Effects of structural defects on the compressive buckling of boron nitride nanotubes

In this paper, we examined the buckling of perfect and defective armchair boron nitride nanotubes with three types of vacancy defects, i.e. B- and N- single vacancy defects and B–N- double vacancy defect, using molecular dynamics simulations. To this end, all systems were modeled with a Tersoff-type potential, which is able to accurately describe covalent bonding of BN systems. We applied external uniaxial compressive forces to the nanotubes in vacuum and derived the critical buckling loads and strains, at room temperature in an NVT-ensemble. Our results showed significant differences between the critical buckling strengths of pristine and defective nanotubes. The resistance to axial buckling decreased with the introduction of one vacancy defect, and the B–N- double vacancy was the most seriously damaged structure, followed by B-vacancy and N-vacancy defects. Furthermore, the B-vacancy was shown to have the most significant effect on the decrease of the critical buckling strain. This can be attributed to the excessive asymmetries and perturbations induced in the structure of the nanotube and the local deformations around the defective site around the B-vacancy, even before loading. Moreover, results show that reduction in the buckling strength of the nanotube due to the presence of more than one B-vacancy defect depends on their distribution. If the two or three defects are close to each other, they act as a single point of weakness and the critical buckling load is only slightly reduced (similar to the existence of only one vacancy defect). However, if the defects are at more distant points, the critical buckling load may experience a higher decrease. Results show that vacancy defects play a critical role in the compressive buckling performance of boron nitride nanotubes and special attention must be paid to the presence of structural defects when designing members against buckling, especially for micro- and nano-electro-mechanical systems. On the other hand, defect engineering is a great means for tailoring the buckling strength of boron nitride nanotubes, in cases where the nanotube is expected to absorb energy through compressive buckling deformation and is not designed against, but for buckling.     

Transitional failure of hybrid carbon nanotubes under multiaxial loads

Transitional failure envelopes of hybrid single-walled carbon nanotubes functionalized by functional groups and filled with butane molecules under combined tension–torsion are predicted using classical molecular dynamics simulations. The observations reveal that while the tensile failure load decreases with combined torsion, the torsional buckling moment increases with combined tension. As a result, the failure envelopes under combined tension–torsion are definitely different from those under pure tension or torsion. In such combined loading, there is a multitude of failure modes (tensile failure and torsional buckling), and the failure therefore exhibits the feature of transitional failure envelopes. In addition, the functionalization by functional groups decreases both tensile failure load and torsional buckling moment, while filling with butane molecules increases only the torsional buckling moment. Consequently, the transitional failure envelopes of functionalized and filled nanotubes are absolutely different relative to what is predicted for pristine nanotubes.     

单壁碳纳米管非线性力学行为的数值模拟

单壁碳纳米管的力学行为是纳米复合材料和纳米器械的基本问题之一.使用有限元方法系统地研究了单壁碳纳米管的轴压和纯弯变形，并将有限元模拟结果和分子动力学模拟结果进行了比较.研究结果表明单壁碳纳米管的轴压屈曲载荷受直径变化的影响；单壁碳纳米管在弯曲载荷作用下的屈曲和后屈曲行为强烈地依赖于管长和管径的变化，合理地选择碳纳米管的弹性模量和壁厚，有限元方法能够很好地解释碳纳米管的屈曲机理.研究大尺度的纳米力学问题时，有限元方法将会成为更加准确、快捷的数值模拟方法.     

单壁碳纳米管非线性力学行为的数值模拟

单壁碳纳米管的力学行为是纳米复合材料和纳米器械的基本问题之一.使用有限元方法系统地研究了单壁碳纳米管的轴压和纯弯变形,并将有限元模拟结果和分子动力学模拟结果进行了比较.研究结果表明单壁碳纳米管的轴压屈曲载荷受直径变化的影响;单壁碳纳米管在弯曲载荷作用下的屈曲和后屈曲行为强烈地依赖于管长和管径的变化,合理地选择碳纳米管的弹性模量和壁厚,有限元方法能够很好地解释碳纳米管的屈曲机理.研究大尺度的纳米力学问题时,有限元方法将会成为更加准确、快捷的数值模拟方法. 关键词： 单壁碳纳米管 非线性力学行为 有限元     

