TEACHING OF CLASSICAL MECHANICS WITH THE HELP OF THE HISTORY OF MECHANICS1)

经典力学主要涵盖牛顿力学、拉格朗日力学及哈密顿力学等三大部分内容。现行高校教育体系下所开设的理论力学课程,承担了经典力学基础知识普及的教学重担。历经数百年发展所臻于完善的经典力学体系,对于绝大数理工科学生来说不啻为一大挑战。在教学中,融入并贯彻力学史主线的经典力学教学,可带来意想不到的良好效果。     

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本文阐述时变力学这一新的研究方向,对其基本课题、特征及力学、数学方法与进展作了较为系统概述,并结合工程实践说明时变固体力学方向研究的重要性与发展前景．     

Frictional energy dissipation in materials containing cracks

Kachanov's simplified model of microcrack interaction is applied to an investigation of the behaviour of a cracked body under predominantly compressive periodic loading, so that the cracks experience periods of closure and slip, with frictional dissipation. The model is shown to be equivalent to a discrete elastic frictional system with each crack representing one node. Theorems and algorithms from such systems are applied to determine the conditions under which the system shakes down to a state with no slip and hence no energy dissipation in friction. For conditions not too far beyond the shakedown state, the dissipation is significantly affected by the initial conditions, but with larger oscillating loads, it becomes a unique and increasing function of load amplitude. The effect of crack interaction is assessed by comparison with an uncoupled model, for which the dissipation is obtained as a summation of closed form expressions over the crack population. For small numbers of cracks, the results are significantly dependent on the randomly chosen crack locations and sizes, but with larger populations, a statistically significant decrease in dissipation is observed with increasing interaction terms.     

高瞻远瞩加强力学基础研究

本文简要回顾了力学学科的性质与作用;近代力学的发展与现状;我国力学研究的概况;对发展力学学科提出了若干建议。      

工程科学前沿的拓荒者——郑哲敏

郑哲敏先生是著名力学家, 我国爆炸力学的奠基人和开拓者, 2012年度国家最高科学技术奖获得者. 本文回顾了郑哲敏先生在过去60多年中非常丰富的科研活动, 特别是他在爆炸加工、地下核爆、爆炸排淤、穿破甲、煤与瓦斯突出、水合物开采、水弹性动力学、材料力学行为等方面的杰出学术贡献. 这些工作闪耀着鲜明的工程科学特点, 即着眼国家重大需求, 从错综复杂的问题中概括提炼关键物理因素, 创新理论, 进而指导实践. 郑哲敏先生的科学贡献和学术思想, 对于力学学科发展, 有着重要的现实意义和参考价值.     

ON AN INTERDISCIPLINARY TEACHING METHOD OF FLUID MECHANICS AND OTHER MECHANICS RELATED COURSES1)

流体力学是力学和机械等专业本科生的一门专业基础课。由于其涉及数学、物理的概念多、公式复杂、理论抽象而实际应用广,是公认的难教、难学的课程之一。笔者提出了将流体力学与理论力学、材料力学、电动力学等其他力学课程交叉教学的方法,充分利用各门力学课程知识间的联系,使得学生在学习流体力学的同时复习其他力学的知识,通过对比深化理解流体、固体、刚体和电磁场,最终获得对力学学科的整体视野,增强教学效果。     

Trans-scale mechanics： looking for the missing links between continuum and micro/nanoscopic reality

Problems involving coupled multiple space and time scales offer a real challenge for conventional frame-works of either particle or continuum mechanics. In this paper, four cases studies （shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics） are provided to illustrate the three levels of trans-scale problems （problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/ molecules and a finite size body at micro/nano-level） and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.     

实验力学在未来国际上的地位

本文论述了测量和实验技术当前和未来在分析结构、结构单元以及技术系统的位移、应变和应力中所起的作用.今天比以往任何时候都有更多的原因在广泛的领域中采用实验力学的方法。现代先进的新技术,新的测量设备,自动的量测和评价过程已应运而生。先进的测量技术和计算机技术的结合——杂交技术已得到了发展,这些技术使我们能对结构和产品进行优化设计:节省能源和原材料,提高产品质量以及结构和技术系统的可靠性和安全度,管理生产的过程,监控运行系统的安全。这些方法能用于减少技术系统的危险性和对环境的破坏,对发展中国家传授先进的实验力学方法的知识,显得更为重要。     

Effect of thickness and boundary conditions on the behavior of viscoelastic layers in sliding contact with wavy profiles

