An approach to multi-body interactions in a continuum-atomistic context: Application to analysis of tension instability in carbon nanotubes

K. Y. Volokh, K. T. Ramesh

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8 Scopus citations


The tensile strength of single-walled carbon nanotubes (CNT) is examined using a continuum-atomistic (CA) approach. The strength is identified with the onset of the CNT instability in tension. The focus of this study is on the effects of multi-body atomic interactions. Multiscale simulations of nanostructures usually make use of two- and/or three-body interatomic potentials. The three-body potentials describe the changes of angles between the adjacent bonds - bond bending. We propose an alternative and simple way to approximately account for the multi-body interactions. We preserve the pair structure of the potentials and consider the multi-body interaction by splitting the changing bond length into two terms. The first term corresponds to the self-similar deformation of the lattice, which does not lead to bond bending. The second term corresponds to the distortional deformation of the lattice, which does lead to bond bending. Such a split of the bond length is accomplished by means of the spherical-deviatoric decomposition of the Green strain tensor. After the split, the continuum-atomistic potential can be written as a function of two bond lengths corresponding to the bond stretching and bending independently. We apply an example exponential continuum-atomistic potential with the split bond length to the study of tension instability of the armchair and zigzag CNTs. The results of the study are compared with those obtained by Zhang et al. (2004. J. Mech. Phys. Solids 52, 977-998) who studied tension instability of carbon nanotubes by using the Tersoff-Brenner three-body potential, and with recent experimental results on the tensile failure of single walled carbon nanotubes.

Original languageEnglish
Pages (from-to)7609-7627
Number of pages19
JournalInternational Journal of Solids and Structures
Issue number25-26
StatePublished - 1 Dec 2006
Externally publishedYes


  • Carbon nanotube
  • Continuum-atomistic analysis
  • Interatomic potential

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science (all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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