Nanomechanics on the deformation of single- and multi-walled carbon nanotubes under radial pressure

In this paper, the deformation of single- and multi-walled carbon nanotubes under radial pressure has been studied by using an analytical molecular structural mechanics model. The elastic in-plane properties (in-plane stiffness in the hoop direction, Yθ) and Poisson's ratio (vθzvθz) of single-walled carbon nanotubes (SWCNTs) has been derived and shown to be equal to the axial direction in-plane properties (Yz, vzθvzθ) for all tube diameters. In-plane properties are sensitive to tube diameter at small diameter ranges and insensitive to tube size at large diameters. Using the obtained hoop stiffness, the radial deformation of SWCNTs under radial pressure is formulated. The effect of van der Waals forces between layers in multi-walled carbon nanotubes (MWCNTs) has been incorporated within the analytical molecular structural mechanics model to analyze the radial deformation of MWCNTs. Closed form solution for the radial deformation of MWCNTs is obtained by using the universal graphite potential function for the interlayer van der Waals interactions. Load transfer between layers is considered. The behavior of MWCNTs under large radial deformation has also been studied by incorporating nonlinear van der Waals interactions. The present theoretical investigation provides a very simple approach to predict the mechanical properties of carbon nanotubes.