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.     

碳纳米管分子间联结压缩屈曲行为研究

由两个任意的碳纳米管组成的分子间联结IMJ(Intramolecular Junctions)可以应用于电子电路或电子仪器中.本文首先应用分子动力学模拟研究IMJ在大变形情况下的压缩屈曲行为.分子动力学模拟结果显示,应变率较小时,对临界压缩应变没有实质性影响;但当应变率较大时,对临界压缩应变有明显影响.这一结论为确定分...     

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.     

纳米碳管与刚性壁的正碰撞

用分子动力学方法模拟纳米碳管与刚性壁的正碰撞过程,并与弹性动力学方法的结果进行对比在分子动力学模拟中,采用Tersoff-Brenner势描述碳管的原子间相互作用,用6~12形式的Lennard-Jones势描述碳管与刚性壁间相互作用结果表明,两种方法所得到的应力波传播速度吻合较好与弹性动力学分析结果不同的是,在发生屈曲以前,纳米碳管与刚性壁的接触时间不仅与纳米碳管的长度近似成线性关系,还与管径及碰撞初速度有关.碰撞过程中,纳米碳管端部应力并非定值,但其平均值与弹性动力学计算结果相差不大.     

Ar掺杂碳纳米豆荚的压缩与拉伸力学特性

以C60富勒烯外部、C60富勒烯内部以及C60富勒烯内/外同时掺杂不同数量Ar原子的碳纳米豆荚为研究对象,采用分子动力学方法,模拟了这些碳纳米豆荚的压缩与拉伸过程,讨论了Ar掺杂形式、Ar掺杂量对纳米豆荚压缩与拉伸力学特性的影响。研究表明,Ar掺杂后,碳纳米豆荚的压缩力学特性有所改善,且Ar掺杂量多的压缩力学特性越好;C60富勒烯内部、外部同时掺杂Ar原子的纳米豆荚的承压能力最好,其次是C60富勒烯内部掺杂纳米豆荚,再次是C60富勒烯外部掺杂纳米豆荚;Ar掺杂形式、掺杂量对纳米豆荚的拉伸力学特性无显著影响。     

纳米力学的数值模拟方法

纳米力学是一支新兴学科,主要研究100nm以下尺度上物质的行为和变化规律.物质在纳米尺度上所具有的特殊效应如量子效应、微尺度效应等导致了其特异的性能和行为.人们对纳米力学行为的认识,目前主要通过试验观测和数值模拟等方法.本文概要回顾了分子动力学模拟、蒙特卡罗模拟等纳米力学计算方法的研究进展及现状,提出了以量子力学为基础、多学科交叉、多层次融合发展纳米力学研究方法的构思,并对纳米力学研究方法所面临的问题及其发展趋势做了初步展望.      

基于严格范德华力作用的多壁碳纳米管磁弹性振动

给出了一种求解在任意两管之间严格范德华力相互作用下多壁碳纳米管磁弹性振动频率的解析方法.研究结果表明,在轴向磁场的作用下,严格范德华力相互作用对多壁碳纳米管最高磁弹性振动频率的影响大于对最低振动频率的影响;严格范德华力作用下多壁碳纳米管的最高磁弹性振动频率要高于经典范德华力作用下多壁碳纳米管的最高磁弹性振动频率;严格范德华力对磁弹性振动频率的影响依赖于碳纳米管层间距的变化和管的层数,且随着多壁碳纳米管层数的增加而趋于一个稳定值.本文的研究结果对于碳纳米管作为基本元件在纳米电子元件中的实际应用具有一定的参考价值.     

