范德华力对多壁纳米碳管力学性质的影响

用分子动力学方法模拟了多壁纳米碳管在压缩、弯曲变形下力与变形的关系．通过与组成多壁碳管的各单壁碳管的比较分析,揭示了多壁纳米碳管层间范德华力对碳管力学性质的影响．采用Tersoff-Brenner势描述每一单壁纳米碳管内原子间作用,采用Lennard-Jones势描述碳管壁间范德华力．计算结果表明：多壁纳米碳管的比强度明显高于单壁纳米碳管．纳米碳管的半径虽然对杨氏模量影响不大,但对纳米碳管的曲屈行为影响却相当显著。     

考虑范德华力曲率效应的双壁碳纳米管外压屈曲

针对双壁碳纳米管外压屈曲问题，研究了层间范德华力的曲率效应对临界外压的影响。应用弹性双层圆柱壳模型，考虑层间范德华力不仅与层间距有关而且与挠度曲率的变化有关，导出了外压屈曲临界压力解析公式。计算得出在不同半径、不同长细比下，外压屈曲临界压力的数值结果，并与经典壳的结果和忽略范德华力曲率效应的结果做了比较。结果显示，对于小半径的双壁碳纳米管曲率效应对外压屈曲有效明显的影响。     

单壁碳纳米管的扭转力学特性研究

利用基于高阶Cauchy-Born准则所建立的单壁碳纳米管本构模型,针对不同手性的单壁碳纳米管的扭转力学特性进行了研究.研究发现结构呈现对称性的锯齿型和扶手型单壁碳纳米管具有完全对称的扭转特性,而结构不对称的手性型单壁碳纳米管具有正反相异的扭转特性.同时,针对一系列手性不同的单壁碳纳米管的扭转力学特性展开了详细的研究.研究的部分结果与采用其他方法得到的结果进行了对比,证实了所提出方法以及预测结果的有效性和可行性.     

金属-碳管复合结构的计算力学研究

系统地研究了金属-碳纳米管复合结构的力学行为,考察了单轴压缩载荷作用下填充管的临界屈曲应变对管内金属原子数目的依赖性,分析了管的几何特征,包括管径、管长及手性,对填充管变形与力学行为的影响,并与连续体力学模型的预测进+行了对比分析.本文的研究结果对金属-碳管复合结构的理论研究和工程应用都具有较好的指导意义.     

冲击扭矩作用下碳纳米管动力屈曲的研究

为了研究碳纳米管在冲击扭矩作用下的动力屈曲,采用了连续模型将碳纳米管模拟成半无限长的弹性连续圆柱壳。将冲击扭矩作用下碳纳米管的动力屈曲问题归结为由于扭转应力波传播导致的分叉问题,此分叉问题被化为一个非线性方程组的求解。最后进行了数值分析,讨论了碳纳米管的不同参数对动力屈曲的影响,发现碳纳米管有极强的抗冲击性,临界屈曲剪应力可高达几百吉帕。     

碳纳米管的等价柔性节点空间框架模型

小变形情况下,碳纳米管C-C共价键间的相互作用可以用基于分子力学的宏观力学模型进行模拟.其中,基于分子结构力学的等价结构力学模型是最为有效的碳纳米管弹性参数的预测模型.现有的碳纳米管的等价结构力学模型是用具有刚性节点的空间框架结构模拟碳纳米管的原子晶格受力和变形的关系.根据碳纳米管的原子晶格的变形特点,本文首次提出了一个用柔性节点空间框架模拟碳纳米管原子晶格键角变化的分析模型,再通过应变能等价推导了柔性节点的等价抗弯刚度与分子力学中力常数的关系,从而给出了一个更精确的计算碳纳米管等价弹性参数的分子结构力学模型.文中用ANSYS计算了不同尺寸的锯齿型(zigzag)和扶手型(armchair)单壁碳纳米管的轴向杨氏模量、泊松比、剪切模量及径向杨氏模量,分析了碳纳米管的尺寸效应,并且与其它各种模型所得结果进行了比较.计算结果表明,本文所给碳纳米管的等价柔性节点空间框架模型不仅计算简单、高效,而且准确;并可以直接推广到多壁碳纳米管等价弹性模量的计算及碳纳米管的稳定和动力分析.     

