Nonlinear mechanical response and rippling of thick multiwalled carbon nanotubes
M. Arroyo and T. Belytschko
Physical Review Letters, 45, 215505 (2003).

ABSTRACT
The measured drop of the effective bending stiffness of multiwalled carbon
nanotubes (MWCNTs) with increasing diameter is investigated by a generalized
local quasicontinuum method. The previous hypothesis that this reduction is due
to a rippling mode is confirmed by the calculations. The observed ripples result
from a complex three-dimensional deformation similar to the Yoshimura buckling
pattern. It is found that thick MWCNTs exhibit a well-defined nonlinear
moment-curvature relation, even for small deformations, governed by the
interplay of strain energy relaxation and intertube interactions. Rippling
deformations are also predicted for MWCNTs subject to torsion, resulting in an
effective torsional modulus much smaller than that predicted by linear
elasticity.