静态堆积颗粒中的力链分布

颗粒物质是由众多离散颗粒组成的软凝聚态物质,涉及多个物理层次结构和机制,是多尺度问题. 首先阐述了颗粒物质多尺度力学的研究框架,指出颗粒间接触力链构成的细观尺度是核心,颗粒物质显示出的独特静态堆积特性和动态流变特性都与细观尺度力链的复杂演变规律直接相关. 围绕着定量描述力链特征这一目标,采用严格的球形颗粒Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论,对重力作用下12000个球心共面的二维等径颗粒静态堆积进行了离散动力学模拟,对力链分布特征、接触力规律等做了量化分析,考察了颗粒 关键词： 颗粒物质 力链 离散模型 多尺度力学     

颗粒介质尺度效应的抗剪试验及物理机理分析

针对颗粒介质力学特性的颗粒尺度效应研究,选用土矿物颗粒制备不同颗粒尺度的抗剪试样,进行一系列直剪快剪和三轴抗剪试验,测得了不同颗粒粒径和体分比试样的变形曲线及剪应力强度;基于颗粒间微观作用力与重力比值和胞元体模型,首次从微观和细观角度解释颗粒尺度效应的物理机理.结果表明,随着介质中粗颗粒的比例增加和粒径减小,介质变形特性增强,剪应力强度也随之提高;体分比对变形和强度特性的影响比粒径的影响更加显著.基于介质特性尺度效应物理机理分析,提出衡量介质颗粒聚集和摩擦效应的微重比判别参数以及应变梯度和变形协调微裂纹引起颗粒尺度效应的细观机理解释;文中提出的胞元体模型大大减少了颗粒物质体系的计算自由度,为工业和工程设计的计算建模提供一种可行途径.     

水-气-颗粒固体三相混合系统的流体动力学

按照经典物理中处理混合物的一般热力学方法, 将近年来报道的颗粒固体流体动力 学进一步推广到孔隙被水和气填充的情形, 建立了其自由能的初步模型. 水-气-颗粒三相体系是与岩土工程和地质灾害密切相关的材料, 但其经典宏观物理基础却一直未能全面澄清.目前用于分析这类混合物力学行为的基本工程理论含Darcy渗流定律、Terzaghi有效应力及其运动方程(即本构方程)等内容. 通过与经典物理对比, 本文澄清了渗流对应于不同相之间的质量扩散, 有效应力与这类材料特有的体积填充形式自由能有关, 这两部分内容工程与物理是一致的.目前的分歧具体体现在材料建模对象上, 前者认为是本构方程, 而后者是自由能和迁移系数. 该分歧的解决将是建立这类材料的连续介质物理基础、突破本构方法面临的困境的一个关键. 关键词： 颗粒物质 混合物 应力 流体动力学     

颗粒物质的多尺度结构及其研究框架

颗粒物质力学的研究刚刚起步,目前很多方面还不完善.文章作者认为,该学科是应用性很强的基础学科,因此提出了从实际应用中去发现科学问题,进而促进颗粒物质力学基础理论发展的研究思路,并以土力学为例做了说明.土是岩石经风化作用,由重力、流水和风力等搬运和沉积而成的产物,是密集颗粒物质体系之一.土粒是构成土体骨架、传递载荷的基本单元,与颗粒间复杂分布的孔隙水、气体共同决定了土体的非线件本构关系、剪胀(剪缩)和应力路径相关等复杂特征.以研究密集分布颗粒体系的颗粒物质力学在近20年内得到充分发展,它侧重现象的机理分析和实验的精细检测,为土力学的基础研究提供了重要启示.基于文章作者多年土力学和颗粒物质力学的研究经验,提出了土体具有多尺度结构的观点:除微观的单颗粒尺度和宏观土体尺度外,细观尺度的力链是颗粒接触力传递的路径,足存在于土体内的相对稳定的结构体.建立了初步的理论研究框架,提出了力链网络的复杂动力学响应决定土体复杂本构关系的基本没想.下一阶段将从理论分析、物理试验和基于自主开发的颗粒离散元模拟3个方面进行研究,逐渐充实土力学多尺度理论体系,以期取得突破.     

