An elastic model for bioinspired design of carbon nanotube bundles

Collagen fibers provide a good example of making strong micro-or mesoscale fibers from nanoscale tropocollagen molecules through a staggered and crosslinked organization in a bottom-up manner.Mimicking the architectural features of collagen fibers has been shown to be a promising approach to develop carbon nanotube(CNT)fibers of high performance.In the present work,an elastic model is developed to describe the load transfer and failure propagation within the bioinspired CNT bundles,and to establish the relations of the mechanical properties of the bundles with a number of geometrical and physical parameters such as the CNT aspect ratio and longitudinal gap,interface cross-link density,and the functionalizationinduced degradation in CNTs,etc.With the model,the stress distributions along the CNT-CNT interface as well as in every individual CNT are well captured,and the failure propagation along the interface and its effects on the mechanical properties of the CNT bundles are predicted.The work may provide useful guidelines for the design of novel CNT fibers in practice.     

Modulus, Fracture Strength, and Brittle vs. Plastic Response of the Outer Shell of Arc-grown Multi-walled Carbon Nanotubes

The fracture strengths and elastic moduli of arc-grown multi-walled carbon nanotubes (MWCNTs) were measured by tensile loading inside of a scanning electron microscope (SEM). Eighteen tensile tests were performed on 14 MWCNTs with three of them being tested multiple times (3×, 2×, and 2×, respectively). All the MWCNTs fractured in the “sword-in-sheath” mode. The diameters of the MWCNTs were measured in a transmission electron microscope (TEM), and the outer diameter with an assumed 0.34 nm shell thickness was used to convert measured load-displacement data to stress and strain values. An unusual yielding before fracture was observed in two tensile loading experiments. The 18 outer shell fracture strength values ranged from 10 to 66 GPa, and the 18 Young's modulus values, obtained from a linear fit of the stress–strain data, ranged from 620 to 1,200 GPa, with a mean of 940 GPa. The possible influence of stress concentration at the clamps is discussed.     

Torsional buckling of a double-walled carbon nanotube embedded in an elastic medium

The torsional buckling of a double-walled carbon nanotube embedded in an elastic medium is studied in this paper. The effects of surrounding elastic medium and van der Waals forces between the inner and outer nanotubes are taken into account. Using continuum mechanics, an elastic double-shell model is presented for the torsional buckling of a double-walled carbon nanotube. Based on the model, a condition is derived in terms of the buckling modes of the shell and the parameters describing the effect of van der Waals interaction and surrounding elastic medium. A simplified analysis is also carried out estimate the critical torque for torsional buckling of the double-walled carbon nanotube.     

Mechanical properties of single-walled carbon nanotube bundles as bulk materials

Single-walled carbon nanotubes (SWNTs) in crystalline bundles may exhibit a transition in which the cross-sections of tubes turn from perfectly circular to hexagonal, depending upon the tube diameter and externally applied pressure, and this structural instability leads to an abrupt change in the bulk elastic properties of SWNT bundles. This paper presents a hybrid atom/continuum model to study the bulk elastic properties of SWNT bundles, and the predicted characteristics of this structural instability agree well with the experimental observations available in the literature. Linearized bulk elastic properties of SWNT bundles with respect to a stable configuration are transversely isotropic and hence can be characterized by five independent elastic moduli. A complete set of these five moduli is predicted for the first time. It is found that the deformability of tube cross-sections play a dominant role in characterizing the transverse moduli.     

