基于金属型碳纳米管在电场中变形的柱壳理论

提出了关于金属型碳纳米管在电场中变形的柱壳理论．借助于半球模型,得到了金属型碳纳米管在电场中的电荷与电场分布的解析解．将带电碳原子所受的电场力看作是碳纳米管的内力,根据柱壳理论碳纳米管在电场中的变形被解析地给出．结果表明:碳纳米管的长径比对碳纳米管在电场中的变形有重大影响,长径比越大,碳纳米管的变形越明显;碳纳米管的径向变形沿轴向是不均匀的,最大的径向变形出现于碳纳米管的端部;更为有意义的是,即使外加电场不够大,对于长径比很大的碳纳米管仍然可以表现出明显的变形．     

Numerical Studies of the Influence of the Porosity on Macroscopic Elastic Properties of Carbon/Carbon Composites

Material parameter identification of the carbon/carbon composites was provided using numerical implementation of semi-analytical methods and FE-calculations. The distribution of the fibers and pores obtained from microstructural studies is used as input for homogenization schemes for the determination of the effective elastic constants. The predictions are compared to experimental results. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multifractal Parametrization of the Structure of Deformed Carbon Fibers

Deformed carbon fibers are investigated, and their failure model is proposed based on the Sierpinski set and the hypothesis of two — brittle and viscous — fracture modes, whose existence is confirmed by examples of a correlation between the mechanical strength and elastic modulus of the fibers. For the first time, a multifractal diagram is obtained, which allows one to justify the classification of carbon fibers into brittle and inelastic ones.     

Nonlinear vibrations of embedded multi-walled carbon nanotubes using a variational approach

The present work deals with the problem of the nonlinear vibrations of multi-walled carbon nanotubes embedded in an elastic medium. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals interlayer force. The variational iteration method (VIM) is adopted to obtain the amplitude–frequency curves for large-amplitude vibrations of single-, double- and triple-walled carbon nanotubes. The influences of changes in material constants of the surrounding elastic medium and the geometric parameters on the vibration characteristics of multi-walled carbon nanotubes are investigated. The results from the VIM solution are compared and shown to be in excellent agreement with the available solutions from the open literature. The capability of the present analytical technique is clarified in terms of numerical accuracy as well as computational efficiency.     

考虑非局部剪切效应的碳纳米管弯曲特性研究

基于Hamilton(哈密顿)变分原理和非局部连续介质弹性理论,建立了新型非局部Timoshenko(铁木辛柯)梁模型（ANT）,推导了碳纳米管（CNT）的ANT弯曲平衡方程以及两端简支梁、悬臂梁和简支 固定梁的边界条件表达式,分析了剪切变形效应和非局部微观尺度效应对碳纳米管弯曲特性的影响.数值计算结果显示,碳纳米管的弯曲刚度随着小尺度效应的增强而升高.其次,这种小尺度效应对自由端受集中力的悬臂梁碳纳米管有明显作用,其刚度变化规律和其它约束条件的碳纳米管一样,这一点是ANT模型区别于普通非局部纳米梁模型的主要特点.经分子动力学模拟验证,ANT模型是合理分析碳纳米管力学特性的有效方法.     

Buckling Analysis of Carbon Nanotubes

In this work, an atomistic-continuum model is applied to single-walled carbon nanotubes. The constitutive behaviour is described by the interatomic Tersoff-Brenner potential. The coupling between atomistic deformation and the deformation of the continuum is done by an expanded Cauchy-Born rule. With the help of this model, the buckling behaviour of carbon nanotubes under different loading conditions is studied. Numerical simulation results are given for two different types of loading (axial compression, torsion). (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bounds for the Elastic Properties of Pyrolytic Carbon

The elastic properties of heterogeneous materials without defects depend on both the constitutive properties of the constituents and the microstructural characteristics. In this paper the first-order bounds of aggregates of domains with hexagonal material symmetry are determined in terms of tensorial texture coefficients. The predictive capability of these bounds is compared to higher-order bounds for pyrolytic carbon. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlocal elasticity effect on column buckling of multiwalled carbon nanotubes under temperature field

Based on nonlocal 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. The present model treats each of the nested tubes as an individual column interacting with adjacent nanotubes through the intertube van der Waals forces. The thermal effect is incorporated in the formulation. In particular, an explicit expression is derived for the critical axial strain of a double-walled carbon nanotube which clearly demonstrates that small scale effects contribute significantly to the thermo-mechanical behavior of multiwalled carbon nanotubes and cannot be ignored.     