功和能教学中两个被忽略的问题

在物理教学中,功和能的教学是力学中的重点,而用功和能解决力学问题也是学生学习的难点.要使学生掌握这部分内容,以下两问题值得引起注意.1 机械能的相对性 重力势能、弹性势能属于系统所有,其大小与零势能点(面)的选择有关;即系统的势能是相对于零势能点而言.具有相对性.然而,系统的动能也具有相对性,相对于参考系.     

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.     

聚酰亚胺/铜纳米颗粒复合物的分子动力学模拟研究

通过分子动力学模拟对聚酰亚胺/铜纳米颗粒复合物的形态结构、 热力学性质、力学特性进行计算, 分析其随模拟温度和纳米颗粒尺寸的变化规律. 模拟结果表明, 聚酰亚胺/铜纳米颗粒复合物为各向同性的无定形态结构, 铜纳米颗粒与聚酰亚胺基体之间通过较强的范德华作用结合在一起使结构更加稳定, 铜纳米颗粒表面多个原子层呈现无定形状态, 在铜颗粒和聚酰亚胺基体之间形成界面层, 界面区域随颗粒尺寸和温度的增加分别减小和增加. 聚酰亚胺/铜纳米颗粒复合物的等容热容随着颗粒尺寸增大而明显增高, 随温度变化比聚酰亚胺体系更为缓慢, 在较低温度下较小颗粒尺寸复合物的热容比聚酰亚胺体系更低. 聚酰亚胺/铜纳米颗粒复合物的热压力系数随颗粒尺寸增加而显著增大, 比聚酰亚胺体系的热压力系数更小, 且随温度升高而减小的程度要小得多. 聚酰亚胺/铜纳米颗粒复合物的热力学性质表现出明显的尺度效应, 温度稳定性明显高于聚酰亚胺体系. 聚酰亚胺/铜纳米颗粒复合物的力学特性表现出各向同性材料的弹性常数张量, 具有比聚酰亚胺体系更低的杨氏模量和泊松比, 随温度升高分别减小和增大, 与聚酰亚胺体系随温度的变化趋势相反, 且杨氏模量的温度稳定性显著提高, 同时泊松比随纳米颗粒尺寸增大而减小, 具有明显的尺度效应. 加入铜纳米颗粒形成复合物可获得与聚酰亚胺体系显著不同的力学新特性. 关键词： 分子动力学模拟 聚合物纳米复合物 聚酰亚胺 纳米颗粒     

径向“有效势能”的性质及其应用

推导了质点在有心力作用下在极坐标系中具有的总能量表达式，引出了质点在转动参考系中的有效势能公式，得出了有效势能的取值范围和极值条件，指出了有效势能在平衡点关于矢径的二阶导数的物理意义，利用有效势能的性质巧妙解答两道物理竞赛题.     

计入固液界面作用的润滑热力学模型与分析

摩擦与润滑过程是典型的能量耗散过程, 在机理上与非平衡热力学中的熵增、耗散结构等理论颇有相似之处. 通过热力学分析可以对一些典型的摩擦磨损过程做出合理的机理揭示与推测. 本文利用热力学理论对典型的润滑过程进行了建模分析. 采用分离压模型表征和计入了微尺度下的固液界面作用, 揭示分析了润滑热力学模型与润滑状态Stribeck曲线的联系. 从分析计算结果来看, 润滑Stribeck曲线的摩擦系数最低点与系统热力学上的熵增率最低点具有相当好的对应关系, 而润滑状态从弹流润滑向薄膜润滑的转变过程, 可以用耗散结构理论加以机理解释. 文中的热力学模型和方法能够有效地体现出润滑过程中多物理要素跨尺度非线性耦合的作用, 对实际工程与实验有着重要的指导作用.     

