A structural mechanics study of single-walled carbon nanotubes generalized from atomistic simulation

A new structural mechanics model is developed to closely duplicate the atomic configuration and behaviours of single-walled carbon nanotubes (SWCNTs). The SWCNTs are effectively represented by a space frame, where primary and secondary beams are used to bridge the nearest and next-nearest carbon atoms, to mimic energies associated with bond stretching and angle variation, respectively. The elastic properties of the frame components are generalized from molecular dynamics (MD) simulation based on an accurate ab initio force field, and numerical analyses of tension, bending, and torsion are carried out on nine different SWCNTs. The space-frame model also closely duplicates the buckling behaviours of SWCNTs in torsion and bending. In addition, by repeating the same process with continuum shell and beam models, new elastic and section parameters are fitted from the MD benchmark experiments. As an application, all three models are employed to study the thermal vibration behaviours of SWCNTs, and excellent agreements with MD analyses are found. The present analysis is a systematic structural mechanics attempt to fit SWCNT properties for several basic deformation modes and applicable to a variety of SWCNTs. The continuum models and fitted parameters may be used to effectively simulate the overall deformation behaviours of SWCNTs at much larger length- and timescales than pure MD analysis.