碳纳米管在简单荷载作用下的变形屈曲行为研究

采用分子动力学方法研究了不同螺旋性的单壁碳纳米管在轴压、扭转和外压分别作用下的变形屈曲行为。针对每种加载形式，给出了宏观形式的内力一变形曲线来反映碳原子间相互作用力的变化与碳管变形量之间的关系。对碳管在这三种不同荷载作用下的失稳特性、微观结构和应变能的变化进行了详细的分析。结合经典弹性理论和本文的模拟结果，得出了单壁碳纳米管的等效壁厚、弹性模量和Poisson比。另外，通过对比不同螺旋性碳管的模拟结果，讨论了螺旋性对碳纳米管力学行为的影响。文中采用的势能函数为Brenner多体势。     

纳米力学进展(续)

概述2002年度在纳米力学方面的若干新进展.在纳观计算力学方面,讨论了在微结构质流演化算法、纳米结构中应变的量子效应算法、LMPM并行算法等方面的进展.在纳观实验力学范畴,着重介绍了立体刻蚀的微加载系统.然后,我们展述了在纳米晶体力学、纳米管力学和纳米压痕力学等方面的新进展.      

碳纳米管改性的双马来酰亚胺树脂力学性质的分子尺度模拟研究

双马来酰亚胺树脂是高性能碳纤维复合材料的新型基体材料,在航空航天等领域具有广泛的应用。目前,相关材料的改性技术、制备工艺以及材料性能等考察仍以实验为主,数值模型及相应的分析方法则相对较少。本文构建了4,4′—二苯甲烷双马来酰亚胺(BDM)和二烯丙基双酚A(DABPA,固化剂)的分子尺度数值模型,实现了与实验过程基本一致的交联反应过程,考察了BDM/DABPA树脂材料的力学性质以及由碳纳米管填充所引起的强化规律和机理。结果表明,树脂材料的力学性质随着交联程度的提高而增加,而短碳纳米管的掺杂也可以进一步增强力学性质。研究工作为基于双马树脂的复合材料设计构建了数值分析技术,为相关材料的性能改进从微观层次提供了有价值的参考。     

Coarse-grained potentials of single-walled carbon nanotubes

We develop the coarse-grained (CG) potentials of single-walled carbon nanotubes (SWCNTs) in CNT bundles and buckypaper for the study of the static and dynamic behaviors. The explicit expressions of the CG stretching, bending and torsion potentials for the nanotubes are obtained by the stick-spiral and the beam models, respectively. The non-bonded CG potentials between two different CG beads are derived from analytical results based on the cohesive energy between two parallel and crossing SWCNTs from the van der Waals interactions. We show that the CG model is applicable to large deformations of complex CNT systems by combining the bonded potentials with non-bonded potentials. Checking against full atom molecular dynamics calculations and our analytical results shows that the present CG potentials have high accuracy. The established CG potentials are used to study the mechanical properties of the CNT bundles and buckypaper efficiently at minor computational cost, which shows great potential for the design of micro- and nanomechanical devices and systems.     

Finite deformation continuum model for single-walled carbon nanotubes

A continuum-based model for computing strain energies and estimating Young’s modulus of single-walled carbon nanotubes (SWCNTs) is developed by using an energy equivalence-based multi-scale approach. A SWCNT is viewed as a continuum hollow cylinder formed by rolling up a flat graphite sheet that is treated as an isotropic continuum plate. Kinematic analysis is performed on the continuum level, with the Hencky (true) strain and the Cauchy (true) stress being employed to account for finite deformations. Based on the equivalence of the strain energy and the molecular potential energy, a formula for calculating Young’s modulus of SWCNTs is derived. This formula, containing both the molecular and continuum scale parameters, directly links macroscopic responses of nanotubes to their molecular structures. Sample numerical results show that the predictions by the new model compare favorably with those by several existing continuum and molecular dynamics models.     

金沙江虎跳峡河段岸坡变形破坏的相关动力因子研究

石墨层和单臂碳纳米管都是以C---C共价键结合的. 在小变形条件下C---C键的势能可用谐和函 数来描述，这与梁单元的变形能具有相同的形式，因此可以用梁单元等效C---C键的作用. 提出了一种C---C键的等效梁单元有限元模型，该模型能够完备地替代谐和势描述C---C键的 伸长、面内键角变化、离面键角变化和扭转. 通过分析石墨层的典型受载情况得到了等效梁 单元的参数，以及等效梁单元参数与谐和势参数的关系，并用该模型计算了单臂碳纳米管的 杨氏模量和泊松比，计算结果为相关文献所验证.     

