An atomistic-continuum Cosserat rod model of carbon nanotubes

Karthick Chandraseker, Subrata Mukherjee, Jeffrey T. Paci, George C Schatz

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

The focus of the present work is an atomistic-continuum model of single-walled carbon nanotubes (CNTs) based on an elastic rod theory which can exhibit geometric as well as material nonlinearity [Healey, T.J., 2002. Material symmetry and chirality in nonlinearly elastic rods. Mathematics and Mechanics of Solids 7, 405-420]. In particular, the single-walled carbon nanotube (SWNT) is modeled as a one-dimensional elastic continuum with some finite thickness bounded by the lateral surface. Exploitation of certain symmetries in the underlying atomic structure leads to suitable representations of the continuum elastic strain energy density in terms of strain measures that capture extension, twist, bending, and shear deformations [Healey, T.J., 2002. Material symmetry and chirality in nonlinearly elastic rods. Mathematics and Mechanics of Solids 7, 405-420]. Bridging between the atomic scale and the effective continuum is carried out by parameterization of the continuum elastic energy and determination of the parameters using unit cell atomistic simulations over a range of deformation magnitudes and types. Specifically, the proposed model takes into account (a) bending, (b) twist, (c) shear, (d) extension, (e) coupled extension and twist, and (f) coupled bending and shear deformations. The extracted parameters reveal benefits of accounting for important anisotropic and large-strain effects as improvements over employing traditional, linearly elastic, isotropic, small-strain, continuum models to simulate deformations of atomic systems such as SWNTs. It is envisioned that the proposed approach and the extracted model parameters can serve as a useful input to simulations of SWNT deformations using existing nonlinearly elastic continuum codes based, for example, on the finite element method (FEM).

Original languageEnglish
Pages (from-to)932-958
Number of pages27
JournalJournal of the Mechanics and Physics of Solids
Volume57
Issue number6
DOIs
Publication statusPublished - Jun 2009

Fingerprint

Carbon nanotubes
Single-walled carbon nanotubes (SWCN)
rods
carbon nanotubes
continuums
Chirality
Shear deformation
Mechanics
Bending (deformation)
mathematics
shear
chirality
Strain energy
Parameterization
symmetry
Finite element method
exploitation
parameterization
atomic structure
finite element method

Keywords

  • Atomistic-continuum rod
  • Constitutive behavior
  • Elastic material
  • Finite deflections
  • Finite strain

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

An atomistic-continuum Cosserat rod model of carbon nanotubes. / Chandraseker, Karthick; Mukherjee, Subrata; Paci, Jeffrey T.; Schatz, George C.

In: Journal of the Mechanics and Physics of Solids, Vol. 57, No. 6, 06.2009, p. 932-958.

Research output: Contribution to journalArticle

Chandraseker, Karthick ; Mukherjee, Subrata ; Paci, Jeffrey T. ; Schatz, George C. / An atomistic-continuum Cosserat rod model of carbon nanotubes. In: Journal of the Mechanics and Physics of Solids. 2009 ; Vol. 57, No. 6. pp. 932-958.
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