In this work, the sliding contact of viscoelastic layers of finite thickness on rigid sinusoidal substrates is investigated within the framework of Green's functions approach. The periodic Green's functions are determined by means of a novel formalism, which can be applied, in general, to either 2D and 3D viscoelastic periodic contacts, regardless of the contact geometry and boundary conditions.Specifically, two different configurations are considered here: a free layer with a uniform pressure applied on the top, and a layer rigidly confined on the upper boundary. It is shown that the thickness affects the contact behavior differently, depending on the boundary conditions. In particular, the confined layer exhibits increasing contact stiffness when the thickness is reduced, leading to higher loads for complete contact to occur. The free layer, instead, becomes more and more compliant as thickness is reduced.We find that, in partial contact, the layer thickness and the boundary conditions significantly affect the frictional behavior. In fact, at low contact penetrations, the confined layer shows higher friction coefficients compared to the free layer case; whereas, the scenario is reversed at large contact penetrations. Furthermore, for confined layers, the sliding speed related to the friction coefficient peak is shifted as the contact penetration increases. However, once full contact is established, the friction coefficient shows a unique behavior regardless of the layer thickness and boundary conditions.     

高速切削实验平台在力学实验教学中的应用

传统的力学实验已无法满足研究生创新性实验教学的需要。为了使研究生在科学研究中掌握实验分析的基本方法和技能,本文基于Hopkinson压杆加载技术建立了一套高速切削实验系统。该实验系统作为一个科研平台,能够实现切削过程的瞬态冻结并完成变形场和切削力的实时测量,可为高速切削机理研究提供基础实验数据。同时,该实验系统也是一个综合性的实验平台。基于该平台,可以完成金相分析、光栅光纤测力、变形场测量以及塑性本构分析等力学实验教学。高速切削实验平台将力学实验与科学研究相结合,有利于培养研究生独立分析与研究的能力,为研究生未来的科研工作打下基础。     

New inroads in an old subject: Plasticity, from around the atomic to the macroscopic scale

Nonsingular, stressed, dislocation (wall) profiles are shown to be 1-d equilibria of a non-equilibrium theory of Field Dislocation Mechanics (FDM). It is also shown that such equilibrium profiles corresponding to a given level of load cannot generally serve as a travelling wave profile of the governing equation for other values of nearby constant load; however, one case of soft loading with a special form of the dislocation velocity law is demonstrated to have no ‘Peierls barrier’ in this sense. The analysis is facilitated by the formulation of a 1-d, scalar, time-dependent, Hamilton-Jacobi equation as an exact special case of the full 3-d FDM theory accounting for non-convex elastic energy, small, Nye-tensor-dependent core energy, and possibly an energy contribution based on incompatible slip. Relevant nonlinear stability questions, including that of nucleation, are formulated in a non-equilibrium setting. Elementary averaging ideas show a singular perturbation structure in the evolution of the (unsymmetric) macroscopic plastic distortion, thus pointing to the possibility of predicting generally rate-insensitive slow response constrained to a tensorial ‘yield’ surface, while allowing fast excursions off it, even though only simple kinetic assumptions are employed in the microscopic FDM theory. The emergent small viscosity on averaging that serves as the small parameter for the perturbation structure is a robust, almost-geometric consequence of large gradients of slip in the dislocation core and the persistent presence of a large number of dislocations in the averaging volume. In the simplest approximation, the macroscopic yield criterion displays anisotropy based on the microscopic dislocation line and Burgers vector distribution, a dependence on the Laplacian of the incompatible slip tensor and a nonlocal term related to a Stokes-Helmholtz-curl projection of an ‘internal stress’ derived from the incompatible slip energy.     

Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model

An analytical model based on a molecular mechanics approach is presented to relate the elastic properties of a single-walled carbon nanotube to its atomic structure. We derive closed-form expressions for elastic modulus and Poisson's ratio as a function of the nanotube diameter. Properties at different length scales are directly connected via these expressions. The analytically calculated elastic properties for achiral nanotubes using force constants obtained from experimental data of graphite are compared to those based on tight binding numerical calculations. This study represents a preliminary effort to develop analytical methods of molecular mechanics for applications in nanostructure modeling.     

