周期性结构热动力时间-空间多尺度分析

研究一种时间-空间多尺度渐近均匀化分析方法，模拟不同的极端热和动力载荷下微尺度多 相周期性结构中热动力响应问题，并建立一个广义的波动函数场控制方程描述热动力响应. 通过引入一个放大空间尺度和两个缩小时间尺度，在不同时间尺度上获得由空间非均匀性引 起的波动效应和非局部效应. 根据高阶均匀化理论在空间和时间上进行均匀化，获得高阶非 局部函数场波动方程. 并进一步用C0连续修正了高阶非局部函数场波动方程的有限元近 似解，使问题的求解避免了对有限元离散的C1连续性要求. 并与经典的空间均匀化方法 相比较，指出了经典的空间均匀化方法的局限性，进一步以一维非傅立叶热传导和热动力问 题为例，讨论了各种情况下方法的正确性与有效性.     

多尺度模拟与计算研究进展

简要介绍了多尺问题与研究方法.重点论述了两类常见多尺度问题的模拟计算方法与研究进展,分析了各自的优缺点和使用范围.对现有研究的局限性和存在的问题进行分析,指出了进一步研究多尺度模拟与计算的必要性.介绍了求解含有孤立缺陷问题的非局部准连续体法,MAAD等方法以及求解基于微观模型本构模拟问题的局部连续体法、HMM等方法.文章对多尺度模拟与计算的前景进行展望,提出了一些亟待解决的问题.     

微/纳尺度接触问题计算方法研究进展

接触问题广泛存在于现实生活的众多领域,近来随着微/纳米技术的不断发展,接触力学在基础理论和研究方法上面临许多新的挑战.本文在摩擦学的范畴内,对近年发展的若干求解微/纳尺度接触问题的计算方法及理论进行了综述.按发展先后及所解决问题的尺度范围划分,主要有3类评估微/纳尺度接触性能的计算方法:(1)连续介质力学方法;(2)分子动力学模拟; (3)多尺度方法.介绍了这3类计算方法的典型理论和主要数学描述,给出了这些方法对解决若干微/纳观接触问题如黏着效应、粗糙表面描述、表面摩擦及润滑、表面热效应、生物接触等的主要应用.最后, 探讨了微/纳尺度接触问题计算方法可能的发展方向及应用领域.      

大型土木结构多尺度模拟与损伤分析——————从材料多尺度力学到结构多尺度

从阐述重大土木工程结构安全运营面临的挑战性课题------结构多尺度力学问题开始, 对多尺度力学中的材料多尺度模拟和结构多尺度模拟的工程背景、多尺度特征和关键研究内容进行比较性评述;在此基础上, 重点介绍了对研究大型土木结构多尺度力学问题可能有参考价值的材料多尺度模拟和分析方法如周期性异质材料问题的平均化与渐进分析方法、单位分解法和多尺度重构核函数法, 以及大型土木结构多尺度模拟与分析领域的研究现状,由此引出结构多尺度力学研究中亟待解决的关键问题并加以评述;通过认识与比较结构多尺度与材料多尺度问题的共性与个性, 文中综述了在大型土木结构多尺度问题的研究进程中可供参考的理论与方法, 提出了这类结构多尺度力学问题研究的几个关键科学问题为: 结构多尺度模拟中的连接与跨越问题、多尺度模型的修正和验证、结构损伤的时间多尺度模拟与分析、结构强度和损伤失效过程中多尺度分析的跨尺度敏感性与随机性因素, 以及适用于大型土木结构多尺度模拟和计算分析的实施策略与技术.      

固体的统计细观力学——-连接多个耦合的时空尺度

从固体力学所面临的新的挑战------多物理、多尺度耦合及其现状的描述开始, 以层裂 过程为例, 说明了这些多尺度非平衡问题的基本困难在于, 在固体中不同尺度上有不同的微 结构层次及不同的演化物理和速率. 接下来, 概述了一些针对这一困难的独特的思路及 其成果. 第3部分强调了一些统计平均方法的范式, 以及处理包含多个时间和空间尺度的问 题的新思路, 特别是非平衡损伤演化导致宏观失效的问题. 在第4部分, 简要评述了一些连 接多个空间和时间尺度的细观力学框架, 如位错理论, 物理细观力学, Weibull理论, 随机 理论等, 并且阐述了其中蕴含的跨尺度耦合的机理. 然后, 在第5部分, 回到了描述损 伤演化过程的框架, 也就是统计细观损伤力学以及它的跨尺度封闭近似. 基于这些跨尺度框 架, 在第6部分, 对控制跨尺度耦合的可能机理进行了评述和比较. 由于对失效时灾变 的洞察与跨尺度强耦合紧密相关, 一些非平衡和强相互作用的新概念在第7部分进行了讨 论. 最后, 以一个简短的总结和一些建议结束.     

