CHARACTERISTIC DIMENSIONLESS NUMBERS IN MULTl-SCALE AND RATE-DEPENDENT PROCESSES

Multi-scale modeling of materials properties and chemical processes has drawn great attention from science and engineering. For these multi-scale and rate-dependent processes, how to characterize their trans-scale for-mulation is a key point. Three questions should be addressed:How do multi-sizes affect the problems?How are length scales coupled with time scales?How to identify emergence of new structure in process and its effect?For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transforma-tions should form a unified set that be solved simultaneously.As a case study of coupling length and time scales, the trans-scale formulation of wave-induced damage evolution due to mesoscopic nucleation and growth is discussed. In this problem, the trans-scaling could be reduced to two inde-pendent dimensionless numbers: the imposed Deborah number De=(ac)/(LV) and the intrinsic Deborah num-ber D = (nNc5)/V* ,where a. L, c, V and nN are wave speed, sample size, micr     

CHARACTERISTIC DIMENSIONLESS NUMBERS IN MULTI—SCALE AND RATE—DEPENDENT PROCESSES

Multi-scale modeling of materials properties and chemical processes has drawn great attention from science and engineering. For these multi-scale and rate-dependent processes, how to characterize their trans-scale formulation is a key point. Three questions should be addressed:*How do multi-sizes affect the problems? *How are length scales coupled with time scales?*How to identify emergence of new structure in process and its effect? For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transformations should form a unified set that be solved simultaneously. As a case study of coupling length and time scales, the trans-scale formulation of wave-induced damage evolution due to mesoscopic nucleation and growth is discussed. In this problem, the trans-scalina could be reduced to two independent dimensionless numbers:the imposed Deborah number De*(ac)^*/(LV^*) and the intrinsic Deborah number D^*=(nN^*C^*5)/V^*,where a,L,c^*,V^* and nN^* are wave speed, sample size, microcrack size, the rate of micro-crack growth and the rate of microcrack nucleation density, respectively. Clearly, the dimensionless number De^*(ac^*)/(LV^*) includes length and time scales on both meso- and macro- levels and governs the proqressive process.Whereas, the intrinsic Deborah number D^* indicates the characteristic transition of microdamage to macroscopic rupture since D“ is related to the criterion of damage localization, which is a precursor of macroscopic rupture. This case study may highlight the scaling in multi-scale and rate-dependent problems.Then, more generally, we compare some historical examples to see how trans-scale formulations were achieved and what are still open now. The comparison of various mechanisms governing the enhancement of meso-size effects reminds us of the importance of analyzing multi-scale and rate-dependent processes case by case. For multi-scale and rate-dependent processes with chemical reactions and diffusions, there seems to be a need of trans-scale formulation of coupling effect of multi-scales and corresponding rates. Perhaps, two trans-scale effects may need special attention. One is to clarify what dimensionless group is a proper trans-scale formulation in coupled multiscale and rate-dependent processes with reactions and diffusion. The second is the effect of emergent structures and its lenath scale effect.     

CELL AND MOLECULAR BIOMECHANICS: PERSPECTIVES AND CHALLENGES

As an intriguing interdisciplinary research field,cell and molecular biomechanics is at the cutting edge of mechanics in general and biomechanics in particular.It has the potential to provide a quantitative understanding of how forces and deformation at tissue,cellular and molecular levels affect human health and disease.In this article,we review the recent advances in cell and molecular biomechanics,examine the available computational and experimental tools,and discuss important issues including protein deformation in mechanotransduction,cell deformation and constitutive behavior,cell adhesion and migration,and the associated models and theories.The opportunities and challenges in cell and molecular biomechanics are also discussed.We hope to provide readers a clear picture of the current status of this field,and to stimulate a broader interest in the applied mechanics community.     

