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     

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.     

Mechanical properties of nickel-coated single-walled carbon nanotubes and their embedded gold matrix composites

The effects of nickel coating on the mechanical behaviors of armchair single-walled carbon nanotubes (SWCNTs) and their embedded gold matrix composites under axial tension are investigated using molecular dynamics (MD) simulation method. The results show that the Young's moduli and tensile strength of SWCNTs obviously decrease after nickel coating. For armchair SWCNTs, the decreased ratio of the Young's moduli of SWCNTs with smaller radius is larger than that of SWCNTs with larger radius. A comparison is made between the response to Young's modulus of a composite with parallel embedded nanotube and the response of a composite with vertically embedded nanotube. The results show that the uncoated SWCNT can enhance the Young's modulus of composite under the condition of parallel embedment, but such improvement disappears under the condition of vertical embedment because the interaction between SWCNT and gold matrix is too weak for effective load transfer. However, the nickel-coated SWCNT can indeed significantly improve the composite behavior.     

Molecular Dynamics Study of Effects of Si-Doping Upon Structure and Mechanical Properties of Carbon Nanotube

In this paper, a Si-doped single-walled carbon nanotube (SWCNT) (7,7) and several perfect armchair SWCNTs are investigated using the classical molecular dynamics simulations method. The inter-atomic short-range interaction is represented by empirical Tersoff bond order potential. The computational results show that the axial Young's modulus of the perfect SWCNTs are in the range of 1.099 ± 0.005 TPa, which is in good agreement with the existing experimental results. From our simulation, the Si-doping decreases the Young's modulus of SWCNT, and with the increased strain levels, the effect of Si-doped layer in enhancing the local stress level increases. The Young's modulus of armchair SWCNTs are weakly affected by tube radius.     

A computational prediction of total carbo-merization on single-walled carbon nanotubes

The total carbo-mer of single-walled carbon nanotubes (C-SWCNTs) are constructed by inserting two sp carbon atoms into each C-C bond in pristine single-walled carbon nanotubes (SWCNTs). The geometric, mechanical and electronic properties for these novel structures are investigated by self-consistent-field crystal calculations. The calculated zigzag and chiral C-SWCNTs are all small gap semiconductors, whereas the metallic property is still kept in the armchair C-SWCNT. The calculated Young's moduli of C-SWCNTs are smaller than those of SWCNTs. Our calculations show that the zigzag C-SWCNTs have higher mobility than the corresponding SWCNTs. Moreover, the calculated mobility of the C-SWCNTs has a periodic change with the change of the tube diameters.     

单壁碳纳米管弹性性质的羟基接枝效应

用分子动力学方法研究了端口接枝不同数量羟基对扶手椅型和锯齿型单壁碳纳米管弹性模量的影响.结果表明,未接枝的扶手椅型(5, 5),(10,10)管和锯齿型(9, 0),(18, 0)管杨氏模量分别为948,901和804,860GPa.在接枝2—8个羟基情况下,锯齿型单壁碳纳米管拉伸杨氏模量基本不随接枝数量增加发生变化,而扶手椅单壁碳纳米管则不同,接枝状态下的弹性模量比未接枝状态小很多,但接枝一定数量后,其杨氏模量又略增到某一稳定值.分别从接枝后碳纳米管变形电子密度等值线结构、C—C键长和系统结合能变化规律等方面,对单壁碳纳米管弹性模量的接枝效应进行了分析. 关键词： 碳纳米管 羟基 接枝效应 杨氏模量     

On the characterization of the elastic properties of asymmetric single-walled carbon nanotubes

In order to characterize asymmetric single-walled carbon nanotubes, an algorithm has been developed based on numerical simulation to relate the physical geometry to the elastic properties of asymmetric single-walled carbon nanotubes (SWCNTs). A large number of finite element results for the stiffness of asymmetric SWCNTs has been used to develop a best surface fitting function to define the relationship between the geometry of SWCNTs and their stiffness. However, since the stiffness of asymmetric nanotubes depends upon the configuration parameters, n and m, it was impossible to define any diameter dependency. Based on the maximum reaction force concept and in order to account for the hidden mechanical behavior of asymmetric SWCNTs, the chiral factor (CF) has been employed in this study. The proposed CF converts any asymmetric geometry (n and m) into a value between 0 and 1. A group of the SWCNTs with the same applied boundary condition (n+m=30) and different range of the CF was also used for studying of the shear contribution. The chiral factor dependency, which is developed in this study, is applicable for characterising and selecting asymmetric SWCNTs in the design of advanced nanomaterials. Furthermore, the equation which is calculated in this study can be useful for finding the best criteria for selecting asymmetric SWCNTs.     

