An atomistic-based finite deformation membrane for single layer crystalline films
Author (s): Arroyo, M., Belytschko, T.
Journal: Journal of the Mechanics and Physics of Solids
Volume: 50, Issue 9
Pages: 1941 – 1977
Date: 2002
Abstract:
A general methodology to develop hyper-elastic membrane models applicable to crystalline fi(lms one-atom thick is presented. In this method, an extension of the Born rule based on the
exponential map is proposed. The exponential map accounts for the fact that the lattice vectors
of the crystal lie along the chords of the curved membrane, and consequently a tangent map
like the standard Born rule is inadequate. In order to obtain practical methods, the exponential
map is locally approximated. The effectiveness of our approach is demonstrated by numerical
studies of carbon nanotubes. Deformed con(gurations as well as equilibrium energies of atomistic
simulations are compared with those provided by the continuum membrane resulting from this
method discretized by finite elements.
Bibtex:
@article{2002-JMPS-AB,
author = "Marino Arroyo and Ted Belytschko",
title = "An atomistic-based finite deformation membrane for single layer crystalline films ",
journal = "Journal of the Mechanics and Physics of Solids ",
volume = "50",
number = "9",
pages = "1941 - 1977",
year = "2002",
note = "",
issn = "0022-5096",
doi = "http://dx.doi.org/10.1016/S0022-5096(02)00002-9",
url = "http://www.sciencedirect.com/science/article/pii/S0022509602000029",
}