Signatures of granular microstructure in dense shear flows

Granular materials and ordinary fluids react differently to shear stresses. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands--narrow zones of large relative particle motion, with essentially rigid adjacent regions. Because shear bands mark areas of flow, material failure and energy dissipation, they are important in many industrial, civil engineering and geophysical processes. They are also relevant to lubricating fluids confined to ultrathin molecular layers. However, detailed three-dimensional information on motion within a shear band, including the degree of particle rotation and interparticle slip, is lacking. Similarly, very little is known about how the microstructure of individual grains affects movement in densely packed material. Here we combine magnetic resonance imaging, X-ray tomography and high-speed-video particle tracking to obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.     

A Taylor vortex analogy in granular flows

Fluids sheared between concentric rotating cylinders undergo a series of three-dimensional instabilities. Since Taylor's archetypal 1923 study, these have proved pivotal to understanding how fluid flows become unstable and eventually undergo transitions to chaotic or turbulent states. In contrast, predicting the dynamics of granular systems--from nano-sized particles to debris flows--is far less reliable. Under shear these materials resemble fluids, but solid-like responses, non-equilibrium structures and segregation patterns develop unexpectedly. As a result, the analysis of geophysical events and the performance of largely empirical particle technologies might suffer. Here, using gas fluidization to overcome jamming, we show experimentally that granular materials develop vortices consistent with the primary Taylor instability in fluids. However, the vortices observed in our fluidized granular bed are unlike those in fluids in that they are accompanied by novel mixing-segregation transitions. The vortices seem to alleviate increased strain by spawning new vortices, directly modifying the scale of kinetic interactions. Our observations provide insights into the mechanisms of shear transmission by particles and their consequent convective mixing.     

Sound scattering in dense granular media

The sound propagation in a dense granular medium is basically characterized by the ratio of wavelength to the grain size. Two types of wave transport are distinguished： one corresponds to coherent waves in the long wavelength limit, the other to short-wavelength scattered waves by the inhomogeneous contact force networks. These multiply scattered elastic waves are shown to exhibit a diffusive characteristics of transport over long distances of propagation. Determination of the transport mean free path l^＊ and the inelastic absorption （Q^-1） allows the inference of the structural properties of the material such as the heterogeneity and internal dissipation. The relevance of our experiments for seismological applications is discussed. Moreover, we apply the correlation technique of the configuration-specific sound scattering to monitoring the dynamic behaviour of the granular medium （irreversible rearrangements） under strong vibration, shearing and thermal cycling, respectively.     

Shear instabilities in granular flows.

Unstable waves have been long studied in fluid shear layers. These waves affect transport in the atmosphere and oceans, in addition to slipstream stability behind ships, aeroplanes and heat-transfer devices. Corresponding instabilities in granular flows have not been previously documented, despite the importance of these flows in geophysical and industrial systems. Here we report that breaking waves can form at the interface between two streams of identical grains flowing on an inclined plane downstream of a splitter plate. Changes in either the shear rate or the angle of incline cause such waves to appear abruptly. We analyse a granular flow model that agrees qualitatively with our experimental data; the model suggests that the waves result from competition between shear and extensional strains in the flowing granular bed. We propose a dimensionless shear number that governs the transition between steady and wavy flows.     

黄土湿陷变形本构关系研究

根据黄土湿陷变形的结构性原理,分析了湿陷变形的塑性特性,引用增湿软化模型ZSM体作为增湿变形的力学模型,应用常规三轴浸水试验研究了不同的应力状态下湿陷性黄土在水和力共同作用下的湿陷变形特性,将增湿含水量作为内应力考虑,并由试验拟台得出湿陷体积屈服面和剪切屈服面,基于广义塑性力学原理建立了湿陷变形的增量本构模型,该模型考虑了湿陷变形中的湿陷体积变形和湿陷剪切变形以及球应力和偏应力对湿陷体积变形和湿陷剪切变形的交叉影响,反映了黄土湿陷变形的特性。     

