Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium

An elastic double-shell model is presented for infinitesimal buckling of a double-walled carbon nanotube embedded in an elastic matrix under axial compression. The analysis is based on a Winkler model for the surrounding elastic medium and a simplified model for the van der Waals interaction between the inner and outer nanotubes. An explicit formula is derived for the critical axial strain, which indicates the effects of the surrounding elastic matrix combined with the intertube van der Waals forces. In particular, the present model predicts that the critical axial strain of the embedded double-walled nanotube is lower than that of an embedded single-walled nanotube under otherwise identical conditions. This implies that inserting an inner tube lowers the critical axial strain of an embedded single-walled carbon nanotube, although the total critical compressive force could be increased due to the increase in the cross-sectional area of the nanotube. The reduced critical axial strain is attributed to the intertube slips between the inner and outer tubes. This result indicates that embedded multi-walled carbon nanotubes could be even more susceptible to infinitesimal axial buckling than embedded single-walled carbon nanotubes.