A Finite element model for thermal dilatation of carbon nanotubes

The paper presents a finite element model that can be used for modelling of a nanotube thermal contraction with temperature increase. Since carbon nanotubes exhibit anisotropic thermal contraction, the ordinary structural mechanics approach based on the beam finite elements acting as interatomic bonds cannot be directly applied. To circumvent this problem, a set of additional rod elements is introduced into the model. If different coefficients of thermal expansion are used for the beam and rod elements, anisotropic thermal contraction can be modelled. An exact calculation procedure for these thermal expansion coefficients is presented. The proposed model is tested on one carbon nanotube and results are compared to the data available in literature. Influence of the stiffness of additional rod elements on the obtained results is not noticed.