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How shell-like is a carbon nanotube?

Pradeep Sharma's picture

(Carbon) Nanotubes have attracted considerable attention from the mechanics community; probably second to none when it comes to nanotechnologies. Although I personally have done very little in this particular topic, I have enjoyed reading about the many developments made by mechanicians in terms of modeling the behavior of nanotubes and the applicability of standard continuum mechanics notions. A post on this subject on iMechanica, which received a fair amount of attention from many mechanicians involved in this topic, may be found here .

As discussed in the aforementioned post, graphene is often modeled as a thin shell. The ensuing scatter in the "apparent" Young's modulus reported in the literature (and the corresponding thickness of the so-called shell) turns out to be much debated topic. A recent paper by Young Huang , his graduate student Jian Wu, and co-workers discusses this issue in more depth. In particular, they establish a finite deformation shell theory from an appropriate interatomic force field to analytically asses the error in modeling nanotube as a thin shell. I enjoyed reading the paper in big part because the entire development is analytical and thus also serves a pedagogical purpose. One of the major conclusions of this work is that constant thickness isotropic thin shell assumption is only valid to the order of a/R; where a is the interatomic spacing and R is the nanotube radius. This non-dimensional number can be quite large for sub-nm single walled nanotubes. For O[(a/R)2], a carbon nanotube can be modeled as an orthotropic thin shell. For O[(a/R)3], it cannot be modeled as a classical thin shell anymore. I am also attaching a preprint of the paper kindly provided by Young.


PDF icon CNT_Shell.pdf185.13 KB


Teng Li's picture


Thanks for pointing out Young's paper.  It seems the link to the paper in your post somewhat doesn't work (at least at my end).

Would you mind give the full citation or a DOI link? Thanks. 

Pradeep Sharma's picture

Teng, thanks for pointing this out. The link should work now. A preprint is also attached (obtained from Young).

Pradeep Sharma's picture

It always nice to celebrate when a mechanics paper gets noticed in the broader engineering and science community. I just found out that a related paper (by the same authors) was identified by Essential Science Indicators as the freatured hot paper in engineering (---this is based on the number and rate of citatons in a short period). This service (owned by the Thomas-Reuters which also owns ISI and comes up with journal impact factors) selects one "hot" paper every two months in about 22 fields One of them is engineering. Young Huang's paper is the one selected in this round (congratulations to him and his co-workers!). ScienceWatch has also featured a nice interview by the first author, Jian Wu.

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