Abstract In this paper, the deformation of single- and multi-walled carbon nanotubes under radial pressure has been studied by using an analytical molecular structural mechanics model. The elastic in-plane properties (in-plane stiffness in the hoop direction, Y θ ) and Poisson's ratio ( v θ z ) of single-walled carbon nanotubes (SWCNTs) has been derived and shown to be equal to the axial direction in-plane properties ( Y z , v z θ ) for all tube diameters. In-plane properties are sensitive to tube diameter at small diameter ranges and insensitive to tube size at large diameters. Using the obtained hoop stiffness, the radial deformation of SWCNTs under radial pressure is formulated. The effect of van der Waals forces between layers in multi-walled carbon nanotubes (MWCNTs) has been incorporated within the analytical molecular structural mechanics model to analyze the radial deformation of MWCNTs. Closed form solution for the radial deformation of MWCNTs is obtained by using the universal graphite potential function for the interlayer van der Waals interactions. Load transfer between layers is considered. The behavior of MWCNTs under large radial deformation has also been studied by incorporating nonlinear van der Waals interactions. The present theoretical investigation provides a very simple approach to predict the mechanical properties of carbon nanotubes.
Abstract An analytical molecular structural mechanics model for the prediction of mechanical properties of defect-free carbon nanotubes is developed by incorporating the modified Morse potential with an analytical molecular structural model. The developed model is capable of predicting Young’s moduli, Poisson’s ratios and stress–strain relationships of carbon nanotubes under tension and torsion loading conditions. Results on the mechanical properties of single-walled carbon nanotubes show that Y...
Abstract Molecular-mechanics based finite element approach was used to predict the tensile stiffness and strength of single-walled carbon nanotubes. Different types of nanotubes, such as Arm-Chair, Zig-Zag, and chiral type, were discussed in detail. Nanotube stiffness was predicted to be independent of both the nanotube diameter and the nanotube helicity, but Poisson ratio was dependent of the nanotube diameter. In addition to the stiffness, nanotube strength was also analyzed by molecular-mecha...
#1Antonio Pantano(MIT: Massachusetts Institute of Technology)H-Index: 16
#2David M. Parks(MIT: Massachusetts Institute of Technology)H-Index: 45
Last. Mary C. Boyce(MIT: Massachusetts Institute of Technology)H-Index: 86
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Abstract An effective continuum/finite element (FE) approach for modeling the structure and the deformation of single- and multi-wall carbon nanotubes (CNTs) is presented. Individual tubes are modeled using shell 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 incorporation and role of an initial internal distributed stress through the thickness of the wall, due to the cylindrica...
#1Chunyu Li(UD: University of Delaware)H-Index: 28
#2Tsu-Wei Chou(UD: University of Delaware)H-Index: 86
The elastic deformation of single-walled carbon nanotubes under hydrostatic pressure has been modeled using the molecular structural mechanics method. The computational results indicate that the radial direction elastic modulus deceases with the increase in tube diameter. The circumferential direction elastic modulus is insensitive to tube diameter, and roughly equal to the axial direction modulus. The hydrostatic pressure for tube buckling also deceases with increasing tube diameter and is in t...
The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard crystal elasticity to curved monolayer lattices by means of the exponential Cauchy-Born rule. The constitutive model for a two-dimensional continuum deforming in three dimensions (a surface) is written explicitly in terms of the underlying atomistic model. The resulting hyper-elastic potential depends on the stretch and ...
Last. Keh-Chih Hwang(UConn: University of Connecticut)H-Index: 30
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Abstract We investigate the effect of nanotube radius on the constitutive model of single wall carbon nanotubes. We adopt a modified Cauchy–Born rule to incorporate the interatomic potential into the continuum analysis, and such an approach ensures the equilibrium of atoms. It is shown that the nanotube radius has little effect on the mechanical behavior of single wall carbon nanotubes subject to simple tension or pure torsion, while the nanotube orientation has somewhat larger influences.
#2Huajian Gao(MPG: Max Planck Society)H-Index: 111
An analytical model based on a molecular mechanics approach is presented to relate the elastic properties of a single-walled carbon nanotube to its atomic structure. We derive closed-form expressions for elastic modulus and Poisson's ratio as a function of the nanotube diameter. Properties at different length scales are directly connected via these expressions. The analytically calculated elastic properties for achiral nanotubes using force constants obtained from experimental data of graphite a...
#1Chunyu Li(UD: University of Delaware)H-Index: 28
#2Tsu-Wei Chou(UD: University of Delaware)H-Index: 86
Abstract This paper presents a structural mechanics approach to modeling the deformation of carbon nanotubes. Fundamental to the proposed concept is the notion that a carbon nanotube is a geometrical frame-like structure and the primary bonds between two nearest-neighboring atoms act like load-bearing beam members, whereas an individual atom acts as the joint of the related load-bearing beam members. By establishing a linkage between structural mechanics and molecular mechanics, the sectional pr...
