On the buckling behavior of connected carbon nanotubes with parallel longitudinal axes

The application of hetero-junction carbon nanotubes (CNTs) is increasing continuously due to their outstanding properties in nano-mechanical systems. Several investigations have been conducted to study the behavior of CNTs. In this paper, straight hetero-junctions and their constituent CNTs (armchair and zigzag) were simulated by a commercial finite element package. Then, the buckling behavior of CNTs was evaluated by comparing the critical buckling load of each straight hetero-junction and its constituent CNTs. Both obtained, i.e. analytical calculations and computational, results were compared. The investigations showed that, first, the behavior of homogeneous CNTs under cantilevered boundary conditions follows the assumption of the classical Euler equation. Second, the analytical solutions are in good agreement with the finite element simulation results. In addition, it was shown that the first critical buckling load of hetero-junctions lies within the value of the fundamental homogeneous CNT range. It was also concluded that the buckling load of straight hetero-junctions and their fundamental CNTs increases by increasing the chiral number of both armchair and zigzag CNTs. The current study provides a better insight towards the prediction of straight hetero-junction CNTs behavior.     

Structure of connections of single-walled carbon nanotubes with the use of the combined 5–7 and 4–8 topological defects

The structures of zigzag-zigzag, armchair-zigzag, zigzag-chiral, armchair-armchair, armchair-chiral, and chiral-chiral pair connections produced by single-walled carbon nanotubes 1.5–5.0 diameter with the use of the combined 5–7 and 4–8 topological defects have been calculated by molecular mechanics methods. It has been established that the use of the combined 5–7 topological defect makes it possible to produce connections between pairs of single-walled carbon nanotubes with any conductivities, chiralities, and diameters, whereas the use of the combined 4–8 topological defect provides a means for forming connections between nanotubes only with the same type of conductivity. The angles between the axes of nanotubes connected by the combined 5–7 and 4–8 topological defects lie in the ranges 145°–180° and 112°–178°, respectively. It has been revealed that there are correlations between structural parameters of the connections and the relative arrangement of the simple topological defects in the combined topological defects.     

Combined torsional buckling of double-walled carbon nanotubes with axial load in the multi-field coupled condition

The present study has theoretically investigated the combined torsional buckling of double-walled carbon nanotubes (DWCNTs) with axial load in the multi-field coupled condition. The effects of torsion, axial load, thermal-electrical change, surrounding elastic medium and the Van der Waals forces are all taken into consideration. The governing equation of buckling for CNTs subjected to thermo-electro-mechanical loadings has been established based on an elastic shell model of continuum mechanics. Reasonable s...     

Buckling analysis of carbon nanotube bundles under axial compressive,bending and torsional loadings via a structural mechanics model

A structural mechanics model is employed for the investigation of the buckling behavior of carbon nanotube bundles of three single-walled carbon nanotubes (SWCNTs) under axial compressive, bending and torsional loadings. The effects of van der Waals (vdW) forces are further modeled using a nonlinear spring element.The effects of different types of boundary conditions are studied for nanotubes with various aspect ratios. The results reveal that bundles comprising longer SWCNTs exhibit lower critical buckling load. Moreover, for the fixed-free boundary condition the rate of critical buckling load reduction is highest, while the lowest critical buckling load occurs. Simulations show good agreement between our model and molecular dynamics results.     

Molecular dynamics study of the torsional vibration characteristics of boron-nitride nanotubes

In recent years, synthesizing inorganic nanostructures such as boron nitride nanotubes (BNNTs) has led to extensive studies on their exceptional properties. In this study, the torsional vibration behavior of boron-nitride nanotubes (BNNTs) is explored on the basis of molecular dynamics (MD) simulation. The results show that the torsional frequency is sensitive to geometrical parameters such as length and boundary conditions. The axial vibration is found to be induced by torsional vibration of nanotubes which can cause instability in the nanostructure. It is also observed that the torsional frequency of BNNTs is higher than that of their carbon counterpart. Moreover, the shear modulus is predicted by incorporating MD simulation numerical results into torsional vibration frequency obtained through continuum-based model of tubes. Finally, it is seen that the torsional frequency of double-walled boron-nitride nanotubes (DWBNNTs) is between the frequencies of their constituent inner and outer tubes.     