轴压和扭转复合载荷作用下氮化硼纳米管屈曲行为的分子动力学模拟

采用分子动力学方法模拟了氮化硼纳米管在轴压和扭转复合荷载作用下的屈曲和后屈曲行为.在各加载比例下,给出了初始线性变形阶段和后屈曲阶段原子间相互作用力的变化,确定了屈曲临界荷载关系.通过对屈曲模态的细致研究,从微观变形机理上分析了纳米管对不同外荷载力学响应的差异.研究结果表明,扶手型和锯齿型纳米管均呈现出非线性的屈曲临界荷载关系,复合加载下的屈曲行为具有强烈的尺寸依赖性.温度升高将导致屈曲临界荷载的下降,且温度的影响随加载比例的变化而变化.无论在简单加载或复合加载中,同尺寸的碳纳米管均比氮化硼纳米管具有更强地抵抗屈曲荷载的能力.     

Assessment of Timoshenko Beam Models for Vibrational Behavior of Single-Walled Carbon Nanotubes Using Molecular Dynamics

In this paper, we study the flexural vibration behavior of single-walled carbon nanotubes (SWCNTs) for the assessment of Timoshenko beam models. Extensive molecular dynamics (MD) simulations based on second-generation reactive empirical bond-order (REBO) potential and Timoshenko beam modeling are performed to determine the vibration frequencies for SWCNTs with various length-to-diameter ratios, boundary conditions, chiral angles and initial strain. The effectiveness of the local and nonlocal Timoshenko beam models in the vibration analysis is assessed using the vibration frequencies of MD simulations as the benchmark. It is shown herein that the Timoshenko beam models with properly chosen parameters are applicable for the vibration analysis of SWCNTs. The simulation results show that the fundamental frequencies are independent of the chiral angles, but the chirality has an appreciable effect on higher vibration frequencies. The SWCNTs is very sensitive to the initial strain even if the strain is extremely small.     

Torsional buckling behavior of boron-nitride nanotubes using molecular dynamics simulations

Based on molecular dynamics simulations, the mechanical properties and buckling behavior of boron-nitride nanotubes under the action of torsional load are investigated. According to the results, the torsional properties of a boron-nitride nanotube are higher than those of its carbon counterpart. The effect of geometrical parameters on these parameters is also investigated. It is observed that by increasing the radius of nanotubes of the same length, unlike the critical shear strain, the critical torque considerably increases. The effect of chirality is also found to be negligible in the cases of critical shear strain and buckling mode, unlike the critical torque.     

轴向冲击载荷作用下双壁碳纳米管的动力屈曲

应用改进的有限元方法,建立考虑层间范德华力作用的壳-弹簧非线性有限元模型,基于B-R运动准则,系统地研究了双壁碳纳米管的动力屈曲问题,得到了轴向冲击载荷作用下双壁碳纳米管的临界动力屈曲载荷和临界动力失效载荷. 研究结果表明,在动力屈曲过程中,双壁碳纳米管层间距的变化非常小,各管的变形相互协调;碳纳米管中应力波的传播导致碳纳米管出现非对称屈曲模态,可明显观测到四个环向波瓣,沿着碳纳米管的轴线方向,四个波瓣的波峰和波谷交替变化. 对碳纳米管动力屈曲问题的研究表明,冲击载荷的大小和持续时间对碳纳米管的动力屈曲有 关键词： 碳纳米管 动力屈曲 冲击载荷     

Nonlocal shear deformable shell model for thermal postbuckling of axially compressed double-walled carbon nanotubes

An investigation is reported of the thermal buckling and postbuckling of axially compressed double-walled carbon nanotubes (CNTs) subjected to a uniform temperature rise. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell, which contains small-scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. Temperature-dependent material properties, which come from molecular dynamics (MD) simulations, and an initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. The small-scale parameter, e ₀ a, is estimated by matching the buckling temperature of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The numerical illustrations concern the thermal postbuckling response of perfect and imperfect, single- and double-walled CNTs with different values of compressive load ratio. The results show that buckling temperature and postbuckling behavior of nanotubes are very sensitive to the small-scale parameter. The results reveal that temperature-dependent material properties have a significant effect on the thermal postbuckling behavior of both single- and double-walled CNTs.     

