Summary: Nonlinear Mechanical Response and Rippling of Thick Multiwalled Carbon Nanotubes
M. Arroyo* and T. Belytschko
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA
(Received 5 May 2003; published 21 November 2003)
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 theYoshimura 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.
DOI: 10.1103/PhysRevLett.91.215505 PACS numbers: 62.25.+g, 02.70.Dh, 46.32.+x, 61.46.+w
A number of experiments have suggested that multi-
walled carbon nanotubes (MWCNTs) can be used as
basic elements of nanoelectromechanical systems
(NEMS). In particular, nano-oscillators and actuators
with MWCNTs in bending  and torsion [2,3] have
been experimentally studied. In , the resonant frequen-
cies of cantilevered MWCNTs excited electrically are