Mechanics and morphology of single-walled carbon nanotubes: from graphene to the elastica

Abstract

The elastica is referred to the shape of the curve into which the centreline of a flexible lamina is bent. Hence, single-walled carbon nanotubes (SWCNTs) are treated as the elastica obtained from bending of graphene. The corresponding large deformation accompanies both the material and geometrical non-linearities. The morphology of the free-standing SWCNTs such as the natural angle of twist, bond lengths, tube radius and wall thickness are determined. Moreover, it is shown that the induced self-equilibriated strain field has a remarkable impact on the mechanical behaviour of the nanotube. Utilization of an appropriate non-linear continuum constitutive relation for graphene leads to exact formulation of the governing equations of SWCNTs. Subsequently, through perturbation analysis, the asymptotic solutions of the initial elastic fields for the SWCNTs are presented. By performing ab initio calculations, the components of the fourth and sixth-order elastic moduli tensors in the constitutive model of graphene needed in this study are computed.     

Mechanical Properties of Single-Walled （5,5） Carbon Nanotubes with Vacancy Defects

First-principles simulation is used to investigate the structural and mechanical properties of vacancy defective single-walled （5,5） carbon nanotubes. The relations of the defect concentration, distribution and characteristic of defects to Young＇s modulus of nanotubes are quantitatively studied. It is found that each dangling-bond structure （per supercell） decreases Young＇s modulus of nanotube by 6.1% for symmetrical distribution cases. However the concentrative vacancy structure with saturated atoms has less influence on carbon nanotubes. It is suggested that the mechanical properties of carbon nanotubes depend strongly upon the structure and relative position of vacancies in a certain defect concentration.     

空位结构缺陷对C纳米管弹性性质的影响

用分子动力学方法对不同空位缺陷的扶手椅型与锯齿型单壁C纳米管杨氏弹性模量进行了计算和分析. 结果表明：扶手椅型（5, 5）, （10,10）和锯齿型（9, 0）, （18, 0） 纳米管在无缺陷时其杨氏模量分别为948,901和804,860 GPa. 随管径的增大,扶手椅型和锯齿型单壁C纳米管弹性模量分别减小和增大,表现出完全不同的变化规律. 随着C纳米管中单点空位缺陷的均匀增加,杨氏模量下降,当缺陷比率增加到一定程度时,杨氏模量下降骤然趋缓,形成一下降平台;双空位缺陷对C纳米管杨氏模量的影响与其分布方向有关;随单点空位缺陷间原子数的增加,在轴向上,杨氏模量下降到某一值小幅波动,而在周向上杨氏模量先下降,然后上升到某一稳定值. 随两单点空位缺陷的空间距离进一步增大,杨氏模量又呈微降趋势. 通过分子间σ键与π键特征及缺陷间近程电子云耦合作用规律与空位缺陷内部5-1DB缺陷的形成特点等理论对上述规律进行了分析. 关键词： 空位缺陷 C纳米管 分子动力学 杨氏模量     

Effects of temperature and vacancy defects on tensile deformation of single-walled carbon nanotubes

This study adopts the Tersoff-Brenner interaction potential function in a series of molecular dynamic (MD) simulations which investigate the mechanical properties under tensile loading of (10,0) zigzag, (8,3) chiral and (6,6) armchair single-walled carbon nanotubes (SWCNTs) of similar radii. The Young's modulus values of the (10,0), (8,3) and (6,6) nanotubes are determined to be approximately 0.92, 0.95, and 1.03 TPa, respectively. Of these nanotubes, the results reveal that the (6,6) nanotube possesses the best tensile strength and toughness properties under tension. Although it is noted that under small tensions, the mechanical properties such as Young's modulus are essentially insensitive to helicity, under larger plastic deformations, they may be influenced by helicity effects. Finally, the simulations demonstrate that the values of the majority of the considered mechanical properties decrease with increasing temperature and increasing vacancy percentage.     

Effect of ending surface on energy and Young's modulus of single-walled carbon nanotubes studied using linear scaling quantum mechanical method

By using a linear scaling self-consistent charge, density functional tight-binding (SCC-DFTB) method and an ab intio Dmol3 calculation, the energy and Young's modulus as a function of tube length for (10, 0) single-walled carbon nanotubes (SWCNTs) are investigated. It was found that with increasing the length of SWCNTs the Young's modulus increases rapidly, then, there is a slow increase, which ultimately approaches a constant value after the length is increased to ~20 nm, whereas a reversed variation tendency was found for the average energy of atoms in SWCNTs with a change of the tube length. We found that the characters of the length-dependent energy and Young's modulus stem from the changed P_y-DOS of atoms in the ending region of the tube. Here one simple formula is proposed for quantitatively explaining the length-dependent energy and modulus.     