基于高阶Cauchy-Born准则的单壁碳纳米管本构模型

提出了一种基于高阶Cauchy—Born准则建立单壁碳纳米管本构模型的方法。通过引入高阶变形梯度,合理地修正了传统Cauchy—Born准则在描述纳米管变形几何关系时所存在的缺陷。利用原子间相互作用势以及能量等效原理,得到了基于广义连续介质模型的单壁碳纳米管的本构关系。由此得到的本构参数不仅与变形梯度张量F,而且与其梯度F相关,因此是一种广义连续介质模型。利用这样的本构模型,本文还对单壁碳纳米管的杨氏模量进行了预测,并与采用其他方法得到的结果进行了对比,从而证实了所提出方法的有效性。     

碳纳米管应变传感器的性能分析：实验偏振模式的影响机制

碳纳米管作为一种拉曼力学传感介质具有优异的力学性质及共振、偏振拉曼特性。将碳纳米管散布在基体材料中,即可实现局部应力/应变的测量。受到光学衍射极限的限制,常规的远场拉曼光谱得到的是一定区域内众多碳管的平均散射信息。本文综合考虑了采样点内各方向碳管的影响,并对碳管散射的共振状态、碳管的分布状态、拉曼系统的偏振构型及偏振方向等实验因素对碳纳米管应变传感器性能的影响进行了深入分析,采用分峰和重构的方法定量地给出了不同实验模式下采样点内的拉曼信息组成以及各种实验模式的测量精度。分析和对比表明,采用双偏振构型且偏振方向沿荷载施加方向时的测量精度最高,即最优的实验模式。     

轴向随动分布载荷作用下FGMs Timoshenko梁的后屈曲特性

研究了Timoshenko功能梯度材料梁在随动分布载荷作用下的后屈曲问题。在考虑轴线伸长和一阶横向剪切变形基础上,建立了在轴向分布随动载荷作用下一端简支一端固定Timoshenko功能梯度梁的过屈曲控制方程。其中假设功能梯度材料性质只沿厚度方向变化,并以成分含量的幂指数函数形式变化。采用打靶法求解了所得线性常微分两点边值问题,获得了随动载荷作用下Timoshenko功能梯度梁的过屈曲平衡路径和平衡构形。对比了Timoshenko梁和Euler梁的后屈曲行为,并分析了材料的体积分数指数和长细比对梁屈曲行为的影响。结果表明:考虑剪切变形的Timoshenko梁的后屈曲行为与Euler梁的后屈曲行为明显不同;体积分数指数一定时,随着长细比的增加,梁的临界载荷减小;长细比一定时,随着体积分数指数的增加,梁的临界载荷也减小。     

超音速气流中受热壁板的稳定性分析

采用Galerkin方法建立二维壁板的非线性气动弹性运动方程，用一阶活塞理论模拟壁板 受到的气动力. 基于李雅普诺夫间接法分析了平壁板的稳定性，得到了壁板失稳的边界 曲线；采用牛顿迭代法分析了壁板的屈曲变形，进而分析了后屈曲状态下壁板的稳定性； 在时域中分析了后屈曲状态下壁板的颤振边界. 分析结果表明，为了保证计算精度， 在二维壁板的静态失稳及过屈曲变形分析中，至少要取二阶谐波模态；在平壁板的超音速颤 振(动态失稳)边界分析中至少应取四阶模态. 还对壁板的温升，壁板长厚比、壁板密 度和气流马赫数作了无量纲变参分析，研究了这些参数的变化对壁板稳定性的影响规律. 研 究中发现，当气流速压较低时壁板一般会稳定在低阶谐波模态的屈曲变形位置，但是如果系 统出现多个渐近稳定的不动点，即使作用在壁板上的气流速压很低，壁板也有可能在较低速 压下发生二次失稳型颤振.     

