Buckling of single-wall carbon nanotubes from molecular mechanics to continuum models

In the last years carbon nanotubes (CNTs) have received considerable attention, due to the wide number of applications in electronic nanodevices, energy generation and storage, biotechnologies, composites. The study of the CNTs mechanical behaviour plays an important role for their manufacturing and integration in devices, for tuning their performances in certain applications as well as for controlling the mechanics of their composites. For this reason, considerable research efforts have been done for modelling the CNTs mechanical behaviour through the solid state physics methods, molecular mechanics models or continua. The most of the existing literature has focused only on the CNTs linear behaviour, while there is a lack of studies in the nonlinear range, especially of buckling. With this in mind, a nonlinear molecular mechanics model of single-wall CNTs is presented. The model accounts for standard binary and ternary interactions between the atoms and for dihedral angles. Numerical analyses regarding the buckling of single-wall CNTs are addressed directly at the nanoscale. The equilibrium paths and the deformed configurations are critically discussed in comparisons with 1D models endowed with suitable microstructure and considerations on the role of the various energy contributions are also provided.