牛顿力学体系中固体力学研究框架的几点注记

本文从四十多年前遇到并解决的三个与固体力学和结构力学相关的机械强度与振动的问题谈起。当时在分析与解决这些问题的方法时,思考并领悟到如何从结构的构形与几何约束、结构承受的外载的性质和结构材料的秉性与行为着眼,实质上就是从以牛顿力学体系的外载(F)、质点质量(m)和物体运动的加速度(a)(即物体的位移、速度、加速度等运动表现的力学运动的几何量)的运动行为作为三个最基本的视点并描述它们之间的联系,在拓广后给出可变形固体力学分析的基本框架。进而刻画出在20世纪70年代、90年代和21世纪初的固体力学的基本框架及其框架内每个不同构元的联系与演进,并以图1,2,3表示。随着现代科技的发展,这一框架下的分析方法近些年已经扩展到更广泛的科技疆域,并在与其他学科的交缘的过程中揭示新的交缘变量的演化方程。人们还期望进入更小和更大尺度时空,研究更广泛的物质包括信息的生成与传递、有生命物质的运动和各种“极端”的力学环境条件下的力学现象,这些新的疆域将是明天的力学工作者耕耘的新天地。     

Phase-Transition Fronts in Deformable Ferromagnets

The notions of material inhomogeneity and balance of pseudomomentum are exploited to construct a thermodynamical framework for propagating coherent phase-transition fronts in ferromagnetic thermoelastic materials. This analysis results in the proposal of thermodynamically admissible criteria of progress for the fronts. Magnetoelastic domain walls may be viewed as special cases of such fronts.     

关于结构力学发展的思考

关于结构力学发展的思考钱令希（大连理工大学１１６０２３）编者按：作者长期从事工程力学教学及科研工作。７０年代倡导计算力学，为国际计算力学协会发起人之一。１９８４年创办本刊，是本刊的创始人。值此本刊创办十周年之际，作者建议出版纪念文集，以资纪念，希望为...     

离散元法研究的评述

介绍了离散元法的基本理论、计算方法及其应用的现状和最新进展.从离散元法的离散模型特点及便于甄别与其它数值计算方法的关系的角度给予离散元法一个比较宽松的定义.在此基础上阐明了离散元方法与刚体-弹簧模型(rigid body spring model, RBSM)方法,不连续变形分析(discontinuous deformation analysis, DDA)方法,分子动力学(moleculardynamics, MD)方法,三维离散元(discrete meso-element dynamicmethod, DM$^2$)方法及无网格方法(meshless method)等数值计算方法的关系, 并讨论了离散元法研究中亟待解决的问题和今后的发展方向.      

LEONARDO DA VINCI AND FLUID MECHANICS 1)

旷世全才列奥纳多·达·芬奇(Leonardo da Vinci),被世人誉为画家、雕刻家、天文学家、发明家、音乐家、数学家、解剖学家、生理学家、地质学家、植物学家、作家、军事、建筑工程和制图师,是意大利文艺复兴时期人文主义的代表人物。本文对其流体力学相关思想及湍流、飞行、波浪和风暴等几个方面的研究贡献进行梳理,认为他是流体力学科学研究的先驱和奠基人,也是一位“流体力学家”。     

Intellectual Consumerism

The great revolution in theoretical fluid mechanics (brought along by the advent of computers in the middle of the century) that replaced search for a formal solution of a general problem with the analysis of evolutions, is in turn threatened by consumerism replacing physical thought with easy, uncontrolled output.Sommario. La grande rivoluzione nello studio della meccanica dei fluidi (conseguente alla nascita dei calcolatori a metà del secolo) consistette nel sostituire alla ricerca formale di una soluzione generale, l'analisi delle evoluzioni fisiche; ma il consumismo imperante minaccia ora di sostituire l'interpretazione fisica con la facile produzione di risultati incontrollati.     

A KIND OF STRUCTURAL MECHANICS TEACHING MODEL1)

基于目前土木工程本科生教学课程结构力学的教学现状,特别是几何体系讲解过于抽象的问题,本文借鉴国外相关经验,提出了基于实物的一种解决方案,即基于计算简图模拟几何体系的结构力学教学模型,并论述其必要性。通过介绍其组成构件、典型用途及使用示例,表明了其具有良好的教学辅助效果,体现了土木工程专业本科重要的专业基础课结构力学教学中,传统授课与创新探索相共存、简化图示和实物呈现相结合的重要作用。     

Kinematics and elasticity framework for materials with two fiber families

A kinematics framework is developed for materials with two fiber families that are not necessarily orthogonal or mechanically equivalent. These two latter conditions represent important subclasses that are analyzed. To succinctly define the strain, six scalar strain attributes are developed that have direct physical interpretation. In the hyperelastic limit, this approach allows the Cauchy stress t to be expressed as the sum of six response terms, almost all of which are mutually orthogonal (i.e. 14 of the 15 inner products vanish). For small deformations, the response terms are entirely orthogonal (i.e. all 15 inner products vanish). Experimental advantage is demonstrated for finite strain hyperelastic materials by showing that common tests, for the first time, can directly determine terms in the strain energy function of two fiber composites.Received: 18 September 2002, Accepted: 5 May 2003, Published online: 29 July 2003