Chemistry Reference
In-Depth Information
question. Moreover, it was extensively observed that almost all properties
of CNTs (mechanical, buckling, vibrations and thermal properties) depend
on the chirality of CNT; thus continuum modeling cannot address this im-
portant issue.
Recently, nano-scale continuum mechanics methods are developed as
an efficient way of modeling CNT. These modeling techniques are not
computationally intensive like atomistic modeling and thus they are able to
be applied to more complex system with-out limitation of short time and/
or length scales. Moreover, the discrete nature of the CNT lattice structure
is kept in the modeling by replacing C-C bonds with a continuum element.
Since the continuum modeling is employed at the scale of nano, therefore
the modeling is called as nanoscale continuum modeling.
The performed investigations in literature addressing mechanical prop-
erties, buckling, vibrations and thermal behavior of CNT are reviewed
and classified on the basis of three aforementioned modeling techniques.
While atomistic modeling is a reasonable modeling technique for this pur-
pose, its applicability is limited to the small systems. On the other hand,
the continuum modeling neglects the discrete structure of CNT leading to
inaccurate results.
Nano scale continuum modeling can be considered as an accept-able
compromise in the modeling presenting results in a close agreement with
than that of atomistic modeling. Employing FEM as a computationally
powerful tool in nanoscale continuum modeling, the influence of CNT
chirality, diameter, thickness and other involved parameters can be evalu-
ated conveniently in comparison with other methods. Concerning CNTs
buckling properties, many researchers have conducted the simulation us-
ing MD methods. The shell theories and molecular mechanic structure
simulation are also applied to assess the CNTs buckling in order to avoid
time consuming simulations. But, for the specific case of buckling behav-
ior, it is not recommended to scarify the lattice structure of CNT for less
time consuming computations. But instead, nanoscale continuum model-
ing is preferred.
Comparing the results with the obtained results of MD simulation, it
can be inferred from literature that for large aspect ratios (i.e., length to
diameter ratio L/d > 10) the simple Euler-Bernoulli beam is reliable to
predict the buckling strains of CNTs while there fined Timoshenko's beam
model or their nonlocal counterparts theory is needed for CNTs with in-
termediate aspect ratios (i.e., 8 <L/d < 10). The Donnell thin shell theory
