Mechanics of the folding of a nanotube

Nanotubes fold due to the competition between their mechanical stability and van der Waals interactions. The caused dramatic morphology change promises exciting applications of nanotubes in responsive and reconfigurable nanodevices. To investigate the folding mechanism, a curvature-based finite-deformation theoretical model simultaneously considering both the folding of a nanotube and the possible collapsing of the cross-section is developed. The predicted critical condition and the profiles in both axial and transverse directions agree well with molecular dynamics (MD) solutions, demonstrating that the cross-sectional deformation should be taken into account when investigating the folding of a nanotube with a large diameter. Moreover, simple scaling laws of the critical conditions are proposed through a small-deformation theoretical model. With these scaling laws, one can easily and quickly determine both the collapsing state of the cross-section and the folding state of the nanotube with only geometrical parameters [Formula: see text] rather than the difficult-to-determine material properties [Formula: see text].