颗粒材料热力学理论在简单剪切流中的应用

颗粒物质由大量离散的粗大固体颗粒聚集而成,在外界作用下可能发生准静态变形、变形局部化和破坏,直至流动,其中采用固体力学和流体力学对准静态变形和流动开展的研究较为系统,而变形局部化和破坏的研究非常薄弱．分析内部结构演化规律,建立颗粒体系非平衡态热力学,统一描述颗粒体系力学行为是重要的基础研究课题,Granular Solid Hydrodynamics（GSH）理论为该研究提供了基础．本文完善了该理论涉及的颗粒温度表达式,确定了相应参数数值;与动理学理论和离散元模拟一起对恒定体积简单剪切流进行了分析,对比了三种方法得到的正应力与颗粒体积分数的关系,发现由于基本假设的限制,动理学理论只能适用于稀疏颗粒流,而完善后的颗粒体系热力学理论比动理学涵盖范围更广,可以从稀疏体系到密集体系．这样该理论可以连贯地描述颗粒体系准静态变形、变形局部化和破坏,直至流动的力学行为．     

颗粒流本构关系的实验研究

基于"拟流体"的思想,给出了测量颗粒流本构关系的实验方法.在颗粒斜槽流实验中,通过颗粒的抛物线运动计算流层速度分布,根据非牛顿流体理论求得颗粒流黏性的本构关系;建立了颗粒斜槽流的数学模型,流层的速度为指数分布,流量为斜槽倾角和流层厚度的函数.以小麦颗粒为例,实验结果与用"拟流体"方法所得的预测值进行比较,相对误差在13%以内.     

微波照射下花岗岩损伤演化规律及本构模型研究

为进一步分析微波破岩机理,对微波照射下硬岩损伤演化规律及其本构行为进行了研究。首先,对岩石进行弹性微元假设,结合微元强度准则和三参数Weibull分布,推导出微波作用后硬岩损伤演化方程和本构模型以及各参数确定公式,然后,采用不同微波功率照射后的花岗岩超声波检测和单轴压缩试验结果对模型进行验证。结果表明,建立的模型理论曲线与试验曲线具有较高的吻合度,能反映出花岗岩破裂的应力应变过程,且模型各参数的物理意义及对模型的影响规律明确,虽然峰后拟合存在一定偏差,但仍可以基本反映岩石经微波照射后的弱化规律。对经微波照射后的岩石本构方程进行深入研究,可为微波照射岩石的相关计算和数值模拟提供一定的参考,有助于促进微波辅助破岩技术的发展。     

一种岩石的损伤流变模型

根据石膏角砾岩的蠕变特性,建立了石膏角砾岩的粘弹塑性流变组合模型;在此基础上,采用统计损伤理论,并考虑了损伤门槛的影响,建立了考虑损伤门槛的统计损伤本构方程;根据应变等效原理,建立了石膏角砾岩的损伤流变模型。通过试验验证,理论计算结果与石膏角砾岩蠕变试验结果吻合较好,表明所提出的损伤流变模型可以较好的描述石膏角砾岩的非线性流变。     

密实散粒体宏微观特性的直剪试验离散元数值分析

为了分析直剪试验中试样内部的应力、应变状态,采用离散元商业软件PFC2D在不同围压下对密实散粒体进行了大量的数值模拟,分析了试验的边界效应,应力偏转,应力、应变路径以及颗粒群的微观运动状态.模拟结果表明:边界摩擦影响室内直剪试验的测试结果,所得密实散粒体的强度指标偏高,内摩擦角存在1.5°的误差;剪切过程中,主应力大小和方向均发生变化,中心点主应力偏转约44°.由剪切带内外颗粒运动状态和应力、应变路径分析可知,剪切带内部是主要的剪胀区,存在大幅度的加卸载反应,并且应力路径峰值超出了试样峰值强度包线;剪切带外体变较小,主要处于加载状态,应力路径峰值未超出试样残余强度包线.     

低浓度固液两相流颗粒相本构关系的动理学分析

固液两相流的动理学理论认为固体颗粒相可用Boltzmann方程描述。从流场中的颗粒受力分析出发 ,应用动理学的 Chapman- Enskog法 ,探讨了低浓度固液两相流下的 Boltzmann方程的二阶近似解和颗粒相本构关系。结果表明 ,尽管颗粒所受相间力与两相脉动速度有关 ,但在两相脉动速度近乎无关的极限条件下 ,颗粒速度分布函数和颗粒相本构关系与快速颗粒流的相同。这样的极限条件在含粗重颗粒的两相流中可以近似实现     

一种基于粒计算的知识隐藏方法

对数据中蕴涵的敏感知识的隐藏与保护是私有保护数据挖掘中重要一个研究课题。粒计算具有在不同的粒度层次上进行问题求解的能力。本文讨论了基于粗糙集粒计算模型的数据中知识隐藏与保护方法。首先,介绍了不完备信息系统下的相容关系、相容信息粒和信息粒度;其次,提出基于粒计算的知识隐藏与保护方法;最后,通过具体实例和在真实数据集上的测试表明了所提出方法的可行性。     