拉格朗日陀螺转动的有效势能和可视化

对《对称陀螺在重力场中定点转动的分析》一文中的能量守恒公式提出质疑,并推导证明了正确的公式.在有效势能的公式中引入了两个守恒参数,求出了有效势能的导数和二阶导数,并且求出了导数为零时的有效势能和二阶导数,通过作图和分析,说明了陀螺转动中章动角的变化范围和在平衡点的稳定性.     

Generalized formulation of the interactions between soft spheres

The goal of this paper is to identify the most general formulation that consistently links the different degrees of freedom in a contact between spherical soft particles. These contact laws have two parts: a set of “generalized contact velocities” that characterize the relative motion of the two particles, and a set of “generalized contact forces” that characterize the interparticle forces. One well known constraint on contact models is that the contact velocities must be objective. This requirement fixes the number of linearly independent contact velocities. We also present a previously unnoticed (in this context) constraint, namely, that the velocities and forces must be related in such a way that the stiffness matrix is symmetric. This constraint also places restrictions on the coupling between the contact forces. Within our generalized contact model, we discuss the expression for rolling velocity that need to be used in the calculation of rolling resistance, and the risk or producing perpetual mobile when other expressions of rolling velocity are using instead.     

Laser measurement of torsional vibrations/longitudinal creepage of a railway wheel set on a scaled test bench

Since more than one century, test benches remain an essential tool to study various aspects of the railway dynamics such as for instance running stability, safety or even ride comfort. For each of these applications, the knowledge of the contact conditions (forces and relative displacements) between the wheel and the rail is a necessary condition to develop a sound understanding of the physical phenomena. More specifically, as soon as the longitudinal dynamics of the vehicle-track system is involved in the study (like for the performance of a locomotive, the rolling noise or rail corrugation), a precise measure of the longitudinal creepage between the wheel and the rail is needed to verify numerical predictions from theoretical models. In this paper, we focus on the measurement of torsional vibrations of a scaled wheel set which is rolling on a roller (representing infinite rails). First, a theoretical overview of the conditions under which these torsional vibrations are excited is given. Then, the experimental set-up used to study the phenomenon is presented. During the experiment, the wheel set torsional vibrations are measured using the rotational laser Doppler vibrometer, and the measure is used to calculate the longitudinal creepage of the wheel. Results are compared with outputs of a multi-body model of the test bench.     

On the validity of Hertz contact law for granular material acoustics

We discuss the acoustical behavior of a 1D model of granular medium, which is a chain of identical spherical beads. In this geometry, we are able to test quantitatively alternative models to the Hertz theory of contact between elastic solids. We compare the predictions of the different models to experimental results that concern linear sound wave propagation in the chain submitted to a static force, and nonlinear solitary wave propagation in an unconstrained chain. We use elastic, elastic-plastic and brittle materials, the beads roughness extends on one order of magnitude, and we also use oxidized metallic beads. We demonstrate experimentally that at low static forces, for all types of beads, the linear acoustic waves propagate in the system as predicted by Hertz's theory. At larger forces, after onset of permanent plastic deformation at the contacts, the brass beads exhibit non Hertzian behavior, and hysteresis. Except in the case of brass beads, the nonlinear waves follow the predictions of Hertz theory. Revised: 28 May 1998 / Accepted: 27 July 1998     

Tyre–road contact using a particle–envelope surface model

Determination of the contact forces is the central problem in all aspects of road-tyre interaction: i.e. noise, energy loss and friction. A procedure to find the contact forces under a rolling tyre is presented in four stages. First, the contact stiffness of a uniform peak array from indentations in the rubber tread, and also tyre carcass deflection, is described by some new simplified expressions. Second, a routine divides a single surface profile into equal search intervals, in which the highest peaks are identified. These are used to obtain the parameters for the interval, i.e. the mean envelope and the mean interval. The process is repeated at geometrically decreasing search intervals until the level of the data resolution, thereby describing the profile by a set of envelopes. The ‘strip profile’ ultimately used to describe the surface, is obtained by selecting the highest points across the profiles of one stone's width. The third stage is to combine the strip profile envelopes with the contact stiffness expressions, yielding the nonlinear stiffness–displacement, and force–displacement relationships for the chosen road–tyre combination. Finally the contact pressure distribution from a steady-state rolling tyre model is applied to the strip profile, via the force–displacement relationship, giving the local tyre displacements on the road texture. This displacement pattern is shown to be proportional to the time and space varying contact pressure, which then is incorporated into a wave equation for rolling contact.     