Clifford algebra,theory of its function and their applicaton to mechanics

As is Wellknown in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems.One of the causes is that there has been a complete theory about the complex Junction and the analytic junction, hut in space problems, the case is quite different.We have no effective method to deal with these problems.In this paper, we first introduces general theories of Clifford algebra.Then we emphatically explain Clifford algebra in three dimensions and establish theories of regular Junction in three dimensions analogically to analytic function in plane.Thus we extend some results of plane problem-la three dimensions or high dimensions.Obviously, it is very important for elastic and fluid mechanics.But because Clifford algebra is not a commutative algebra, we can’t simply extend the results of two dimensions to high dimensions.The left problems are yet to be found out.     

Elastodynamic analysis of anisotropic liquid-saturated porous medium due to mechanical sources

Elastodynamic analysis of an anisotropic liquid-saturated porous medium is made to study a deformation problem of a transversely isotropic liquid-saturated porous medium due to mechanical sources.Certain physical problems are of the nature,in which the deformation takes place only in one direction,e.g.,the problem relating to deformed structures and columns.In soil mechanics,an assumption of only vertical subsidence is often invoked and this leads to the one dimensional model of poroelasticity.By consid- ering a model of one-dimensional deformation of the anisotropic liquid-saturated porous medium,variations in disturbances are observed with reference to time and distance. The distributions of displacements and stresses are affected due to the anisotropy of the medium,and also due to the type of sources causing the disturbances.     

CLIFFORD ALGEBRA,THEORY OF ITS FUNCTION AND THEIR APPLICATION TO MECHANICS

As is well-known in both elastic mechanics and fluid mechanics.the plane problems aremore convenienl,than space problems.One of the canses is that there has been a completetheory about the complex finction and the analytic function,but in space problems.the caseis quite different We have no effective method to deal with these problems In this paper.wefirst introduces gencral theories of Clifford algebra.Then we emphatically explain Cliffordalgebra in three dimensions and establish theories of regular function in three dimensionsanalogically to analytic function in plane Thus we extend some results of plane problem-tothree dimensions or high dimensions.Obviously.it is very important for clastic and fluidmechanics.But because Clifford algebra is not a comnutative algebra.we can’t simplyextend the results of two dimensions to high dimensions.The left problems are yet to befound out.     

PERSPECTIVES IN MECHANICS OF HETEROGENEOUS SOLIDS

The Microand Nano-mechanics Working Group of the Chinese Society of Theoretical and Applied Mechanics organized a forum to discuss the perspectives,trends,and directions in mechanics of heterogeneous materials in January 2010.The international journal,Acta Mechanica Solida Sinica,is devoted to all fields of solid mechanics and relevant disciplines in science,technology,and engineering,with a balanced coverage on analytical,experimental,numerical and applied investigations.On the occasion of the 30 th anniversary of Acta Mechanica Solida Sinica,its editor-in-chief,Professor Q.S.Zheng invited some of the forum participants to review the state-of-the-art of mechanics of heterogeneous solids,with a particular emphasis on the recent research development results of Chinese scientists.Their reviews are organized into five research areas as reported in different sections of this paper.§I firstly brings in focus on microand nano-mechanics,with regards to several selective topics,including multiscale coupled models and computational methods,nanocrystal superlattices,surface effects,micromechanical damage mechanics,and microstructural evolution of metals and shape memory alloys.§II shows discussions on multifield coupled mechanical phenomena,e.g.,multi-fields actuations of liquid crystal polymer networks,mechanical behavior of materials under radiations,and micromechanics of heterogeneous materials.In §III,we mainly address the multiscale mechanics of biological nanocomposites,biological adhesive surface mechanics,wetting and dewetting phenomena on microstructured solid surfaces.The phononic crystals and manipulation of elastic waves were elaborated in §IV.Finally,we conclude with a series of perspectives on solid mechanics.This review will set a primary goal of future science research and engineering application on solid mechanics with the effort of social and economic development.     