Investigation of stress-strain behavior of single walled carbon nanotube/rubber composites by a multi-scale finite element method

The excellent properties of carbon nanotubes have generated technological interests in the development of nanotube/rubber composites. This paper describes a finite element formulation that is appropriate for the numerical prediction of the mechanical behavior of rubber-like materials which are reinforced with single walled carbon nanotubes. The considered composite material consists of continuous aligned single walled carbon nanotubes which are uniformly distributed within the rubber material. It is assumed that the carbon nanotubes are imperfectly bonded with the matrix. Based on the micromechanical theory, the mechanical behavior of the composite may be predicted by utilizing a representative volume element. Within the representative volume element, the reinforcement is modeled according to its atomistic microstructure. Therefore, non-linear spring-based line elements are employed to simulate the discrete geometrical structure and behavior of the single-walled carbon nanotube. On the other hand, the matrix is modeled as a continuum medium by utilizing solid elements. In order to describe its behavior an appropriate constitutive material model is adopted. Finally, the interfacial region is simulated via the use of special joint elements of variable stiffness which interconnect the two materials in a discrete manner. Using the proposed multi-scale model, the stress-strain behavior for various values of reinforcement volume fraction and interfacial stiffness is extracted. The influence of the single walled carbon nanotube addition within the rubber is clearly illustrated and discussed.     

Nonlinear free vibration of nanotube with small scale effects embedded in viscous matrix

In this paper, the nonlinear free vibration of the nanotube with damping effects is studied. Based on the nonlocal elastic theory and Hamilton principle, the governing equation of the nonlinear free vibration for the nanotube is obtained. The Galerkin method is employed to reduce the nonlinear equation with the integral and partial differential characteristics into a nonlinear ordinary differential equation. Then the relation is solved by the multiple scale method and the approximate analytical solution is derived. The nonlinear vibration behaviors are discussed with the effects of damping, elastic matrix stiffness, small scales and initial displacements. From the results, it can be observed that the nonlinear vibration can be reduced by the matrix damping. The elastic matrix stiffness has significant influences on the nonlinear vibration properties. The nonlinear behaviors can be changed by the small scale effects, especially for the structure with large initial displacement.     

Elongational and shear rheology of carbon nanotube suspensions

Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids—castor oil or its blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated. The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear and elongational measurements is addressed and interpreted. The results conform to the Herschel–Bulkley rheological constitutive equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple shear flow, which suggests that the original Herschel–Bulkley model need modification with the yield stress being a function of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning of Herschel–Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes.     

Optimization design of strong and tough nacreous nanocomposites through tuning characteristic lengths

How nacreous nanocomposites with optimal combinations of stiffness, strength and toughness depend on constituent property and microstructure parameters is studied using a nonlinear shear-lag model. We show that the interfacial elasto-plasticity and the overlapping length between bricks dependent on the brick size and brick staggering mode significantly affect the nonuniformity of the shear stress, the stress-transfer efficiency and thus the failure path. There are two characteristic lengths at which the strength and toughness are optimized respectively. Simultaneous optimization of the strength and toughness is achieved by matching these lengths as close as possible in the nacreous nanocomposite with regularly staggered brick-and-mortar (BM) structure where simultaneous uniform failures of the brick and interface occur. In the randomly staggered BM structure, as the overlapping length is distributed, the nacreous nanocomposite turns the simultaneous uniform failure into progressive interface or brick failure with moderate decrease of the strength and toughness. Specifically there is a parametric range at which the strength and toughness are insensitive to the brick staggering randomness. The obtained results propose a parametric selection guideline based on the length matching for rational design of nacreous nanocomposites. Such guideline explains why nacre is strong and tough while most artificial nacreous nanocomposites aere not.     

Dynamic controller design for a class of nonlinear uncertain systems subjected to time-varying disturbance

Inheriting advantages of both proportional-integral-derivative controller and standard sliding mode control theory, a synthetic controller design for a class of nonlinear system is presented. Regarding the architecture of the developed controller, it does not include model-based nominal control term so that the method eliminates complicated processes for system parameters identification and design of extra compensators. With simple gain tuning rules, the proposed control algorithm provides global asymptotical stability and is capable of alleviating discontinuous control switching considerably. A self-sustained oscillations phenomenon caused by the proposed control configuration is also further addressed. Simulations and experiments are conducted to verify the feasibility and applicability of the proposed approach.     