单、双原子空位缺陷对扶手椅型单层碳纳米管屈曲性能的不同影响

采用分子动力学方法,对完善和含缺陷扶手椅型单层碳纳米管进行轴向压缩的数值模拟,对比研究三种不同的温度环境下单、双原子空位缺陷对碳纳米管轴压变形性能的特殊影响.研究结果表明管壁缺陷显著降低了纳米管低温时的承载能力,由于单原子空位缺陷造成的特殊应力集中效应会引发纳米管过早发生局部屈曲,单原子缺陷管的屈曲强度反而小于双原子管的屈曲强度. 关键词： 分子动力学 碳纳米管 屈曲 缺陷     

Influence of temperature change on column buckling of multiwalled carbon nanotubes

Based on theory of thermal elasticity mechanics, an elastic multiple column model is developed for column buckling of MWNTs with large aspect ratios under axial compression coupling with temperature change. In this model, each of the nested concentric tubes is regarded as an individual column and the deflection of all the columns is coupled together through the van der Waals interactions between adjacent tubes. The thermal effect is incorporated in the formulation. Following this model, an explicit expression is derived for the critical buckling strain for a double-walled carbon nanotube. The influence of temperature change on the buckling strain is investigated. It is concluded that the effect of temperature change on the buckling strain is dependent on the temperature changes, the aspect ratios, and the buckling modes of carbon nanotubes.     

Methane in carbon nanotube: molecular dynamics simulation

The behaviour of methane molecules inside carbon nanotubes at room temperature is studied using classical molecular dynamics simulations. A methane molecule is represented either by a shapeless super-atom or by a rigid set of five interaction centres localized on atoms. Different loadings of methane molecules ranging from the dense gas density to the liquid density, and the influence of flexibility of the CNT on structural and dynamic properties of confined molecules are considered. The simulation results show the decreases of the diffusion coefficient of methane molecules with density. At higher densities diffusion coefficient values are almost independent of molecular shape, but at low densities one observes faster motion of the super-atom molecule than that for the tetrahedral model of the molecule. For loadings of methane considered here the nanotube flexibility, introduced by the reactive empirical bond order (REBO) potential for interactions between carbon atoms of nanotube, does not have an effect on diffusivity of methane molecules, and its impact on the molecular structure is weak. It is found that methane molecules in the vicinity of the nanotube wall show tripod orientation with respect to the nanotube surface.     

A novel method for studying the buckling of nanotubes considering geometrical imperfections

Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.     

Numerical distortion and effects of thermostat in molecular dynamics simulations of single-walled carbon nanotubes

In this paper, single-walled carbon nanotubes （SWCNTs） are studied through molecular dynamics （MD） simulation. The simulations are performed at temperatures of 1 and 300K separately, with atomic interactions characterized by the second Reactive Empirical Bond Order （REBO） potential, and temperature controlled by a certain thermostat, i.e. by separately using the velocity scaling, the Berendsen scheme, the Nose-Hoover scheme, and the generalized Langevin scheme. Results for a （5,5） SWCNT with a length of 24.5 nm show apparent distortions in nanotube configuration, which can further enter into periodic vibrations, except in simulations using the generalized Langevin thermostat, which is ascribed to periodic boundary conditions used in simulation. The periodic boundary conditions may implicitly be applied in the form of an inconsistent constraint along the axis of the nanotube. The combination of the inconsistent constraint with the cumulative errors in calculation causes the distortions of nanotubes. When the generalized Langevin thermostat is applied, inconsistently distributed errors are dispersed by the random forces, and so the distortions and vibrations disappear. This speculation is confirmed by simulation in the case without periodic boundary conditions, where no apparent distortion and vibration occur. It is also revealed that numerically induced distortions and vibrations occur only in simulation of nanotubes with a small diameter and a large length-to-diameter ratio. When MD simulation is applied to a system with a particular geometry, attention should be paid to avoiding the numerical distortion and the result infidelity.     

Coarse nonlinear dynamics and metastability of filling-emptying transitions: water in carbon nanotubes

Using a coarse-grained molecular dynamics (CMD) approach we study the apparent nonlinear dynamics of water molecules filling or emptying carbon nanotubes as a function of system parameters. Different levels of the pore hydrophobicity give rise to tubes that are empty, water-filled, or fluctuate between these two long-lived metastable states. The corresponding coarse-grained free-energy surfaces and their hysteretic parameter dependence are explored by linking MD to continuum fixed point and bifurcation algorithms. The results are validated through equilibrium MD simulations.     