岩石连续损伤统计本构模型

基于岩石微元强度概率分布理论 ,以Drucker Prager破坏准则为统计分布变量 ,建立了理论的岩石损伤变量演化方程和三轴条件下岩石损伤弹性统计本构模型。利用任意条件下的三轴试验数据 ,用曲线拟合法和极值法求解了所建模型的参数 ,并用试验结果对所建模型进行了验证。模型计算结果与试验结果吻合较好 ,这说明用Drucker Prager准则为统计分布变量建立的损伤模型能够较好地反映岩石内部缺陷分布和变形特征 ,表征岩石材料在弹性阶段的本构关系。     

岩石连续损伤统计本构模型

基于岩石微元强度概率分布理论，以Drucker-Prager破坏准则为统计分布变量，建立了理论的岩石损伤变量演化方程和三轴条件下岩石损伤弹性统计本构模型。利用任意条件下的三轴试验数据，用曲线拟合法和极值法求解了所建模型的参数，并用试验结果对所建模型进行了验证。模型计算结果与试验结果吻合较好，这说明用Drucker-Prager准则为统计分布变量建立的损伤模型能够较好地反映岩石内部缺陷分布和变形特征，表征岩石材料在弹性阶段的本构关系。     

混凝土的单轴率型本构模型

以不同可逆热力学为基础,构造了混凝土的单轴率型本构模型,该模型可描述混凝土的以下特性;初始屈服强度为零;峰值强度随应变速率的增大而增加,在上升段和下降段都是光滑的;当应变趋于无穷大量,应力是收敛的;峰值点处应变不随加载就变速率的增大而变化。另外,根据前人的实验结果,明确提出了在率型本构关系中一致性条件的适用范围是加载应变速率低于应变速率的临界值,这一速率范围也是单轴率型本构模型的适用范围。     

A scaling law for slow earthquakes

Recently, a series of unusual earthquake phenomena have been discovered, including deep episodic tremor, low-frequency earthquakes, very-low-frequency earthquakes, slow slip events and silent earthquakes. Each of these has been demonstrated to arise from shear slip, just as do regular earthquakes, but with longer characteristic durations and radiating much less seismic energy. Here we show that these slow events follow a simple, unified scaling relationship that clearly differentiates their behaviour from that of regular earthquakes. We find that their seismic moment is proportional to the characteristic duration and their moment rate function is constant, with a spectral high-frequency decay of f(-1). This scaling and spectral behaviour demonstrates that they can be thought of as different manifestations of the same phenomena and that they comprise a new earthquake category. The observed scale dependence of rupture velocity for these events can be explained by either a constant low-stress drop model or a diffusional constant-slip model. This new scaling law unifies a diverse class of slow seismic events and may lead to a better understanding of the plate subduction process and large earthquake generation.     

形状记忆合金本构模型的热力学框架

基于形状记忆合金(SMAs)在相交过程中的热力学势和能量耗散来建立形状记忆合金的本构模型框架，通过采用不同独立变量(应力、应变、温度和熵)的组合来选择不同的能量函数(内能、Helmhohz自由能、Gibbs自由能和焓)，用内状态变量考虑相交过程中的能量耗散，则SMAs的本构模型完全可以由热力学势及能量耗散函数来建立，实例表明其可行性.     

稠密图[T（1,2,n）∪（∪iCui）]补的色等价刻画

研究稠密图[T(1,2,n)∪(∪iCui)]补的色性，并刻画它的色等价图，其中，T（l1,l2,l3,)(l1≤l2≤l3）表示只有一个3点度，三个1度点，且唯一3度点到三个1度点的距离分别为l1,l2,l3的树，P（G，λ）和h(G,x)分别表示图G的色多项式和伴随多项式。     

稠密图“非汉字字符”的色等价刻画

研究稠密图T(1,2 ,n)∪ ∪iCui 的色性 ,并刻画它的色等价图 .其中 ,T(l1 ,l2 ,l3) (l1 l2 l3)表示只有一个3度点 ,三个 1度点 ,且唯一 3度点到三个 1度点的距离分别为l1 ,l2 ,l3的树 ,P(G ,λ)和h(G ,x)分别表示图G的色多项式和伴随多项式 .