Acoustic virtual mass of granular media

Mechanical coupling between grains in a randomly packed unconsolidated granular medium is shown to cause an increase in the effective inertia, hence, a reduction in sound and shear wave speeds, relative to predictions by the standard expressions for a uniform elastic solid. The effect may be represented as a virtual mass term, and directly related to the scintillation index of the grain-to-grain contact stiffness.     

A new statistical mechanics approach to dense granular media

A new statistical mechanics approach to dense granular media is presented. The thermodynamic formalism is set out directly in terms of elastic potential energy, such that the configurational temperature (the intensive property which defines the steady state) relates to a quadratic function of the stresses (rather than other linear functions used in recent developments). Dense granular media are considered as canonical ensembles of noninteracting clusters, which can be identified with repeatable equilibrium configurations. Then, particles can be located in a new proposed phase space (conceived to separate the elastic potential energy levels). Although the importance of this paper lies in the method itself, it has been illustratively applied to the simple case of two-dimensional (2D) dense granular media (an arrangement of frictionless monodisperse elastic disks under isotropic horizontal stress compression). In this case, the temperature is directly replaced by the squared external pressure, and the packing ratio of the most probable microstate is close to the reported value of random close packing. Moreover, some interesting general conclusions arise.     

Crumpling of a stiff tethered membrane

A first-principles numerical model for crumpling of a stiff tethered membrane is introduced. This model displays wrinkles, ridge formation, ridge collapse, and initiation of stiffness divergence. The amplitude and wavelength of the wrinkles and the scaling exponent of the stiffness divergence are consistent with both theory and experiment. Close to the stiffness divergence further buckling is hindered by the nonzero thickness of the membrane, and its elastic behavior becomes similar to that of dry granular media. No change in the distribution of contact forces can be observed at the crossover, implying that the network of ridges is then simultaneously a granular force-chain network.     

Development of elastic force model for wheel/rail contact problems

In this investigation, a new formulation for the wheel/rail contact problem based on the elastic force approach is presented. Crucial to the success of any elastic force formulation for the wheel/rail contact problem is the accurate prediction of the location of the contact points. To this end, features of multibody formulations that allow introducing additional differential equations are exploited in this investigation in order to obtain a good estimate of the rail arc length travelled by the wheel set. In the formulation presented in this paper, four parameters are used to describe the wheel and the rail surfaces. In order to determine the location of the points of contact between the wheel and the rail, a first order differential equation for the rail arc length is introduced and is integrated simultaneously with the multibody equations of motion of the wheel/rail system. The method presented in this paper allows for multiple points of contact between the wheel and the rail by using an optimized search for all possible contact points. The normal contact forces are calculated and used with non-linear expressions for the creepages to determine the creep forces. The paper also discusses two different procedures for the analysis of the two-point contact in the wheel/rail interaction. Numerical results obtained using the elastic force model are presented and compared with the results obtained using the constraint approach.     

Relaxation damping in contacts under superimposed normal and torsional oscillation

It was recently shown that if a contact of two purely elastic bodies with no sliding is subjected to oscillations in normal and tangential directions, a kind of damping occurs due to relaxation of tangential stress in areas of intermittent contact, despite the absence of sliding and corresponding frictional work. In the present paper we show that the same mechanism acts in contacts with superimposed normal and torsional oscillations. A closed-form solution for the torsional and combined (torsional/tangential) relaxation dissipation for a contact of arbitrary bodies of revolution is presented.