒的力学响应研究

通过直剪实验和离散元模拟, 研究掺杂了橡胶软球的玻璃体系的力学响应. 改变颗粒固体中橡胶颗粒的含量, 研究体系剪切强度以及剪胀变化等特性, 发现随着橡胶颗粒的增加, 会出现剪胀到剪缩的相转变现象, 且混合颗粒固体的弹性有了很大的提高. 实验研究发现, 随着体系中橡胶颗粒含量的增加, 剪切屈服强度值逐渐减小, 体积发生从剪胀到剪缩的相转变现象, 但临界剪切强度在一定橡胶颗粒含量范围内保持一致; 实验所采取的剪切速率下, 应力应变曲线能较好重合, 即实验处于率无关区域; 混合样品的屈服强度值随正压力的增大而增大. 离散元模拟也得到了上述结果, 另外模拟还发现, 随着橡胶颗粒含量的增加, 颗粒的平均配位数增大; 橡胶颗粒含量和正压力对剪胀-剪缩相转变的位置有影响, 橡胶颗粒含量较小时, 在较大的正压力下易发生相转变现象, 且剪胀-剪缩相转变点对应的平均配位数在5.6-5.9之间; 在橡胶颗粒含量小于30%时, 混合颗粒样品的残剪强度与不掺杂的颗粒体系相近; 大于30%时, 残剪强度随橡胶颗粒含量的增加而减小; 残剪强度随正压力加大而增加.     

Dark matter and baryogenesis in the Fermi-bounce curvaton mechanism

We elaborate on a toy model of matter bounce, in which the matter content is constituted by two fermion species endowed with four fermion interaction terms. We describe the curvaton mechanism that is thus generated, and then argue that one of the two fermionic species may realize baryogenesis, while the other(lighter) one is compatible with constraints on extra hot dark matter particles.     

Size segregation in granular media induced by phase transition

In order to study analytically the nature of the size segregation in granular mixtures, we introduce a mean field theory in the framework of a statistical mechanics approach, based on Edwards' original ideas. For simplicity we apply the theory to a lattice model for a hard sphere binary mixture under gravity, and we find a new purely thermodynamic mechanism that gives rise to the size segregation phenomenon. By varying the number of small grains and the mass ratio, we find a crossover from the Brazil nut to the reverse Brazil nut effect, which becomes a true phase transition when the number of small grains is larger then a critical value. We suggest that this transition is induced by the effective attraction between large grains due to the presence of small ones (depletion force). Finally the theoretical results are confirmed by numerical simulations of the 3d system under taps.     

Low-frequency behavior of beads constrained on a lattice

We study sound propagation in a triangular lattice of spherical beads under isotropic stress. Polydispersity of real beads breaks some contacts, creating a disordered lattice of contacting beads. At large stress, the sound velocity behaves according to Hertz contact law and departs from it at lower stress. This evolution is reversible, with the same crossover when increasing or decreasing the stress, for a given piling. Correlations are much more sensitive to disorder. When calculated with signals propagated in the same lattice, they evolve reversibly with the stress, being much higher at large stress when the contact lattice is more regular. This leads to an interpretation of the non-Hertzian behavior in terms of progressive activation of contacts, in discrepancy with previous models involving buckling of force chains.     

Magnetic force microscopy studies of domain walls in nickel and cobalt films

A magnetic force microscopy is used to examine the domain walls in nickel and cobalt films deposited by argon ion sputtering. Thin nickel films deposited at high substrate temperatures exhibit coexistent Bloch and Neel walls. Films grown at room temperature display alternative Bloch lines with cap switches. These films agglomerate to form grains after annealed at high temperatures. The film composed of larger grains behaves better nucleation implying magnetic domains of closure, while the film composed of smaller grains exhibits more defects implying alternative Bloch lines. We have also observed domain displacements and cap switches, which occur due to precipitation of particles in small grain size films. Stripe domains are observed for film thicknesses larger than 100 nm. They become zigzag cells when an external field of 1.5 T is applied perpendicular to the surface of the films. This experiment indicates that the domain sizes in thin films and the strip widths for thick films both depend on the square-root of the film thickness, which varies from 5 to 45 nm and from 100 to 450 nm, respectively.