## Papers

### An atomistic-based finite deformation membrane
for crystalline films one atom thick

Marino Arroyo and Ted Belytschko

#### Abstract

A general methodology to develop hyper-elastic membrane models
equivalent to crystalline films one atom thick is presented. This
membrane theory is used to study the mechanics of carbon
nanotubes. The method relies on an extension of the Born based on
the exponential map. 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
models, the exponential map is locally approximated. Numerical
simulations of a membrane for carbon nanotubes discretized by
finite elements are given.
This paper is available in acrobat form (49
pages, ~1 MB) .