Nanoscale finite element models for vibrations of single-walled carbon nanotubes: atomistic versus continuum

By the atomistic and continuum finite element models, the free vibration behavior of single-walled carbon nanotubes （SWCNTs） is studied. In the atomistic finite element model, the bonds and atoms are modeled by the beam and point mass elements, respectively. The molecular mechanics is linked to structural mechanics to determine the elastic properties of the mentioned beam elements. In the continuum finite element approach, by neglecting the discrete nature of the atomic structure of the nanotubes, they are modeled with shell elements. By both models, the natural frequencies of SWCNTs are computed, and the effects of the geometrical parameters, the atomic structure, and the boundary conditions are investigated. The accuracy of the utilized methods is verified in comparison with molecular dynamic simulations. The molecular structural model leads to more reliable results, especially for lower aspect ratios. The present analysis provides valuable information about application of continuum models in the investigation of the mechanical behaviors of nanotubes.     

A FRACTURE-ENERGY-BASED ELASTO-SOFTENING-PLASTIC CONSTITUTIVE MODEL FOR JOINTS OF GEOMATERIALS

On the basis of plasticity and fracture mechanics for quasi-brittle materials , this article presented a constitutive model for gradual softening behavior of joints of geomateri-als . Corresponding numerical tests are carried out at the local level. Characteristics of the model proposed are 1) plastic softening and dilatancy behavior are directly related to the fracture process of joint, and much less material and model parameters are required compared with those proposed by references ; 2) the process of decohesion coupled with friction-al sliding at both micro-scale and macro-scale is described.     

Fracture mechanics analysis on Smart-Cut technology. Part 1： Effects of stiffening wafer and defect interaction

In the present paper, continuum fracture mechanics is used to analyze the Smart-Cut process, a recently established ion cut technology which enables highly efficient fabrication of various silicon-on-insulator （SOI） wafers of high uniformity in thickness. Using integral transform and Cauchy singular integral equation methods, the mode-I and mode-II stress intensity factors, energy release rate, and crack opening displacements are derived in order to examine several important fracture mechanisms involved in the Smart-Cut process. The effects of defect interaction and stiffening wafer on defect growth are investigated. The numerical results indi- cate that a stiffener/handle wafer can effectively prevent the donor wafer from blistering and exfoliation, but it slows down the defect growth by decreasing the magnitudes of SIF＇s. Defect interaction also plays an important role in the splitting process of SOI wafers, but its contribution depends strongly on the size, interval and internal pressure of defects. Finally, an analytical formula is derived to estimate the implantation dose required for splitting a SOI wafer.     

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.     

大飞机研制中的若干复合材料力学问题

简要介绍了先进复合材料在当代大型飞机结构中的应用状况,以及相关的力学问题,着重论述了复合材料及结构的工艺力学、跨尺度材料/结构一体化设计问题和力学性能表征、高效复合材料结构设计和力学分析、复合材料损伤容限与耐久性设计、大型飞机的安全监测和管理系统等. 指出,从目前国际上以及我国复合材料在大型飞机结构上的应用趋势来看,我们需要进一步发挥广大力学工作者与相关领域科研人员和工程师的协同作用,提高我国复合材料基础研究和应用水平,使复合材料在提升我国研制的大飞机的先进性和竞争力方面发挥重要的作用.     

On the contact width in generalized plain strain JKR model for isotropic solids

Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the contact width is assumed to be asymmetric with respect to the structure. Solutions to the asymmetric model are obtained and the effect of the asymmetric contact width on the whole pulling process is mainly discussed. It is found that the smaller the absolute value of Dundurs＇ parameter 13 or the larger the pulling angle O, the more reasonable the symmetric model would be to approximate the asymmetric one.     

Explicit solution of the radial breathing mode frequency of single-walled carbon nanotubes

On the basis of a molecular mechanics model, an analytical solution of the radial breathing mode (RBM) frequency of single-walled carbon nanotubes (SWCNTs) is obtained. The effects of tube chirality and tube diameter on the RBM frequency are investigated and good agreement between the present results and existing data is found. The present analytical formula indicates that the chirality and size dependent elastic properties are responsible for the effects of the chirality and small size on the RBM frequency of an SWCNT. The project supported by the National Natural Science Foundation of China (10402019), Shanghai Rising-Star Program (05QMX1421), Shanghai Leading Academic Discipline Project (Y0103), and Key Project of Shanghai Committee of Science and Technology (04JC14034).     

