Comment on ``Granular Entropy: Explicit Calculations for Planar Assemblies''
Massimo Pica Ciamarra
评拉斐尔·布卢门菲尔德和萨姆·F·塞申斯的信。Edwards，[Phys. Rev. Lett. 90，114303（2003）]。
A Comment on the Letter by Raphael Blumenfeld and Sam F. Edwards, [Phys. Rev. Lett. 90, 114303 (2003)].
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Granular entropy: Explicit calculations for planar assemblies
本文提出了一种新的体积函数来计算平面颗粒集合体的熵。该函数是从一个新的几何张量的反对称部分提取的，并且在谷物上求和时是严格可加的。它导致一个方便的小相空间的识别。几个案例研究，我们明确计算的平均体积和体积波动的体积函数的效用证明。
We study numerical simulations of large (N~10^4) two-dimensional quasi-static granular assemblies subjected to a slowly increasing deviator stress. We report some peculiarities in the behavior of these packings that have not yet been adressed. The number of sliding contacts is not necessarily related to stability: first the number of sliding contacts rises linearly and smoothly with the applied stress. Then, at approximately half the peak stress, the increase slows down, a plateau develops, and a decrease follows.
Packings of macroscopic granular chains capture some of the essential aspects of molecular polymer systems and have been suggested as a paradigm to understand the physics on a molecular scale. However, here we demonstrate that the interparticle friction $μ$ in granular chain packings, which has no counterpart in polymer systems, leads to a nontrivial yielding and rheological response. Based on discrete element simulations we study the nonlinear rheology of random packings of granular chains under large amplitude oscillatory shear. We find that the maximum stress and the penetration depth of th…
Compaction and mobility in randomly agitated granular assemblies
研究了密实颗粒材料在弱随机振动作用下的压实和流度特性。通过将毫米玻璃珠与压电换能器直接接触，我们设法以无序的方式向系统注入能量，加速度远小于重力，导致缓慢的压实动力学和无对流。我们的特点的流动性内的介质通过它拉一个入侵者的粮食以恒定的速度。我们提出了一个广泛的研究阻力和速度之间的关系为不同的振动条件和入侵者的大小。
Mixing properties of bi-disperse ellipsoid assemblies: Mean-field behaviour in a granular matter experiment
本研究通过实验和理论分析，揭示了双分散椭球体堆积在颗粒物质中的平均场行为特性，提出了一种描述其分布的模型。
Effective temperature and jamming transition in dense, gently sheared granular assemblies
我们提出了广泛的计算结果的有效温度，定义的波动耗散关系的均方位移和平均位移的晶粒，在一个弱的，外部扰动的作用下，剪切，双分散颗粒包装的可压缩球体。我们研究了这个参数的剪切速率和体积分数，颗粒的类型和可观察到的波动耗散关系的依赖性。我们发现系统中不同示踪粒子的温度相同。对于足够慢的剪切，温度变得与剪切速率无关，这表明它是堵塞填料的有效温度。然而，我们也表明，协议的有效温度为不同的可观的只是近似的，很长一段时间，这表明，这个定义可能无法捕获系统的全部热力学。另一方面，我们发现之间的动态有效温度和紧凑性计算假设所有堵塞状态是等概率的。因此，温度的这个定义可以捕获颗粒材料的遍历假设的一个实例，如由理论形式主义提出的堵塞。最后，我们的模拟表明，平均剪切应力和表观剪切粘度遵循通常的复杂流体的剪切速率的关系。我们的研究结果表明，剪切的应用诱导堵塞在填料的颗粒相互作用的切向力。
Study of triaxial loading of segregated granular assemblies through experiments and DEM simulations
本研究提出基于位置相关体积力的DEM约束方法模拟三轴试验，验证了分离集合体的宏观响应，并发现界面阻碍应变局部化且小颗粒剪切应变更高。
Comment on the paper J. Solsvik and E. Manger, "Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity," Phys. Fluids \textbf{33}, 043321 (2021).