密集颗粒物质的多尺度结构

颗粒物质是大量离散的固体颗粒相互作用而组成的复杂体系.依据颗粒排布的稀疏程度,体系可分为颗粒气体、颗粒流体和颗粒固体,它们有不同本质的动量传递和能量耗散机制.后两者属于密集颗粒物质体系,内部形成了颗粒→力链→体系的多尺度结构,并涉及多个特征时间尺度,是典型的多尺度体系.合理分割体系结构层次、正确理解不同层次的物理过程、并确定它们之间的关联是密集颗粒物质研究的核心任务.本文依次分析了密集颗粒物质的内在物理图像、多尺度结构层次和特征时间等,并介绍了多尺度研究框架.     

微/纳尺度粘着滑动接触的多尺度分析

采用分子动力学与有限元耦合的多尺度方法,求解二维刚性圆柱表面压头与弹性平面的微/纳尺度粘着滑动接触问题,通过与全分子动力学模拟结果的比较验证了多尺度方法的有效性。对压头半径、滑动速度、下压深度以及是否考虑粘着效应等对滑动接触性能的影响进行了全面研究,通过不同条件下摩擦力及接触力分布的比较,揭示了上述各参数对粘着滑动接触...     

多尺度科学面向21世纪的挑战

多尺度科学是一门研究各种不同长度尺度或时间尺度相互耦合现象的科学．多尺度科学的研究领域十分宽广，涵盖的学科之多难以一一罗列．对于诸如流体动力学、材料科学、生物学、环境科学、化学、地质学、气象学和高能物理之类的各门科学，多尺度科学是它们的核心．多尺度科学目前在国际上处于刚刚起步的阶段．正如非线性现象和随机现象被认为是属于交叉学科并得到广泛重视一样，多尺度科学因其处于当代科学的许多极富挑战性问题的核心地位，发展前途未可限量．因此，在我国有必要抓住机遇，大力开展多尺度科学及其方法的研究．     

箱型结构损伤分析的空间网格多尺度模拟方法

为高效模拟空间效应显著的结构在关键局部的损伤，本文研究建立了以损伤分析为目标的空间网格多尺度模拟方法．首先基于变形协调法和内力平衡法，研究了空间网格多尺度建模中的跨尺度界面连接方法，对比分析了两种界面连接合理性．以三跨连续刚构混凝土箱梁在地震载荷下的损伤为分析案例，验证了空间网格多尺度模型在结构损伤分析中的可行性及其在计算效率上的优越性．分析结果表明：空间网格多尺度模型可以精确模拟结构的静力效应和动力特性；空间网格多尺度模型既考虑了结构空间效应，又可以高效分析箱梁结构局部易损部位的损伤演化过程，从而为空间效应显著的结构损伤分析提供了更为实用精细的计算模拟方法．     

颗粒物质中的多尺度问题

颗粒物质是大量离散的固体颗粒相互作用而组成的复杂体系. 依据颗粒排布的稀疏程度, 体系可分为颗粒气体、颗粒流体和颗粒固体,它们有不同本质的动量传递和能量耗散机制. 后两者属于密集颗粒物质体系,内部形成了颗粒$\to $力链$ \to$体系的多尺度结 构,并涉及多个特征时间尺度,是典型的多尺度体系. 合理分割体系结构层 次、正确理解不同层次的物理过程、并确定它们之间的关联是密集颗粒物质研究的核心任务. 本文依次分析了密集颗粒物质的内在物理图像、多尺度结构层次和特征时间等,并介绍了多 尺度研究框架.     