Dynamical behaviors of fluid-conveyed multi-walled carbon nanotubes

Based on an elastic beam model and potential flow theory, and by adopting N-mode Galerkin discretization technique, the dynamical stability behaviors of fluid-conveyed multi-walled carbon nanotubes (MWCNTs) are studied. The influences of the flow inside the innermost tube and the van der Waals (vdW) interaction between any two walls on the instabilities of the CNTs-fluid system are discussed on the numerical simulations in detail. Also, the effects of the innermost tube radius, the length and the layer quantity of MWCNTs on the critical velocities of the destabilized system are intensively analyzed and compared. The results show that the critical velocities increase sharply as the radius becomes larger, the layer quantity increases, and the length decreases. The bifurcations happen in turn of divergence and Hopf types.     

Stability of the physicomechanical properties of carbon filaments (fibers)

The relationship between the tensile strength and cross-sectional area of high-modulus carbon fibers is examined. An equation is given for the strength of these promising fillers of composite materials; it is shown that the stability of their tensile strength is determined by the average defectiveness of the surface and degree and stretch, as well as variations in these quantities over any particular group of fibers. The elastic modulus and strength of the carbon fibers are related to the degree of stretch.     

Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory

The nonlinear free vibration of double-walled carbon nanotubes based on the nonlocal elasticity theory is studied in this paper. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the von Kármán type geometric nonlinearity and the nonlinear van der Waals forces. The surrounding elastic medium is formulated as the Winkler model. The harmonic balance method and Davidon–Fletcher–Powell method are utilized for the analysis and simulation of the nonlinear vibration. The simulation results show that the nonlocal parameter, aspect ratio and surrounding elastic medium play more important roles in the nonlinear noncoaxial vibration than those in the coaxial vibration of the double-walled carbon nanotubes. The noncoaxial vibration amplitudes of only considering nonlinear van der Waals forces are larger than those of considering both geometric nonlinearity and nonlinear van der Waals forces.     

Properties of a composite prepared using a concentrate of carbon nanotubes in polyethylene

Results of an investigation into the properties of polyethylene (PE) with small, no more than 5 wt.%, additions of multiwall carbon nanotubes (CNTs) are reported. Specimens of the composite were prepared using a concentrate containing 31.6 wt.% of nanotubes in the polyethylene matrix. The concentrate was fabricated by a patent in situ polymerization method. Experimental data on the influence of CNT additions on the thermograms of differential scanning calorimetry, the crystallinity of the polyethylene matrix, and the indices of mechanical properties (yield stress, strength, elastic modulus, ultimate elongation, and long-term creep) of PE/CNT composite are obtained. A theoretical analysis of elastic properties of the PE/CNT composite was carried out by using the Mori–Tanaka theory of an equivalent medium. The calculation results are compared with experimental data.     

Approximate solutions to the nonlinear vibrations of multiwalled carbon nanotubes using Adomian decomposition method

This paper applies the Adomian decomposition method (ADM) to the search for the approximate solutions to the problem of the nonlinear vibrations of multiwalled carbon nanotubes embedded in an elastic medium. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals inter layer forces. The amplitude–frequency curves for large-amplitude vibrations of single-walled, double-walled and triple-walled carbon nanotubes are obtained. The influence of changes in material constants of the surrounding elastic medium and the effect of changes in nanotube geometrical parameters on the vibration characteristics are studied by comparing the results with those from the open literature. This method needs less work in comparison with the traditional methods and decreases considerable volume of calculation, and it’s powerful mathematical tool for solving wide class of nonlinear differential equations. Special attention is given to prove the convergence of the method. Some examples are given to illustrate the determination approximate solutions of the proposed problem.     

