On the Inextensible Elastica Model for the Collapse of Nanotubes

Abstract

In this work, we study the collapse of nanotubes using an inextensible elastica model. Through phase plane analysis, we show that there exist collapsed configurations of different orders, each involving a different number of collapsed layers. Solutions corresponding to each order only exist if the equilibrium separation in the contact zone (a material property) is smaller than a certain value. Below the critical separation, there are two solutions for each order corresponding to each separation, a high energy solution and a low energy one. Some of the collapsed configurations are not physically accessible due to material interpenetration. This work puts a limitation on the applicability of the inextensible elastica model for the collapse of nanotubes.

Keywords

nanotube collapse contact inextensible elastica phase plane

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