Resolving Controversies in the Application of the Method of Multiple Scales and the Generalized Method of Averaging

I compare application of the method of multiple scales with reconstitution and the generalized method of averaging for determining higher-order approximations of three single-degree-of-freedom systems and a two-degree-of-freedom system. Three implementations of the method of multiple scales are considered, namely, application of the method to the system equations expressed as second-order equations, as first-order equations, and in complex-variable form. I show that all of these methods produce the same modulation equations.I address the problem of determining higher-order approximate solutions of the Duffing equation in the case of primary resonance. I show that the conclusions of Rahman and Burton that the method of multiple scales, the generalized method of averaging, and Lie series and transforms might lead to incorrect results, in that spurious solutions occur and the obtained frequency–response curves bear little resemblance to the actual response, is the result of their using parameter values for which the neglected terms are the same order as the retained terms. I show also that spurious solutions cannot be avoided, in general, in any consistent expansion and their presence does not constitute a limitation of the methods. In particular, I show that, for the Duffing equation, the second-order frequency–response equation does not possess spurious solutions for the case of hardening nonlinearity, but possesses spurious solutions for the case of softening nonlinearity. For sufficiently small nonlinearity, the spurious solutions are far removed from the actual response. But as the strength of the nonlinearity increases, these solutions move closer to the backbone and eventually distort it. This is not a drawback of the perturbation methods but an indication of an application of the analysis for parameter values outside the range of validity of the expansion.Also, I address the problem of obtaining non-Hamiltonian modulation equations in the application of the method of multiple scales to multi-degree-of-freedom Hamiltonian systems written as second-order equations in time and how this problem can be overcome by attacking the state-space form of the governing equations. Moreover, I show that application of a variation of the method of Rahman and Burton to multi-degree-of-freedom systems leads to results that do not agree with those obtained with the generalized method of averaging.Contributed by Prof. R.A. Ibrahim.     

多尺度复合材料力学研究进展

多尺度复合材料力学是运用多尺度分析思想研究空间分布非均匀材料力学性能的学科, 近年来,多 组分、多层级先进材料的蓬勃发展和微纳米实验观测手段的不断进步,有力地推动了该学科的研究,论文围绕非均 匀材料力学性能的多尺度分析,首先从微纳米尺度到宏观尺度综述了常用的理论分析方法;接着分别针对非均匀 连续介质和离散体系介绍了常用的多尺度计算模拟方法;然后结合本课题组在纳米复合材料、抗冲击吸能材料、随 机网络材料和多层级自相似材料等方面的研究工作,举例说明了如何综合运用多种方法对各种复杂材料系统进行 多尺度分析;最后,展望了该领域还需进一步发展和完善的若干方向。     

Multiple Scales via Galerkin Projections: Approximate Asymptotics for Strongly Nonlinear Oscillations

The method of multiple scales and the related method of averaging are commonly used tostudy slowly modulated oscillations. If the system of interest is a slightlyperturbed harmonic oscillator, then these techniques can be applied easily. If the unperturbed system is strongly nonlinear (though possiblyconservative), then these methods can run into difficulties due to the impossibilityof carrying out required analytical operations in closed form.In this paper, we abandon the requirement of closed form analyticaltreatment at all stages. Instead, Galerkin projections are used toobtain approximate realizations of the method of multiple scales. Thispaper adapts recent work using similar ideas for approximaterealizations of the method of averaging. A key contribution of thepresent work is in the systematic identification and removal of secularterms in the general nonlinear case, a procedure that is more difficultthan for the perturbed harmonic oscillator case, and that is unnecessaryfor averaging.A strength of the present work is that the heuristics (Galerkin)and asymptotics (multiple scales) are kept distinct,leaving room for systematic refinement of the formerwithout compromising the asymptotic features of the latter.     

On elastocapillarity: A review

Elastocapillary phenomena involving elastic deformation of solid structures coupled with capillary effects of liquid droplets/films can be observed in a diversity of fields,e.g.,biology and microelectromechanical systems(MEMS).Understanding the physical mechanisms underlying these phenomena is of great interest for the design of new materials and devices by utilizing the effects of surface tension at micro and nano scales.In this paper,some recent developments in the investigations on elastocapillary phenomena are briefly reviewed.Especially,we consider the deformation,adhesion,self-assembly,buckling and wrinkling of materials and devices induced by surface tensions or capillary forces.The main attention is paid to the experimental results of these phenomena and the theoretical analysis methods based on continuum mechanics.Additionally,the applications of these studies in the fields of MEMS,micro/nanometrology,and biomimetic design of advanced materials and devices are discussed.     