Effective Models for Excitons in Carbon Nanotubes

We analyse the low lying spectrum of a model of excitons in carbon nanotubes. Consider two particles with opposite charges and a Coulomb self-interaction, placed on an infinitely long cylinder. If the cylinder radius becomes small, the low lying spectrum of their relative motion is well described by a one-dimensional effective Hamiltonian which is exactly solvable. Submitted: February 2, 2006; Accepted: March 24, 2006     

基于能量模型的多壁碳纳米管多边形化的致因分析

建立以横截面为研究对象的多壁碳纳米管能量模型,通过计算碳纳米管中原子之间的势能,分析影响碳纳米管多边形化的因素.本文通过分析与对比双壁和三壁碳纳米管总能量中影响因素的一系列数据,得出其横截面多边形化的影响因素有横截面的半径、管壁的个数以及范德华力等.     

Tensile and tribological properties of a short-carbon-fiber-reinforced peek composite doped with carbon nanotubes

The main objective of this paper is to develop a high-wear-resistant short-carbon-fiber-reinforced polyetheretherketone (PEEK) composite by introducing additional multiwall carbon nanotubes (MWCNTs) into it. The compounds were mixed in a Haake batch mixer and fabricated into sheets by compression molding. Samples with different aspect ratios and concentrations of fillers were tested for wear resistance. The worn surfaces of the samples were examined by using a scanning electron microscope (SEM), and the photomicrographs revealed a higher wear resistance of the samples containing the additional carbon nanotubes. Also, a better interfacial adhesion between the short carbon fibers and vinyl ester in the composite was observed.     

The effect of carbon fibers and carbon nanotubes on the mechanical properties of polyimide composites

In this experimental work, the influence of carbon fibers (CFs) added to polyimide (PI) composite plastics was investigated. Also, the effect of carbon nanotubes (CNTs) on the fiber-matrix interface was studied. The results obtained show that the mechanical properties of CF/CNT/PI nanocomposites are superior to those of CF/PI composites.     

在受轴向周期扰动作用下双壁碳纳米管动力屈曲的研究

对双壁碳纳米管受轴向周期扰动的动力响应进行了研究．采用连续体模型研究双壁碳纳米管的动力屈曲问题,考虑了壁间van der Waals力和周围弹性介质对轴向动力屈曲的影响．给出了受轴向周期扰动的屈曲模型及临界应变和临界频率．发现双壁碳纳米管由于壁间van der Waals力的作用较单壁碳纳米管具有较低的临界应变．van der Waals力和周围弹性介质将影响双壁碳纳米管不稳定区,van der Waals力使受轴向周期性扰动的双壁碳纳米管的临界频率增大,周围弹性介质对双壁碳纳米管的临界频率影响不大．     

Investigation of Multi Wall Carbon Nanotubes and Nanotube assemblies by a molecular mechanics approach

The present work describes the modeling techniques applied for the investigation of assemblies of Carbon Nanotubes (CNTs) and Multi Wall Carbon Nanotubes (MWNTs). Motivated from possible future applications, for instance in new composite materials, the investigations of the interaction behavior of individual Carbon Nanotubes within an assembly of Carbon Nanotubes is mandatory in order to understand the behavior of larger scale structures made from CNTs, e.g. Carbon Nanotube fibers. The present research applies the Lennard-Jones potential for modeling the van-der-Waals interaction occurring between the nanotubes realizing the interaction behavior. The individual Carbon Nanotubes within the assembly are assumed to be rigid. All van-der-Waals bonds are taken into account in order to calculate an overall potential surface describing the behavior of the investigated structure. An example consisting of a Multi Wall Carbon Nanotube made of three armchair Single Wall Carbon Nanotubes (SWNTs) is investigated (with and without additional outer force) with respect to equilibrium positions of the structure. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)