Homogenization of single-walled carbon nanotubes

This work deals with the computation of the overall axial elastic behavior of single-walled carbon nanotubes (SWCNTs). The SWCNTs are modeled as space-frame structures, using beam elements to represent atomic bonds [1].The application of homogenization theory [2] enables to derive rigorously the macroscopic anisotropic beam behavior of the SWCNT, from the solution of three-dimensional basic cell problems. Moreover, taking benefit of the two helical symmetries [3] of the microstructure, the basic cell can be reduced to only one half of an hexagon, as depicted in Fig.1 for a zigzag SWCNT. Therefore, the overall stiffness coefficients can be computed efficiently using very concise FE models (including only 3 beam elements): the helical symmetry properties of the displacement field lead to a set of linear relationships expressed in local cylindrical axes between the opposite nodes m and n (see Fig.1) then acting as boundary conditions [3].The accuracy of this approach has been assessed with respect to reference solutions of the literature [1] and also from comparison with results given by large FE model (left part of Fig.1). This method has been applied for the computation of zigzag and armchair SWCNTs: as shown in Fig.2, the developed procedure allows to study the scale effects