Approximate Group Analysis and Multiple Time Scales Method for the Approximate Boussinesq Equation

This paper is devoted to investigation of the approximate Boussinesq equation by methods of the approximate symmetry analysis of partial differential equations with a small parameter developed by Baikov, Gazizov and Ibragimov. We combine these methods with the method of multiple time scales to extend the domain of definition of approximate group invariant solutions of the approximate Boussinesq equation.     

Remarks on the Perturbation Methods in Solving the Second-Order Delay Differential Equations

The paper presents a study on the validity of perturbation methods, suchas the method of multiple scales, the Lindstedt–Poincaré method and soon, in seeking for the periodic motions of the delayed dynamic systemsthrough an example of a Duffing oscillator with delayed velocityfeedback. An important observation in the paper is that the method ofmultiple scales, which has been widely used in nonlinear dynamics, worksonly for the approximate solutions of the first two orders, and givesrise to a paradox for the third-order approximate solutions of delaydifferential equations. The same problem appears when theLindstedt–Poincaré method is implemented to find the third-orderapproximation of periodic solutions for delay differential equations,though it is effective in seeking for any order approximation ofperiodic solutions for nonlinear ordinary differential equations. Apossible explanation to the paradox is given by the results obtained byusing the method of harmonic balance. The paper also indicates thatthese perturbation methods, despite of some shortcomings, are stilleffective in analyzing the dynamics of a delayed dynamic system sincethe approximate solutions of the first two orders already enable one togain an insight into the primary dynamics of the system.     

岩土类颗粒物质宏-细观力学研究进展

岩土类颗粒物质在自然界、工程建设以及日常生活中普遍存在,其运动特性的研究在力学界已经开展了几十年.在近20年开展的一系列小尺寸物理实验中,颗粒物质表现出许多新奇现象,人们从物理角度开展了系统研究,在统计力学中,颗粒固体的流体动力学等理论研究以及实验检测技术等方面都取得突破性进展,深刻地揭示了颗粒材料的物理机制,促使力学...     

温度场内尺度估算方法的研究

用三维超声风速计测量了合肥地区风速脉动和温度脉动数据, 从Kolmogorov 的4/5定律估算湍流动能耗散率\varepsilon, 从Yaglom的4/3定律估算温度方差 耗散率\varepsilon _\theta, 指出现有文献提供的公式不适合计算温度场的内 尺度. 提出了一种温度场内尺度计算公式, 式中含有温度方差耗散率\varepsilon _\theta , 得到的内尺度大小正确反映了与C_n^2 强弱的对应关系.     

基于光学和探针技术的微纳米固体实验力学研究进展

本文综述了近期微纳米固体实验力学在检测技术和设备平台方面的进展,尤其是基于光学和扫描探针平台的实验技术、方法和相关应用。探讨了不同检测技术的优势以及局限性,涉及微纳米实验力学检测中夹持、加载以及微力与微变形的检测与识别。通过相关的研究事例,介绍巧妙、创新的检测技术和系统在微纳米实验中的重要性,以及微尺度检测中所特有的检测系统与检测对象间的耦合关联等特点。     

Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales: a coupled thermo-viscoelastic example problem

A systematic approach for analyzing multiple physical processes interacting at multiple spatial and temporal scales is developed. The proposed computational framework is applied to the coupled thermo-viscoelastic composites with microscopically periodic mechanical and thermal properties. A rapidly varying spatial and temporal scales are introduced to capture the effects of spatial and temporal fluctuations induced by spatial heterogeneities at diverse time scales. The initial-boundary value problem on the macroscale is derived by using the double scale asymptotic analysis in space and time. It is shown that an extra history-dependent long-term memory term introduced by the homogenization process in space and time can be obtained by solving a first order initial value problem. This is in contrast to the long-term memory term obtained by the classical spatial homogenization, which requires solutions of the initial-boundary value problem in the unit cell domain. The validity limits of the proposed spatial–temporal homogenized solution are established. Numerical example shows a good agreement between the proposed model and the reference solution obtained by using a finite element mesh with element size comparable to that of material heterogeneity.