Morphology instability of substrate-supported carbon atomic layers can be harnessed to modulate physical properties and functions, which has drawn interesting attention. Curvature would be a critical factor affecting surface morphology and its stability characteristics. Infilled carbon nanotubes, that is to say carbon monolayers with curved geometry and infilled substrates, namely nanosleeves, widely exist in the literature and have many potential applications. Here, we reveal an unprecedented rich post-buckling phenomenon of nanosleeves, which involves multiple successive bifurcations: smooth-wrinkle-ridge-sagging transitions. The nanosleeve initially buckles into periodic axisymmetric wrinkles at the threshold and then evolves into a localized mode with one single ridge growing upon further axial compression. Finally, the amplitude of the ridge reaches a limit and the symmetry is broken with the ridge sagging into a recumbent fold that can be axisymmetric or non-axisymmetric. Such rich morphology transition is first revealed by molecular dynamics simulation, and then theoretically predicted by a finite strain core-shell continuum model. An analytical solution of the critical threshold of primary smooth-wrinkle transition is further provided, which explicitly indicates the crucial role played by curvature and van der Waals interaction between the carbon monolayers and infilled metals. Such multiple-bifurcation scenario and curvature-determined mechanism are found to be inherently universal.
J. Mech. Phys. Solids, https://doi.org/10.1016/j.jmps.2021.104398