Equivalent beams for carbon nanotubes

Atomistic-based FE analysis is combined with mechanics of materials to evaluate the geometrical characteristics and elastic properties of beams that possess the same tensile, bending and torsional behavior with carbon nanotubes (CNTs). Using 3D FE analysis and assuming a linear behavior of the C–C bonds, the tensile, bending and torsional rigidities of CNTs are initially derived. Then, for the selected beam, the equivalent dimensions, geometrical constants and elastic moduli are evaluated. Both solid and hollow cylindrical beams are considered. Relations between the equivalent properties and chiral index are obtained for armchair and zigzag nanotubes, thus providing a direct evaluation of the equivalent beam for any CNT of those two types. The comparison between the solid and hollow cylinders shows that the latter is more suitable for use as equivalent beam because its dimensions are much closer to the actual dimensions of the nanotube. The obtained elastic moduli of the equivalent hollow cylinder compare very well with relative results published in the literature.