Dynamic Finite Element Modeling of Carbon Nanotubes Using an Intrinsic Formulation
July 2005
Michael J. Leamy, The MITRE Corporation
ABSTRACT
This article presents an efficient explicit dynamic formulation for
modeling curved and twisted Carbon Nanotubes (CNT's) based on
a recently-developed intrinsic beam description (i.e. the dynamic state
given by curvatures, strains, and velocities only) [Hodges, 2003] together
with a finite element discretization incorporating atomistic potentials.
This approach offers several advantages primarily related to the model's
computational efficiency: 1) the resulting partial differential equations
governing motion are in first-order form (i.e. have first-order time
derivatives only), 2) the system nonlinearities appear at low order,
3) the intrinsic description incorporating curvature allows low-order
interpolation functions to describe generally curved and twisted nanotube
centerlines, 4) inter-element displacements, slopes, and curvatures
are matched at the element boundaries, and 5) finite rotational variables
are absent, along with their inherit complexities. In addition, the
developed model and finite element discretization are able to capture
the nanotube's dynamic response, without the expense of calculating
the dynamic response of individual atoms as per Molecular Dynamics models.
Simulation results are presented which illustrate the dynamic response
of a typical CNT to axial, bending, and torsional loading. Results from
the simulations are compared to similar results available in the literature,
and close agreement is documented.
Additional Search Keywords
nanotube, nanomaterial, finite element, dynamic, computational nanomechanics
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