多壁碳纳米管弯曲导致的扭转

文章介绍了多壁碳纳米管弯曲的分子动力学模拟,从原子尺度上解释了由于屈曲失稳而导致的起皱现象,并发现多壁碳纳米管弯曲时会呈现出非线性的力学响应。同时,在模拟过程中,观察到了弯曲诱发扭转的现象,并揭示出扭转变形的内在起因是曲率诱导的晶格错配。     

Electromechanical buckling analysis of boron nitride nanotube using molecular dynamic simulation

In this paper, the effect of electric field on axial buckling of boron nitride nanotubes is investigated. For this purpose, molecular dynamics simulation and continuum mechanics are used for the first time simultaneously. In molecular dynamics simulation, the potential between boron nitride atoms is considered as Tersoff and Timoshenko beam theory is used in continuum mechanics. In this paper, buckling of zigzag and armchair boron nitride nanotubes are investigated. Here, the effects of the electric field and the length of the boron nitride nanotube on the critical load are investigated and it is shown that the effect of the electric field is different with respect to the arrangement of atoms in the boron nitride nanotubes. In fact, the electric field creates axial and torsional loads on the zigzag and armchair nanotube, respectively. Axial buckling of the zigzag nanotube is dependent on the electric field, whereas in the armchair nanotubes, the electric field changes have no effect on the axial buckling. To better understand the impact of the electric field on axial buckling, these results are compared with the continuum mechanics.     

碳纳米管中点缺陷对热导率影响的正交试验模拟分析

在碳纳米管的制备过程中, 各种点缺陷不可避免地存在于其晶格结构中, 对于碳管的热输运性质造成不可忽视的影响. 使用非平衡分子动力学方法, 选用反应经验键序势能, 模拟计算含有缺陷的碳纳米管的热导率. 尝试采用正交试验方法设计算例, 不但减少了计算量, 并且利于分析缺陷类型、 管长和管径三种结构因素对缺陷造成的热导率下降影响的主次和趋势. 重点研究了掺杂、 吸附和空位三类点缺陷的影响, 与无缺陷完整碳纳米管进行比较, 开展缺陷效应分析, 并进一步考察了环境温度等因素的影响. 模拟结果表明, 相对完整无缺陷碳管, 含有点缺陷的碳管热导率显着下降; 在有缺陷存在的情况下, 缺陷的类型对碳管热导率的影响最大, 管径次之, 管长影响相对最小; 缺陷类型对热导率影响力从大到小依次为: 空位 > 掺杂 > 吸附; 不同环境温度下, 点缺陷对碳管热导率的影响不尽相同.     

The thermal effect on vibration and instability of carbon nanotubes conveying fluid

Based on the theory of thermal elasticity mechanics, an elastic Bernoulli–Euler beam model is developed for vibration and instability analysis of fluid-conveying single-walled carbon nanotubes (SWNTs) considering the thermal effect. Results are demonstrated for the dependence of natural frequencies on the flow velocity as well as temperature change. The influence of temperature change on the critical flow velocity at which buckling instability occurs is investigated. It is concluded that the effect of temperature change on the instability of SWNTs conveying fluid is significant.     

Uniaxial deformation of nanotwinned nanotubes in body-centered cubic tungsten

We perform large-scale molecular dynamics simulations to delve into tensile and compressive loading of nanotubes containing {112} nanoscale twins in body-centered cubic tungsten, as a function of wall thickness, twin boundary spacing, and strain rate. Solid nanopillars without the interior hollow and/or nanotubes without the nanoscale twins are also investigated as references. Our findings demonstrate that both stress-strain response and deformation behavior of nanotwinned nanotubes and nanopillars exhibit a strong tension-compression asymmetry. The yielding of the nanotwinned nanotubes with thick walls is governed by dislocation nucleation from the twin boundary/surface intersections. With a small wall thickness, however, the failure of the nanotwinned nanotubes is dominated by crack formation and buckling under tensile and compressive loading, respectively. In addition, the strain rate effect, which is more pronounced in compressive loading than in tensile loading, increases with a decreasing twin boundary spacing.