Force distributions in 3D granular assemblies: Effects of packing order and inter-particle friction
本文系统地研究了球形静态填充边界上的法向力分布。本文介绍了一种高效构造大尺寸密排六方晶体的新方法，并利用这种方法研究了空间有序性对力分布的影响。在单轴压缩下，我们发现颗粒间的法向力的概率分布形式并不强烈地依赖于结晶度或颗粒间摩擦。在所有情况下，分布在大的力下呈指数衰减，并在平均力附近显示出平台或可能的小峰，但在小的力下不趋于零。
Stress in planar cellular solids and isostatic granular assemblies: Coarse-graining the constitutive equation
最近的一个理论，在均衡颗粒和细胞系统的应力传递预测的本构方程，耦合应力场的局部微观结构。该理论不能应用于宏观系统，因为本构方程变得平凡后，简单的粗粒化。这个问题在这里解决了任意平面结构。该解决方案是基于观察交错的顺序，使得有可能耦合的应力，以减少几何张量，可以粗粒度。这里提出的方法使得有可能将这一想法应用到现实的系统，其交错顺序通常是“挫败”。这是通过重正化过程来实现的，该过程消除了挫折，并且能够使用可升级的约化张量。作为一个例子，我们计算的应力，由于缺陷的周期性固体泡沫。
We study the spontaneous crystallization of an assembly of highly monodisperse steel spheres under shaking, as it evolves from localized icosahedral ordering towards a packing reaching crystalline ordering. Towards this end, real space neutron tomography measurements on the granular assembly are carried out, as it is systematically subjected to a variation of frequency and amplitude. As expected, we see a presence of localized icosahedral ordering in the disordered initial state (packing fraction around 0.62). As the frequency is increased for both the shaking amplitudes (0.2 and 0.6 mm) studi…
We identify the fundamental factors determining the microstructural (MS) statistics of granular systems, using numerical experiments on 2D assemblies of polydisperse frictional discs and studying the emergent properties of quadrons (Qs), the basic structural elements of granular solids, whose statistics are universal-like[1]. The dependence of the structures and of the packing fraction on friction and initial state are analysed and we report the following. 1. Derivation of an analytical formula for the mean Q volume in terms of: the mean coordination number, the packing fraction and the rattle…
Energy dissipation in sheared dry and wet granulates is considered in the presence of an externally applied confining pressure. Discrete element simulations reveal that for sufficiently small confining pressures, the energy dissipation is dominated by the effects related to the presence of cohesive forces between the particles. The residual resistance against shear can be quantitatively explained by a combination of two effects arising in a wet granulate: i) enhanced friction at particle contacts in the presence of attractive capillary forces, and ii) energy dissipation due to the rupture and …
Comment on O. Gendelman, Y. G. Pollack, I. Procaccia, S. Sengupta, and J. Zylberg, Physical Review Letters 116, 078001 (2016).
On the interaction of dilatancy and friction in the behavior of fluid-saturated sheared granular materials: a coupled Computational Fluid Dynamics--Discrete Element Method study
本研究通过耦合CFD-DEM方法，探讨了流体饱和颗粒材料中膨胀与摩擦的相互作用，揭示了破坏模式受孔隙压力控制，并改进了饱和颗粒破坏的机理理解。
Slow dynamics and aging of a confined granular flow
我们目前的实验结果慢流动性能的颗粒组件限制在垂直柱和驱动向上在一个恒定的速度V。对于单分散组件，本研究的证据在低速度（$1<V<100 μm/s$）的硬化行为，即获得一个稳定的状态速度所需的应力大致随速度增加。另一方面，在非常低的驱动速度（$V<1 μm/s$），我们证明了一个不连续的和滞后的过渡到粘滑制度的特点是一个强大的分歧时，速度为零的最大阻塞力。我们表明，所有这些现象都受到周围湿度的强烈影响。我们还提出了一个尝试，以建立颗粒流变学和固体之间的摩擦力的壁和颗粒。我们的讨论基于一个简单的理论模型和独立的晶粒/壁摩擦学测量。我们也使用有限元数值模拟来对抗实验结果的各向同性弹性。第二个系统的玻璃珠的多分散组件进行了研究。我们强调一个新的动力学行为的发病，即大分布的阻塞力证明在粘滑制度。
Multi-phase flows encountered in nature or in industry, exhibit non trivial rheological properties, that can be understood better thanks to model materials and appropriate rheometers. Here, we use model unsaturated granular materials: assemblies of frictional spherical particles bonded by a small quantity of a wetting liquid, over a rough inclined plane. Our results show steady uniform flows for a wide range of parameters (the inclination angle and the mass flow-rate). A theoretical model, based on the Mohr-Coulomb yield criterion extended to inertial flows: $τ$ = $τ$c + $μ$(I)P, in which $τ$c…
1-d granular gas with little dissipation in 0-g : A comment on "Resonance oscillations in Granular gases"
它表明，最近的结果一维粒状气体在容器中的振动活塞，这是由冲击波传播建模，可以理解与建模使用的想法来自“单粒子热力学”。定义e为单次碰撞能量恢复系数的平方根，N为粒子总数，在N（1-e）<<1的限制下计算动量往返过程中的平均损失。当N（1-e）<<1时，系统既不能传播声波，也不能传播冲击波;当N（1-e）<<1时，系统的流体力学方程不能成立。Pacs编号：5.40 ; 45.70 ; 62.20 ; 83.70.Fn
