Postbuckling of carbon nanotubes by atomic-scale finite element

An Atomic Finite Element Analysis is developed in this paper. At atomic scale, the interatomic bonding forces of Van der Waals and the covalent chemical bond are taken into account. The methodology is applied to study the behavior of carbon nanotubes, whose development has experienced strong growth in recent years and that can be used for quality mechanical reinforcement. These carbon nanotubes are formed by repeating zigzag carbon-carbon bonds. Development of atomic finite element method (AFEM) methodology can be traced back to the homogenized elastic properties of various graphene structures (single-layer graphene sheet, Zig-zag single-walled carbon nanotubes, triple-layer graphene sheet).

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The Atomic-Scale Finite Element Method for Post-Buckling of Carbon Nanotubes

Computational Mechanics ◽

10.1007/978-3-540-75999-7_5 ◽

2007 ◽

pp. 48-59

Author(s):

A. Y. T. Leung ◽

Xiang Guo

Keyword(s):

Finite Element Method ◽

Carbon Nanotubes ◽

Finite Element ◽

Atomic Scale ◽

Post Buckling ◽

Element Method

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Critical Strain of Carbon Nanotubes: An Atomic-Scale Finite Element Study

Journal of Applied Mechanics ◽

10.1115/1.2198548 ◽

2006 ◽

Vol 74 (2) ◽

pp. 347-351 ◽

Cited By ~ 14

Author(s):

X. Guo ◽

A. Y. T. Leung ◽

H. Jiang ◽

X. Q. He ◽

Y. Huang

Keyword(s):

Carbon Nanotubes ◽

Finite Element ◽

Critical Strain ◽

Local Buckling ◽

Atomic Scale ◽

Energy Curve ◽

Outer Diameter ◽

Covalent Bonds ◽

Buckling Behavior ◽

Global Buckling

This paper employs the atomic-scale finite element method (AFEM) to study critical strain of axial buckling for carbon nanotubes (CNTs). Brenner et al. “second-generation” empirical potential is used to model covalent bonds among atoms. The computed energy curve and critical strain for (8, 0) single-walled CNT (SWNT) agree well with molecular dynamics simulations. Both local and global buckling are achieved, two corresponding buckling zones are obtained, and the global buckling behavior of SWNT with a larger aspect ratio approaches gradually to that of a column described by Euler’s formula. For double-walled CNTs with smaller ratio of length to outer diameter, the local buckling behavior can be explained by conventional shell theory very well. AFEM is an efficient way to study buckling of CNTs.

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The atomic-scale finite-element modelling of single-walled carbon nanotubes

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406jmes615ft ◽

2007 ◽

Vol 221 (5) ◽

pp. 613-617 ◽

Cited By ~ 8

Author(s):

H Ding ◽

S-J Chen ◽

K Cheng

Keyword(s):

Carbon Nanotubes ◽

Finite Element ◽

Young’S Modulus ◽

Wall Thickness ◽

Young's Modulus ◽

Single Walled Carbon Nanotubes ◽

Atomic Scale ◽

Single Walled Carbon ◽

Beam Elements ◽

Walled Carbon Nanotubes

In this paper, an atomic-scale finite-element (AFE) model is proposed for single-walled carbon nanotubes (SWCNTs), which are considered to behave like space-frame structures when subjected to loadings. To create the AFE models, three-dimensional beam elements are used to model the bonds between carbon atoms as loading-carrying elements, while the nodes are placed at the locations of carbon atoms to connect the loading-carrying elements. The material properties of beam elements can be determined by using a linkage between molecular and continuum mechanics. In order to evaluate the AFE model and its performance, the influence of tube wall thickness on Young's modulus of SWCNTs is investigated. It is found that the selection of wall thickness significantly affects the magnitude of the Young's modulus. For the values of wall thickness used in this study, the obtained values of Young's modulus agree well with the corresponding theoretical results. Furthermore, the results also illustrate that Young's modulus is inversely proportional to the wall thickness. The presented results demonstrate that the proposed AFE model can be used as a valuable tool for studying the mechanical behaviour of carbon nanotubes.

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