An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes

An analytical molecular structural mechanics model for the prediction of mechanical properties of defect-free carbon nanotubes is developed by incorporating the modified Morse potential with an analytical molecular structural model. The developed model is capable of predicting Young’s moduli, Poisson’s ratios and stress–strain relationships of carbon nanotubes under tension and torsion loading conditions. Results on the mechanical properties of single-walled carbon nanotubes show that Young’s moduli of carbon nanotubes are sensitive to the tube diameter and the helicity. Young’s moduli of both armchair and zigzag carbon nanotubes increase monotonically and approach Young’s modulus of graphite when the tube diameter is increased. The nonlinear stress–strain relationships for defect-free nanotubes have been predicted, which gives a good approximation on the ultimate strength and strain to failure of nanotubes. Armchair nanotubes exhibit higher tensile strength than zigzag nanotubes but their torsion strengths are identical based on the present study. The present theoretical investigation provides a very simple approach to predict the mechanical properties of carbon nanotubes.     

Parametric variational principle and quadratic programming method for van der Waals force simulation of parallel and cross nanotubes

A parametric variational principle for van der Waals force simulation between any two adjacent nonbonded atoms and the corresponding improved quadratic programming method for numerical simulation of mechanical behaviors of carbon nanotubes are developed. Carbon nanotubes are modeled and computed based on molecular structural mechanics model. van der Waals force is simulated by the network of bars (called bar network) with a special nonlinear mechanical constitutive law (called generalized parametric constitutive law) in the finite element analysis. Compared with conventional numerical methods, the proposed method does not depend on displacement and stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem. Thus, the model and method developed present very good convergence behavior in computation and provide accurate predictions of the mechanical behaviors and displacement distributions in the nanotubes. Numerical results demonstrate the validity and the efficiency of the proposed method.     

Multiscale computations for carbon nanotubes based on a hybrid QM/QC (quantum mechanical and quasicontinuum) approach

An effective multiscale computing scheme based on QM/QC (quantum mechanics/quasicontinuum) is applied for simulation of Carbon nanotubes (CNTS) mechanics. First, quasicontinuum simulation of deformations of curved crystalline structures is conducted to examine the fully nonlocal behavior of CNTs with the aid of high-order interpolation functions and the “cluster” concept, which facilitates accurate energy approximation for crystals. Next, a multiscale computing approach based on QM/QC hybridization is devised, and applied for simulation of CNT mechanics. The bonding configuration changes, e.g. bond breaking or creation, near defect sites are correctly represented with the QM/QC hybrid model. For studying electronic properties coupled with the mechanical deformation of CNTs, the change of the electrical properties from an initial semiconductor into metal under mechanical bending is investigated. Single-walled CNTs having various types of defects and subjected to uniaxial tension are considered for fracture. The theoretical strength of the CNTs in the presence of each defect is computed based on the QM/QC hybrid scheme, wherein the defect neighborhood is modeled as a QM zone for a first-principle-based calculation using density functional theory (DFT), and the remaining area as a QC zone. This multiscale computing approach greatly improves the accuracy in the prediction of the failure strains of CNTs over a purely molecular mechanical or quasicontinuum method.     

单壁碳纳米管屈曲的原子/连续介质混合模型

用数学和力学研究所，上海 200072)//力学学报.--2004,36(6).--744～748 提供了一种运用原子/连续介质混合(hybrid atomic/continuum,HAC)方法解决纳米力学问题的思路. 通过在连续介质力学模型中引入利用分子力学方法获得物性参数，建立了预测单壁碳纳米管临界屈曲参数的HAC模型. 结果表明, HAC模型具有与连续介质力学模型可比拟的简洁性, 同时可表征纳米管微观结构特征对屈曲参数的影响. 计算结果表明，Zigzag纳米管的抗屈曲性能优于Armchair纳米管. 基于Tersoff-Brenner作用势的分子动力学结果证实了这一结论.     

碳纳米管的力学

在发现碳纳米管后不久,对于这些有趣结构的力学性质--包括高强度、高硬度、低密度和结构的完美性的理论预测,使人们认识到它们可能具有理想的科技应用价值.对这些预测的实验验证或个别验伪以及大量基于不同模型的计算机模拟方法,使得逾10年来对碳纳米管力学的理解日趋深入但远未达到尽头.本文回顾了理论预测,并对这种微小结构的观察和操作中经常用到的富有挑战性的实验技术进行了讨论.略述了采用的计算方法包括从头算法量子力学模拟、经典分子动力学和连续介质模型.多尺度和多物理模型的发展和模拟工具自然而然作为连接基础科学问题和工程应用的结果而出现,而这个主题仍然正在抓紧研究中.这里介绍了研究此主题的一些方法.注意力主要集中于研究力学性质的揭示方面,如杨氏模量、弯曲刚度、屈曲准则、拉伸和压缩强度.最后,讨论了利用这些性质的几个令人兴奋的应用例子,包括纳米绳束、填充的纳米管、纳米机电系统、纳米传感器和纳米管增强复合材料,引用了349篇参考文献. 图41参349     

