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Research Papers

A Finite-Deformation Shell Theory for Carbon Nanotubes Based on the Interatomic Potential—Part I: Basic Theory

[+] Author and Article Information
J. Wu, K. C. Hwang

FML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P. R. China

Y. Huang1

Department of Civil and Environmental Engineering, and Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208y-huang@northwestern.edu

J. Song

Department of Mechanical Science and Engineering, University of Illinois, Urbana, IL 61801

1

Corresponding author.

J. Appl. Mech 75(6), 061006 (Aug 20, 2008) (6 pages) doi:10.1115/1.2965366 History: Received June 16, 2007; Revised May 10, 2008; Published August 20, 2008

A finite-deformation shell theory for carbon nanotubes (CNTs) is established directly from the interatomic potential for carbon to account for the effect of bending and curvature. Its constitutive relation accounts for the nonlinear multibody atomistic interactions and therefore can model the important effect of CNT chirality and radius. The equilibrium equations and boundary conditions are obtained for the symmetric stresses and bending moments, which are different from many existing shell theories that involve asymmetric stress and bending moments. The theory is used in Part II of this paper to study the instability of carbon nanotubes subjected to different loadings.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A schematic of (a) initial undeformed configuration and (b) deformed configuration of carbon nanotubes

Grahic Jump Location
Figure 2

(a) The decomposition of a hexagonal lattice to two triangular sublattices. (b) A shift vector η between the two sublattices to ensure the equilibrium of atoms.

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