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.     

Consideration of mechanical properties of single-walled carbon nanotubes under various loading conditions

In this article, mechanical properties of single-walled carbon nanotubes (SWCNTs) with various radiuses under tensile, compressive and lateral loads are considered. Stress–strain curve, elastic modulus, tensile, compressive and rotational stiffness, buckling behaviour, and critical axial compressive load and pressure of eight different zigzag and armchair SWCNTs are investigated to figure out the effect of radius and chirality on mechanical properties of nanotubes. Using molecular dynamic simulation (MDS) method, it can be explained that SWCNTs have higher Young’s modulus and tensile stiffness than compressive elastic modulus and compressive stiffness. Critical axial force of zigzag SWCNT is independent from the radius, but that of armchair type rises by increasing of radius, also these two types show different buckling modes.     

Molecular dynamic investigation of mechanical properties of armchair and zigzag double-walled carbon nanotubes under various loading conditions

Using molecular dynamic simulation (MDS), effects of chirality and Van der Waals interaction on Young's modulus, elastic compressive modulus, bending, tensile, and compressive stiffness, and critical axial force of double-walled carbon nanotube (DWCNT) and its inner and outer tubes are considered. Achieving the highest safety factor, mechanical properties have been investigated under applied load on both inner and outer tubes simultaneously and on each one of them separately. Results indicate that as a compressive element, DWCNT is more beneficial than single-walled carbon nanotube (SWCNT) since it carries two times higher compression before buckling. Except critical axial pressure and tensile stiffness, in other parameters zigzag DWCNT shows higher amounts than armchair type. Outer tube has lower strength than inner tube; therefore, most reliable design of nanostructures can be attained if the mechanical properties of outer tube taken as the properties of DWCNT.     

(n,n)-(2n, 0)碳纳米管异质结的扭转力学特性

相近直径的锯齿型和扶手椅型碳纳米管可以共轴组合形成5-7碳环交替出现的柱形对称异质结. 本文利用分子动力学方法研究了直径相近且等长锯齿型和扶手椅型碳纳米管形成的(n, n)-(2n, 0)结在扭转过程中的扭矩和轴向应力随扭转角度的变化规律以及应力传递过程. 研究发现, (n, n)-(2n, 0)结扭转应变在达弹性限度内不会产生轴向应力, 该效应对基于碳纳米管扭转特性的纳米振荡器件的设计具有重要意义.     

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.     

单壁碳纳米管轴向压缩变形的研究

采用Tersoff-Brenner势函数描述碳纳米管中碳原子间的相互作用，通过分子动力学方法对不同螺旋型的单壁碳纳米管的轴向压缩变形行为进行了研究.研究发现单臂碳纳米管的杨氏模量低于锯齿形碳纳米管，根据微观结构特征的差异对这一结果进行了分析.同时从能量和结构变化两方面对碳纳米管受压失稳进行了分析，揭示出碳纳米管失稳的微观特征. 关键词： 纳米管 分子动力学 杨氏模量 屈曲     

Radial buckling of multi-walled carbon nanotubes under hydrostatic pressure

Radial buckling stresses of carbon nanotubes (CNTs) need to be studied in high-pressure resonance Raman scattering spectrum. In this work, the closed-form expression of the critical buckling stress of multi-walled carbon nanotubes (MWCNTs) under hydrostatic pressure is derived that can be conveniently employed. Using the derived formulae, the critical buckling stresses of single-walled carbon nanotubes and double-walled carbon nanotubes with different diameters are calculated. The results are in good agreement with other reported literatures. In addition, the critical buckling stresses of each layer of a quintuple-walled CNT in different buckling modes are predicted, showing that the buckling instability can occur not only in the outermost rolled layer, but also in other rolled layer of MWCNTs by considering different diameters and buckling modes.     

