A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes

Author (s): Arroyo, M., Belytschko, T.
Journal: Mechanics of Materials

Volume: 35, Issues 3-6
Pages: 193 – 215
Date: 2003

Abstract:

A finite deformation hyper-elastic membrane theory based on inter-atomic potentials for crystalline films composed of a single atomic layer is developed. For this purpose, an extension of the standard Born rule that exploits the differential geometry concept of the exponential map is proposed to deal with the curvature of the membrane of surfaces. The exponential map approximated locally and strain measures based on the stretch and the curvature of the membrane arise. The methodology is first particularized to atomic chains in two dimensions, and then to graphene sheets. Areduced model for the transverse mechanics of carbon nanotubes is developed in detail, This model is a hyper-elastic constrained membrane which fully exploits the symmetry of the transverse deformation. Additionally, a continuum version of the non-bonded interactions is provided. The continuum model is discretized using finite elements and very good agreement with molecular mechanics simulations is obtained. Finally, several simulations illustrate the strong effect of the van der Waals interactions in the transverse deformation of carbon nanotubes.

  
  

Bibtex:

@article{Arroyo2003193,
title = "A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes ",
journal = "Mechanics of Materials ",
volume = "35",
number = "3–6",
pages = "193 - 215",
year = "2003",
note = "",
issn = "0167-6636",
doi = "http://dx.doi.org/10.1016/S0167-6636(02)00270-3",
url = "http://www.sciencedirect.com/science/article/pii/S0167663602002703",
author = "Marino Arroyo and Ted Belytschko",
keywords = "Crystal elasticity",
keywords = "Quasicontinuum",
keywords = "Born rule",
keywords = "Exponential map",
keywords = "Membrane",
keywords = "Carbon nanotubes "
}