## Summary Nanomechanics at a Glance

In summary, it seems useful to highlight the 'nanomechanics at a glance', based on the knowledge accumulated up-to-date, and omitting technical details and uncertainties. Carbon nanotubes demonstrate very high stiffness to an axial load or a bending of small amplitude, which translates to the record-high efficient linear-elastic moduli. At larger strains, the nano-tubes (especially, the single-walled type) are prone to buckling, kink forming and collapse, due to the hollow shell-like structure. These abrupt changes (bifurcations) manifest themselves as singularities in the non-linear stressstrain curve, but are reversible and involve no bond-breaking or atomic rearrangements. This resilience corresponds, quantitatively, to a very small sub-angstrom effective thickness of the constituent graphitic shells. Irreversible yield of nanotubes begins at extremely high deformation (from several to dozens percent of in-plane strain, depending on the strain rate) and high

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Fig. 21. Right: Relaxed structures of a (6,6) nanotube computed using molecular mechanics as a function of the twisting angle. Left: Computed band-gap energy using extended Huckel theory as a function of the twisting angle [55]

temperature. The atomic relaxation begins with the edge dislocation dipole nucleation, which (in case of carbon) involves a diatomic interchange, i.e. a ninety-degree bond rotation. A sequence of similar diatomic steps ultimately leads to failure of the nanotube filament. The failure threshold (yield strength) turns out to depend explicitly on nanotube helicity, which demonstrates again the profound role of symmetry for the physical properties, either electrical conductivity or mechanical strength. Finally, the manifestation of mechanical strength in the multiwalled or bundled nanotubes (ropes) is obscured by the poor load transfer from the exterior to the core of such larger structure. This must lead to lower apparent strength and even lower linear moduli, as they become limited by the weak lateral interaction between the tubules rather than by their intrinsic carbon bond network. The ultimate strength of nanotubes and their ensembles is an issue that requires the modeling of inherently mesoscopic phenomena, such as plasticity and fracture, on a microscopic, atomistic level, and constitutes a challenge from the theoretical as well as experimental points of view.

Acknowledgements

B.I.Y. acknowledges support from the U.S. AFOSR/AFRL and from the NASA Ames Center.

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Fig. 21. Right: Relaxed structures of a (6,6) nanotube computed using molecular mechanics as a function of the twisting angle. Left: Computed band-gap energy using extended Huckel theory as a function of the twisting angle [55]

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