NUMERICAL STUDY ON CUT-AND-CONNECT OF TWO VORTEX RINGS ALONG PARALLEL AXES

A numerical study has been conducted to investigate the interaction of two viscous vortex rings along parallel axes. The generation of two vortex rings created by the ejection of a fluid through orifices and their cut-and-connect process were numerically simulated by solving the three-dimensional and time-dependent Navier-Stokes equations. Based on the quantitative velocity and pressure data obtained from the Navier-Stokes simulation, the distribution and the evolution of the vorticity, helicity density and energy dissipation function were analyzed. The helicity density and its relation with the energy dissipation function in three-dimensional flow fields were also examined. It was found that the energy dissipation plays an important role in the cancellation of the vortex circulation during the vortex tubes cutting. This energy dissipation process may be used to explain the cut-and-connect of vortex tubes in the high Reynolds number turbulent flow. The numerical solutions were compared with the experimental observations and measurements under the similar condition. The correspondence between the numerical simulation and the experimental measurement was satisfactory.     

A structural mechanics approach for the analysis of carbon nanotubes

This paper presents a structural mechanics approach to modeling the deformation of carbon nanotubes. Fundamental to the proposed concept is the notion that a carbon nanotube is a geometrical frame-like structure and the primary bonds between two nearest-neighboring atoms act like load-bearing beam members, whereas an individual atom acts as the joint of the related load-bearing beam members. By establishing a linkage between structural mechanics and molecular mechanics, the sectional property parameters of these beam members are obtained. The accuracy and stability of the present method is verified by its application to graphite. Computations of the elastic deformation of single-walled carbon nanotubes reveal that the Young’s moduli of carbon nanotubes vary with the tube diameter and are affected by their helicity. With increasing tube diameter, the Young’s moduli of both armchair and zigzag carbon nanotubes increase monotonically and approach the Young’s modulus of graphite. These findings are in good agreement with the existing theoretical and experimental results.     

碳纳米管的力学性能及碳纳米管复合材料研究

对碳纳米管力学行为和碳纳米管复合材料的研究文献进行了综述.首先介绍了碳纳米管结构稳定性和力学性能的研究进展,包括理论模拟和实验的研究结果.结果表明,碳纳米管有着优异的力学性能,其在复合材料应用方面有着巨大的潜力.然后,系统地总结了碳纳米管在增强高分子材料、金属材料和陶瓷材料方面的应用,指出外场力传递效应是值得关注的课题.最后,对该领域工作做了一些讨论和展望.      

Computer simulation of mechanical properties of carbon nanostructures

The aim of the present paper is the theoretical investigation of the mechanical properties of carbon nanostructures of graphene and single-wall carbon nanotubes by using nanoscopic and macroscopic approaches. The nanoobject structures in free and deformed states were considered and the corresponding energies were computed in the framework of quantum mechanics methods by using the original software package of semi-empirical programsNDDO/sp-spd (developed in the Institute of Applied Mechanics, Russian Academy of Sciences) in parallel computations. The nanostructural deformations were prescribed in the approximation of the mechano-chemical deformation coordinate. The deformation forces were described by the energy gradients in selected coordinates of microscopic deformations. The mechanical characteristics of nanoobjects such as Young’s modulus, rigidity coefficients, works done in deformation, critical stresses, and relative elongations in fracture were calculated in the framework of the macroscopic linear theory of elasticity; the deformation forces determined by quantum mechanical calculations were used in the corresponding relations. It was found that the mechanical characteristics of single-wall carbon nanotubes (CNT) depend on their diameter and chirality, and the deformation properties of a graphene sheet are asymmetric with respect to two normal extension modes directed along the “zigzag” and “armchair” on the sheet edges. The calculated mechanical characteristics are in good agreement with the experimental data known fromthe literature, in both the values and the deformation asymmetrywith respect to different deformation modes.