Effects of Radius and Orientation of Single-Walled Carbon Nanotubes on Their Nonlinear Tensile Deformation Behaviour

By capturing the atomic information and reflecting the behaviour governed by a nonlinear potential function, an analytical molecular mechanics approach is applied to establish the constitutive relation for single-walled carbon nanotubes （SWCNTs）. The nonlinear tensile deformation curves of zigzag and armchair nanotubes with different radii are predicted, and the elastic properties of these SWCNTs are obtained. A conclusion is made that the nanotube radius has little effect on the mechanical behaviour of SWCNTs subject to simple tension, while the nanotube orientation has larger influence.     

结构和变形对单壁碳纳米管力学性能的影响

使用分子动力学方法模拟了单壁碳纳米管的拉伸变形行为和泊松比,并从单壁碳纳米管晶胞单元的结构特征角度,系统分析了管径、螺旋性和应变对力学性能的影响．模拟结果显示,单臂性碳纳米管(8,8)-(22,22)和锯齿性碳纳米管(9,0)-(29,0)的拉伸弹性变形可以分别达到35％-38％和20％-27％,拉伸条件下这些碳纳米管的弹性模量随管径的增大从960 GPa下降到750 GPa,并且锯齿性碳纳米管的弹性模量比单臂性碳纳米管的弹性模量要高．通过对三根具有相同直径和不同螺旋性的碳纳米管(9,9),(12,6)和(16,0)分别在拉伸和压缩条件下的模拟发现,随着变形的增大,碳纳米管的泊松比将减小;在相同的拉伸应变下,碳纳米管的泊松比随其螺旋角的减小而减小,而在相同的压缩应变下,碳纳米管的泊松比随其螺旋角的减小而增大．     

Predicting the nonlinear tensile behavior of carbon nanotubes using finite element simulation

Carbon nanotubes (CNTs) possess extremely high mechanical properties and could be the ultimate reinforcing materials for the development of nanocomposites. In this work, a Finite Element (FE) model based on the molecular mechanics theory was developed to evaluate tensile properties of single-walled carbon nanotubes (SWCNTs). The deformation and fracture of carbon nanotubes under tensile strain conditions were studied by common FE software, Ansys. In this model, individual carbon nanotube was simulated as a frame-like structure, and the primary bonds between two nearest-neighboring atoms were treated as beam elements. The beam element properties were determined via the concept of energy equivalence between molecular dynamics and structural mechanics. So far, several researches have studied the elastic behavior of CNTs, and its nonlinearity is not well understood. The novelty of the model lies on the use of nonlinear beam elements to evaluate SWNTs tensile failure. The obtained calculated mechanical properties show good agreement with existing numerical and experimental results.     

一种用于碳纳米管模拟的分子结构力学方法

提出一种基于分子力学的分子结构力学方法,该方法用分子力学中的力场势能函数表述系统的势能,从能量原理出发,在小变形假设的基础上建立系统方程．基于此方法,模拟了单壁碳纳米管的拉伸特性,得到碳纳米管弹性模量的尺度依赖性关系．在碳纳米管的弯曲分析中,将计算结果和材料力学中的理论结果进行了比较,发现随着碳纳米管半径的增大,计算结果与理论值趋于一致．     

Multiscale modeling of the effect of carbon nanotube orientation on the shear deformation properties of reinforced polymer-based composites

A combination of molecular dynamics (MD), continuum elasticity and FEM is used to predict the effect of CNT orientation on the shear modulus of SWCNT-polymer nanocomposites. We first develop a transverse-isotropic elastic model of SWCNTs based on the continuum elasticity and MD to compute the transverse-isotropic elastic constants of SWCNTs. These constants are then used in an FEM-based simulation to investigate the effect of SWCNT alignment on the shear modulus of nanocomposites. Furthermore, shear stress distributions along the nanotube axis and over its cross-sectional area are investigated to study the effect of CNT orientation on the shear load transfer.     

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     

Nonlinear finite-element modeling of graphene and single- and multi-walled carbon nanotubes under axial tension

An effective finite-element (FE) approach for modeling the structure and the deformation of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) is presented. An individual tube was modeled using a frame-like structure with beam elements. The effect of van der Waals forces, crucial in MWCNTs, was modeled by spring elements. The success of this new carbon nanotube (CNT) modeling approach was verified by comparing the simulation results for single- and multi-walled nanotubes and graphene with other experimental and computational results available in the literature. Simulations of final deformed configurations were in excellent agreement with the atomistic models for various deformations. The proposed approach successfully predicts the experimentally observed values for mechanical behavior of SWCNTs and MWCNTs. The results demonstrated that the proposed FE technique could provide a valuable tool for studying the mechanical behavior of different types of nanotubes, as well as their effectiveness as load-bearing entities in nanocomposite materials.