On a nanoscopically-informed shell theory of single-wall carbon nanotubes

This paper proposes a bottom-up sequence of modeling steps leading to a nanoscopically informed macroscopic theory of single-walled carbon nanotubes (SWCNTs). We provide a description of the geometry and the mechanics of the two most representative types of SWCNTs, armchair (A-) and zigzag (Z-), of their modules and of their elementary bond units. We believe ours to be the simplest shell theory that accounts accurately for the linearly elastic response of both A- and Z-CNTs; its main novel feature is perhaps the proposition of chirality-dependent concepts of effective thickness and effective radius, whose evaluation is achieved in terms of nanoscopic information; moreover, as shown in the companion paper (Favata and Podio-Guidugli, 2012b), it can be generalized to fit SWCNTs of whatever chirality.