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.     

Predicting the elastic properties of single-walled carbon nanotubes

Advances in the prediction of the mechanical properties of single-walled carbon nanotubes (SWNTs) are reviewed in this paper. Based on the classical Cauchy-Born rule, a new computational method for the prediction of Young's modulus of SWNTs is investigated. Compared with the existing approaches, the developed method circumvents the difficulties of high computational efforts by taking into consideration of the microstructure of nanotube and the atomic potential of hydrocarbons. Numerical results of Young's modulus and its variation with respect to the deformation gradient tensor are given and discussed. The results obtained are in good agreement with those obtained by laboratory experiments and other numerical methods.     

Thermal vibration and apparent thermal contraction of single-walled carbon nanotubes

It is of fundamental value to understand the thermo-mechanical properties of carbon nanotubes. In this paper, by using molecular dynamics simulation, a systematic numerical investigation is carried out to explore the natural thermal vibration behaviors of single-walled carbon nanotubes and their quantitative contributions to the apparent thermal contraction behaviors. It is found that the thermo-mechanical behavior of single-walled carbon nanotubes is exhibited through the competition between quasi-static thermal expansion and dynamic thermal vibration, while the vibration effect is more prominent and induces apparent contraction in both radial and axial directions. With increasing temperature, the anharmonic interatomic potential helps to increase the bond length, which leads to thermally induced expansion. On the other hand, the higher structural entropy and vibrational entropy of the system cause the carbon nanotube to vibrate, and the apparent length of nanotube decreases due to various vibration modes. Parallel analytical and finite element analyses are used to validate the vibration frequencies and provide helpful insights. The unified multi-scale study has successfully decoupled and systematically analyzed both thermal expansion and contraction behaviors of single-walled carbon nanotube from 100 to 800 K, and obtained detailed information on various vibration modes as well as their quantitative contributions to the coefficient of thermal expansion in axial and radial directions. The results of this paper may provide useful information on the thermo-mechanical integrity of single-walled carbon nanotubes, and become important in practical applications involving finite temperature.     

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 molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT’s) is established to describe the nonlinear stress-strain curve of SWCNT’s and to predict both the elastic properties and breaking strain of SWCNT’s during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT’s. The project supported by the National Natural Science Foundation of China (10121202, 90305015 and 10328203), the Key Grant Project of Chinese Ministry of Education (0306) and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7195/04E).     

Length dependence of critical measures in single-walled carbon nanotubes

This paper presents an investigation on the buckling behaviour of single-walled carbon nanotubes under various loading conditions (compression, bending and torsion) and unveils several aspects concerning the dependence of critical measures (axial strain, bending curvature and twisting angle) on the nanotube length. The buckling results are obtained by means of an atomistic-scale generalized beam theory (GBT) that incorporates local deformation of the nanotube cross-section by means of independent and orthogonal deformation modes. Moreover, some estimates are also obtained by means of non-linear shell finite element analyses using Abaqus code. After classifying the buckling modes of thin-walled tubes (global, local and distortional), the paper addresses the importance of the two-wave distortional mode (flattening or ovalization mode) in their structural behaviour. Then, the well known expression to determine the critical strain of compressed nanotubes, which is based on Donnell theory for shallow shells, is shown to be inadequate for moderately long tubes due to warping displacements appearing in the distortional buckling modes. After that, an in-depth study on the buckling behaviour of nanotubes under compression, bending and torsion is presented. The variation of the critical kinematic measures (axial strain, bending curvature and twisting angle) with the tube length is thoroughly investigated. Concerning this dependence, some uncertainties that exist in the specific literature are meticulously explained, a few useful expressions to determine critical measures of nanotubes are proposed and the results are compared with available data collected from several published works (most of them, obtained from molecular dynamics simulations).