A voxelization based post-processing algorithm is proposed to analyze the packing of non-spherical particle assemblies simulated using the Discrete Element Method. Voxelization of the particle data allows for isolating the geometric features of the granular assembly in various spatial sub-domains (2D surface or 3D region) and investigate the localized packing behaviour. Analyzing the local packing behaviour enables determining con-fined influences such as the wall-effect, stacking behaviour, local expansion/contraction and localized loading. The efficacy of the proposed technique to analyze pr…
The formalism proposed in Phys. Rev. Lett. 116, 078001 (2016) for determination of the normal and tangential inter-particle forces in frictional disks from visual data was criticized in a comment to that paper. However the theory developed in the original publication is aimed at finding the forces when provided with accurate measurements while the comment addresses a different problem, being the statistics of forces in a configuration with uncertainty of the relevant parameters. We address this difference in perspectives and point out that even with experimental errors one can improve the resu…
Granular dynamics in compaction and stress relaxation
通过实验和数值模拟研究了单轴压缩下颗粒集合体的弹性和耗散特性。在不同的振荡压力下的一种新的压实程序，应力响应的步骤应变揭示了一个指数松弛，然后是一个缓慢的对数衰减。模拟结果表明，后者产生的阻尼和集体晶粒运动之间的耦合主要通过滑动。我们描述了一个类似的“玻璃化转变”的包装颗粒，低于该系统显示老化的时间依赖性滑动关联函数。
Granular solids transmit stress as two-phase composites
本文提出基于两相复合材料视角的颗粒固体应力理论，通过思想实验、应力方程解及有效介质近似，为推广至非边际稳定颗粒固体奠定基础。
Stress transmission in planar disordered solid foams
平面开孔多孔固体中的应力传递分析使用最近的理论开发的边缘刚性颗粒组件。这是通过在两个系统之间构建一对一映射而实现的。一般的三价网络映射到粗糙晶粒的组件，而观察到高原规则的网络，映射到光滑晶粒的组件。应力传递方程的本构部分通过新的组构张量将应力直接耦合到细胞结构的局部旋转无序。分析的一个有趣的结果是，应力场可以确定的微观结构独立的应力-应变信息。这重新定义了这些材料的结构-性能关系问题，并对这种形式主义与弹性理论之间的关系提出了问题。偏离传统固体的应力传递方程已被解释为一种新的固体物质状态的颗粒状组件的上下文中，这种解释的相关性的物质状态的细胞固体进行了讨论。
Geometric partition functions of cellular systems: Explicit calculation of the entropy in two and three dimensions
基于颗粒堆积的压实性概念，提出了一种表征胞状结构熵的方法。在二维和三维中构造了类似哈密顿的体积函数，从而能够识别相空间，并能够系统地考虑几何相关性。案例研究的平均顶点密度和孔隙度波动的显式计算作为压实度的函数。形式主义同样适用于二维和三维颗粒集合。
Granular chain packings exhibit a striking emergent strain-stiffening behavior despite the individual looseness of the constitutive chains. Using indentation experiments on such assemblies, we measure an exponential increase in the collective resistance force $F$ with the indentation depth $z$, and with the square root of the number $\mathcal{N}$ of beads per chain. These two observations are respectively reminiscent of the self-amplification of friction in a capstan or in interleaved books, as well as the physics of polymers. The experimental data are well captured by a novel model based on t…
Rheometric measurements on assemblies of wet polystyrene bead assemblies, in steady uniform quasistatic shear flow, for varying liquid content within the small saturation (pendular) range of isolated liquid bridges, are supplemented with a systematic study by discrete numerical simulations. Numerical results and experimental ones agree quantitatively is the intergranular friction coefficient is set to 0.09, suitable for the dry material. Shear resistance and solid fraction are recorded as functions of the reduced pressure p, comparing normal stress to capillary bridge tensile strength. The Moh…
Three Comments on "A Simple Incremental Modelling of Granular-Media Mechanics"
使用最近的增量建模，它表明，在临界状态附近的土力学的相空间中的样本的轨迹不受刚度矩阵，但由其变化。该特性用于预测当B-M-1趋于0时，即在临界点附近，伪杨氏模量趋于0，其中B是轴对称测试期间的垂直与横向应力比。尝试理解和预测不稳定的行为是使用相同的建模。强调了该模型与土壤液化结果的兼容性。
Compacting an assembly of soft balls far beyond the jammed state: insights from 3D imaging
本文利用三维成像实验方法研究极软颗粒组装体在远超堵塞状态下的压缩行为，通过追踪局部应变能揭示其从颗粒状到连续状材料的转变，并验证了描述压实过程的理论框架。
In a recent pair of papers, Eric DeGiuli has developed a field theory of glasses and granular materials based on the Edwards ensemble, extending our earlier theoretical framework. In this comment, we address a misconception regarding the relation between equiprobability of microstates and a flat measure in a field theory, which appears in the DeGiuli papers, and has often plagued discussions surrounding the Edwards ensemble. We point out that modeling this measure is the challenge addressed in both our earlier work and the recent DeGiuli work. Contrary to what is stated in the the DeGiuli pape…
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