#1Weiguang Shi(UWO: University of Western Ontario)H-Index: 3
#2Hao Liu(UWO: University of Western Ontario)H-Index: 1
Last. Xiaoyang Liu(JLU: Jilin University)H-Index: 1
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Abstract In this study, nitrogen-doped carbon nanotubes (CN x -NTs) with a 8.4% nitrogen content were investigated under high pressure using Raman spectroscopy as well as X ray diffraction (XRD) with synchrotron radiation. For comparison purpose, high pressure behaviors of carbon nanotubes (CNTs) without nitrogen were studied as well. Two phase transformations were identified in CN x -NTs, which can be assigned to tube shape change from circular to ellipse-like and then to flatten shape. In stro...
Last. Xiaolong Song(Xi'an Jiaotong University)H-Index: 15
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Abstract Two vastly different types of load-displacement responses observed in graphitic nanostructures under nano-compression are compared in terms of serration behaviors. Different from commonly encountered linear/nonlinear elastic deformation, a periodic serration behavior related to plastic flow is observed in amorphous carbon nanospheres. The true stress-strain relation exhibits a sole feature of type C serration, and comprehensive statistical, dynamical and fractal analyses further demonst...
#2Saied Irani(KNTU: K.N.Toosi University of Technology)H-Index: 8
Abstract Carbon nanotubes (CNTs) and their products such as polymer nanocomposite (PNC) are an undeniable part of future materials. To use such future materials, it is necessary to have an accurate evaluation of their properties. Several uncertainties such as structural defects and their distributions cause change in the properties of CNTs that could be considered probabilistic variables. A novel procedure is presented for evaluating CNTs’ probabilistic fracture properties and structural reliabi...
#1A. M. Fattahi(IAU: Islamic Azad University)H-Index: 18
#2Babak Safaei(IAU: Islamic Azad University)H-Index: 25
Axial buckling characteristics of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) are investigated. Various types of beam theories namely as Euler–Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory are used to analyze the buckling behavior of carbon nanotube-reinforced composite beams. Generalized differential quadrature (GDQ) method is utilized to discretize the governing differential equations along with four commonly used boundary conditions. The mat...
Abstract Carbon nanotubes (CNTs) with and without end caps may be used for fluid storage and transport, respectively, referred to as CNT-nanovessel and CNT-nanopipe. The determination of the stiffness in the hoop (circumferential) and radial directions, ideal hoop strength, and hoop stress–strain curve of such nanostructures is of particular interest. Due to the proposed viewpoint, a chiral free-standing single-walled CNT (SWCNT) has a natural angle of twist and natural extension along the axis ...
Last. William A. Curtin(EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 79
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A finite element study of MWCNT pullout from a ceramic matrix with a rough fibre-matrix interface is presented. MWCNT pullout differs in several ways from pullout of solid, micro-scale fibres, and has not been studied before. Interfacial roughness, due to missing CNT walls and other fabrication defects, is represented as an axisymmetric sinusoidal fibre-matrix interface with Coulomb friction. We find roughness resists pullout and aids push-out of the fibre over different portions of the pullout ...
Polystyrene (PS) grafted multi-walled carbon nanotubes (MWCNTs) were well-organized as bundles by a selfassembly method in tetrahydrofuran (THF). PS was synthesized by atom transfer radical polymerization and grafted to the surface of tubes through covalent bonds. Unmodified tubes agglomerated irregularly and precipitated instantly because of poor compatibility with THF. But soluble PS provides solvent-phobic MWCNTs with suspending stability and dispersibility in the dispersant. Therefore, MWCNT...
Polystyrene (PS) with molecular weight of 2.58 × 104 was grafted to multi-walled carbon nanotubes (MWCNTs) via covalent bonds. The modified tubes can self-assemble as regular bundles in tetrahydrofuran (THF) and benzene while unmodified ones cannot but agglomerate seriously and irregularly in the same solvents. In order to find out the role that polymer plays in self-assembly, a series of PS in different molecular weights were synthesized and grafted on the surface of MWCNTs. THF and benzene are...
Nonlinear thermo free vibration and instability of viscose fluid-conveying double-walled carbon nanocones (DWCNCs) are studied using Hamilton’s principle and differential quadrature method (DQM). The small-size effects on bulk viscosity and slip boundary conditions of nanoflow through Knudsen number (Kn) is considered. The nanocone is simulated as a clamped-clamped Euler-Bernoulli’s beam embedded in an elastic foundation of the Winkler and Pasternak type. The van der Waals (vdW) forces between t...