A note on the numerical simulations of flow past a wavy square-section cylinder

The flow past a square-section cylinder with a geometric disturbance is investigated by numerical simulations. The extra terms, due to the introduction of mapping transformation simulating the effect of disturbance into the transformed Navier-Stokes equations, are correctly derived, and the incorrect ones in the previous literature are pointed out and analyzed. Furthermore, the relationship between the vorticity, especially on the cylinder surface, and the disturbance is derived and explained theoretically. The computations are performed at two Reynolds numbers of 100 and 180 and three amplitudes of waviness of 0.006, 0.025 and 0.167 with another aim to explore the effects of different Reynolds numbers and disturbance on the vortex dynamics in the wake and forces on the body. Numerical results have shown that, at the mild waviness of 0.025, the Kairmain vortex shedding is suppressed completely for Re = 100, while the forced vortex dislocation is appeared in the near wake at the Reynolds number of 180. The drag reduction is up to 21.6% at Re = 100 and 25.7% at Re = 180 for the high waviness of 0.167 compared with the non-wavy cylinder. The lift and the Strouhal number varied with different Reynolds numbers and the wave steepness are also obtained.     

Spallation analysis with a closed trans-scale formulation of damage evolution

A closed, trans-scale formulation of damage evolution based on the statistical microdamage mechanics is summarized in this paper. The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage. The spallation in an aluminium plate is studied with this formulation. It is found that the damage evolution is governed by several dimensionless parameters, i.e., imposed Deborah numbersDe ^* andDe, Mach numberM and damage numberS. In particular, the most critical mode of the macroscopic damage evolution, i.e., the damage localization, is determined by Deborah numberDe ^*. Deborah numberDe ^* reflects the coupling and competition between the macroscopic loading and the microdamage growth. Therefore, our results reveal the multi-scale nature of spallation. In fact, the damage localization results from the nonlinearity of the microdamage growth. In addition, the dependence of the damage rate on imposed Deborah numbersDe ^* andDe, Mach numberM and damage numberS is discussed. The project supported by the National Natural Science Foundation of China (10172084, 10232040, 10232050, 10372012, 10302029) and the Special Funds for Major State Research Project (G200077305)     

应用CBR确定面心立方金属的表面弹性参量

首先从能量变分出发基于同时考虑应变梯度效应和表面效应的跨尺度力学理论, 推导出表面能和表面弹性本构等基本关系, 然后基于简单的准连续Cauchy-Born法则(CBR)建立一种确定表面能密度以及表面弹性参量的方法.进一步以面心立方(face-centre-cubic,FCC)金属为例, 系统地获得了常用FCC金属表面弹性参量的数值, 结果与他人应用分子动力学计算得到的结果相吻合.     

Rayleigh-Marangoni-Benard instability in two-layer fluid system

Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied numerically. The convective instabilities in the system of Silicon Oil (10cSt) and Fluorinert (FC70) liquids have been analyzed. The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0. Numerical results show that the instability of the two-layer system depends strongly on its depth ratio. When the depth ratio increases, the instability mode changes from mechanical coupling to thermal coupling. Between these two typical coupling modes, a time-dependent oscillation is detected. Nevertheless, traveling wave states are found in the case of oscillatory instability. The oscillation mode results from the competition between Rayleigh instability and Marangoni effect. The project supported by the National Natural Science Foundation of China (10372105) and the Knowledge Innovation Program of Chinese Academy of Sciences (KJCX2-SW-L05)     

延性金属层裂模型比较

在平面一维弹塑性流动有限差分计算程序中加入4种延性金属层裂模型,对平板撞击层裂实验进行数值模拟。结果表明：简单最大拉伸应力模型和简单损伤累积模型能定性反映层裂的物理现象,由于忽略损伤对本构的影响,计算结果和实验有偏差,但模型要求参数较少,对于一些精度要求不是很高的工程问题,可以采用;从材料损伤断裂物理本质出发,采用微损伤统计方法得到的NAG模型和封加波损伤度函数模型,能很好地再现实测的自由面速度剖面,数值计算结果与实验吻合很好。