高边坡结构可靠度的二次处理有限元分析

本文依据强度折减理论,利用MIDAS/GTS有限元软件,分析计算了高边坡结构的安全系数K,找到边坡滑裂带的位置。在此基础上,对有限元输入数据和输出结果进行二次处理,建立基本随机变量c,f与滑裂带中单元的最大(和最小)主应力σ1(和σ3)的拟合关系f1(和f3),将其代入高边坡结构的功能函数Z中,使Z由隐式形式变为显式。基于该显式表示的Z,利用Monte Carlo法计算滑裂带中所有失效单元的可靠指标β1,并将其单元面积A1作为权重系数,经过加权平均得到边坡结构的整体可靠指标β。上述方法使得结合有限元软件计算边坡结构的整体可靠度得以简化。经实例分析可知,本文提出的方法是合理可行的,可使边坡结构整体可靠性分析得以简化,也可为高边坡结构整体可靠性分析提供理论参考。     

The generation of nearly isotropic turbulence downstream of streamwise tube bundles

Tube bundles were used to generate a field of nearly isotropic turbulence. A wide range of geometric and aerodynamic parameters were systematically studied, with measurements being made of pressure losses, turbulence intensities, spectra. auto-correlations and length scales. Simple analyses were utilized to correlate effectively these results and to aid in their understanding. The results agree well with other (limited) results published in the literature.     

Dynamic torsional buckling of multi-walled carbon nanotubes embedded in an elastic medium

In this paper the dynamic torsional buckling of multi-walled carbon nanotubes （MWNTs） embedded in an elastic medium is studied by using a continuum mechanics model. By introducing initial imperfections for MWNTs and applying the preferred mode analytical method, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for embedded double-walled carbon nanotubes （DWNTs）. Numerical results show that, for both the DWNTs and embedded DWNTs, the buckling form shifts from the lower buckling mode to the higher buckling mode with increasing the buckling load, but the buckling mode is invari- able for a certain domain of the buckling load. It is also indicated that, the surrounding elastic medium generally has effect on the lower buckling mode of DWNTs only when compared with the corresponding one for individual DWNTs.     

An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems

This paper presents a method for the analytical prediction of sliding motions along discontinuous boundaries in non-smooth dynamical systems. The methodology is demonstrated through investigation of a periodically forced linear oscillator with dry friction. The switching conditions for sliding motions in non-smooth dynamical systems are given. The generic mappings for the friction-induced oscillator are introduced. From the generic mappings, the corresponding criteria for the sliding motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the sliding motions is illustrated. Finally, numerical simulations of sliding motions are carried out to verify the analytical prediction. This analytical prediction provides an accurate prediction of sliding motions in non-smooth dynamical systems. The switching conditions developed in this paper are expressed by the total force of the oscillator, and the nonlinearity and linearity of the spring and viscous damping forces in the oscillator cannot change such switching conditions. Therefore, the achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces processing a C ⁰-discontinuity.     

On hyperelastic stress-strain law of F-actin bundles

Parallel F-actin bundles are a class of organized semiflexible polymers that play a critical role in cell mechanics, including cell adhesion, cell spreading, cell migration, mitosis and intracellular transport. Here we develop an analytical model of hyperelastic behaviors of an F-actin bundle by considering a wormlike chain confined in a harmonic potential. Closed form solutions are obtained for the axial stress—strain relation of an F-actin bundle under stretch.     

Analysis of the entanglements in carbon nanotube fibers using a self-folded nanotube model

Carbon nanotube (CNT) fibers have shown superb mechanical properties, and have high potential to be used as reinforcements in multifunctional composites. CNT entanglements always exist in CNT fibers and play a crucial role in affecting their mechanical properties. In this study, the CNT entanglement is modeled as two connecting self-folded CNTs (SFCNTs). At large aspect ratios, a CNT is energetically favorable to be self-folded due to the van der Waals interactions between different parts of the CNT. The geometrical characteristics of the SFCNTs, such as the critical length for self-folding as well as the critical effective width and length, are investigated by using both an exact theoretical model and an approximate theoretical model. The tensile properties of the SFCNTs have been examined by using both the approximate theoretical model and atomistic simulations. Good agreements are achieved in the results of these two approaches.     

