How shell-like is a carbon nanotube?

(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.