By Y. Gan
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Additional resources for Continuum Mechanics - Progress in Funds., Engrg. Applns.
40 Continuum Mechanics – Progress in Fundamentals and Engineering Applications y s O x s a s πR 2 Fig. 4. Elastica model for a quarter of the CNT, with the arc length s and slope angle ranging from 0 to 90 . In fact, there is another underling assumption that, the deformation along the axis of the nanotube is uniform, which has already been verified by experiments and MD simulations (Ruoff, et al. , 2005b). As a result, we select the cross section representing the whole tube, and model the thin wall as a curvilinear abscissa.
In this study, we assume that the gravity effect is negligible, for the interplay between the surface energy and elasticity is predominant. Let us consider a generalized elastic system denoted by a continuous and smooth curve, where part of the curve is adhered by some special interfacial forces. The position of an arbitrary point in the curve is schematized by the arc length s, the total length of the curve is L, and the segment length dealing with the elastic deformation is a. The kernel problem is how to determine the unknown length a in the equilibrium state according to the principle of least potential energy.
As a reasonable simplification, the van der Waals force between the upper and lower portion of the CNT walls in the non-contact domain is ignored in our calculation. Normally, the van der Waals force between two carbon atoms is repulsive at a very close range, so the CNT wall contact is defined by an equilibrium separation d0 between the flat regions. The distance between the flat contact zone and the extreme point of the CNT is denoted as b. From the experimental picture, we can see that the collapsed shape of CNT is symmetric, which was also verified by the molecular simulations (Tang, et al.