重新认识横力弯曲梁的切应力强度效应

通过多层叠合梁的横力弯曲问题分析, 证明弯曲切应力不仅直接导致多层叠合梁的脱层, 而且这种脱层还会进一步引发弯曲正应力的急剧增加. 这种由弯曲切应力引发的连锁效应和潜在危害, 理应引起同学们的足够重视.     

The effects of stress concentrators on strength of materials at nanoscale: A molecular dynamics study

There is evidence that when at least one spatial dimension of a material component is in the nanometer range, the effects of nanosize stress concentrators (NSCs) such as impurities, inclusions, pores, and cracks are either eliminated or significantly reduced. The aim of the paper is to examine such evidence using atomistic simulation techniques for a crystalline metal and identify the critical dimensions below which the effects of NSCs are minimal or even nonexistent. The preliminary results reported herein show that for Cu single crystals subjected to constant external strain rate, such critical dimensions are larger than about 30 nm. Since atomistic details are crucial in understanding material behavior at such scales, the paper points to the need for multiscale simulations techniques, presently being developed, for identifying critical dimensions and for examining slow strain rates. Based on the results, the paper presents simulation-based explanations why NSCs may be insignificant at nanoscales.     

The thermal effect on axially compressed buckling of a double-walled carbon nanotube

The thermal effect on axially compressed buckling of a double-walled carbon nanotube is studied in this paper. The effects of temperature change, surrounding elastic medium and van der Waals forces between the inner and outer nanotubes are taken into account. Using continuum mechanics, an elastic double-shell model with thermal effect is presented for axially compressed buckling of a double-walled carbon nanotube embedded in an elastic matrix under thermal environment. Based on the model, an explicit formula for the critical axial stress is derived in terms of the buckling modes of the shell and the parameters that indicate the effects of temperature change, surrounding elastic medium and the van der Waals forces. Based on that, some simplified analysis is carried out to estimate the critical axial stress for axially compressed buckling of the double-walled carbon nanotube. Numerical results for the general case are obtained for the thermal effect on axially compressed buckling of a double-walled carbon nanotube. It is shown that the axial buckling load of double-walled carbon nanotube under thermal loads is dependent on the wave number of axially buckling modes. And a conclusion is drawn that at low and room temperature the critical axial stress for infinitesimal buckling of a double-walled carbon nanotube increase as the value of temperature change increases, while at high temperature the critical axial stress for infinitesimal buckling of a double-walled carbon nanotube decrease as the value of temperature change increases.     

The analysis of two-dimensional two-phase flow in horizontal heated tube bundles using drift flux model

This paper presents the experimental study and numerical simulation of two-dimensional two-phase flow in horizontal heated tube bundles. In the experiments, two advanced measuring systems with a single-fibre optical probe and a tri-fibre-optical-probe were developed to measure respectively the local void fraction and vapor bubble velocities among the heated tube bundles. In accordance with the internal circulation characteristics of two-phase flow in the tube bundles, a mathematical model of two-dimensional two-phase low Reynolds number turbulent flow based on the modified drift flux model and the numerical simulation method to analyze the two-phase flow structures have been developed. The modified drift flux model in which both the acceleration by gravity and the acceleration of the average volumetric flow are taken into account for the calculation of the drift velocities enables its application to the analysis of multi-dimensional two-phase flow. In the analysis the distributions of the vapor-phase velocity, liquid-phase velocity and void fraction were numerically obtained by using the modified drift flux model and conventional drift flux model respectively and compared with the experimental results. The numerical analysis results by using the modified drift flux model agree reasonably well with the experimental investigation. It is confirmed that the modified drift flux model has the capability of correctly simulating the two-dimensional two-phase flow. Received on 3 September 1998