Analysis of Single-Walled Carbon Nanotubes Using a Chemical Bond Element Model

提出了一种纳米尺度的有限元方法,碳纳米管中的碳-碳化学键被模拟为键单元．按照平衡关系,根据有限元理论,作用于每个碳原子上的作用力可以写成键单元的刚度矩阵与每个碳原子位移的乘积．在分子力学的基本假设下,键单元刚度矩阵的每个元素可以写为分子力学中力场常数的函数,这样建立起了宏观力学方法(有限元)与纳米尺度力学方法(分子力学)之间的联系．应用该方法模拟了扶椅型与锯齿型单壁碳纳米管的力学行为从而验证了该方法的有效性．分析结果说明单壁碳纳米管的弹性模量与管厚度的选取直接相关．此外,弹性模量对所选取的分子力学中的力场常数非常敏感,管的弹性模量显示出对半径的尺度依赖性,但是管长度对弹性模量的影响小到可以被忽略．     

Nonlinear Deformation Processes and Damage Modes of Super Carbon Nanotubes with Armchair-Armchair Topology

The tensile deformations and fractures of super carbon nanotubes （SCNTs） with armchair-armchair topology are investigated by using the atomic-scale finite element method. SCNTs generated from carbon nanotubes （CNTs） with different characteristic aspect ratios are found to have different nonlinear behaviours under uniaxial tensions. Specifically, an SCNT wi~h higher aspect ratio has three distinct stages： rotation, stretch and rupture, while an SCNT with lower aspect ratio has only two stages. This information may compensate for previous work and enrich our knowledge about Y-branched CNTs and SCNTs.     

Nonlinear structural mechanics based modeling of carbon nanotube deformation

A nonlinear structural mechanics based approach for modeling the structure and the deformation of single-wall and multiwall carbon nanotubes (CNTs) is presented. Individual tubes are modeled using shell finite elements, where a specific pairing of elastic properties and mechanical thickness of the tube wall is identified to enable successful modeling with shell theory. The effects of van der Waals forces are simulated with special interaction elements. This new CNT modeling approach is verified by comparison with molecular dynamics simulations and high-resolution micrographs available in the literature. The mechanics of wrinkling of multiwall CNTs are studied, demonstrating the role of the multiwalled shell structure and interwall van der Waals interactions in governing buckling and postbuckling behavior.     

Molecular dynamics simulation on mechanicalproperty of carbon nanotube torsional deformation

In this paper torsional deformation of the carbon nanotubes is simulated by molecular dynamics method. The Brenner potential is used to set up thesimulation system. Simulation results show that the carbon nanotubes can bear larger torsional deformation, for the armchair type (10,10) single wall carbon nanotubes, with a yielding phenomenon taking place when the torsional angle is up to 63$^{\circ}$(1.1rad). The influence of carbon nanotube helicity in torsional deformation is very small. The shear modulus of single wall carbon nanotubes should be several hundred GPa, not 1\,GPa as others reports.     

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.     

Effects of carbon nanotube structures on mechanical properties

This paper describes a structural mechanics approach to modelling the mechanical properties of carbon nanotubes (CNTs). Based on a model of truss structures linked by inter-atomic potentials, a closed-form elastic solution is obtained to predict the mechanical properties of single-walled carbon nanotubes (SWNTs). Moreover, the elastic modulus of multi-walled carbon nanotubes (MWNTs) is also predicted for a group of the above mentioned SWNTs with uniform interval spacing. Following the structural mechanics approach, the elastic modulus, Poissons ratio, and the deformation behaviors of SWNTs were investigated as a function of the nanotube size and structure. Poissons ratio of SWNTs shows a chirality dependence, while the elastic modulus is insensitive to the chirality. The disposition of the strain energy of bonds shows quite a difference between the zigzag and armchair tubes subjected to axial loading. A zigzag tube is predicted to have a lower elongation property than an armchair tube. PACS 62.20-x; 62.20.Dc; 62.25+g     

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.