Zigzag carbon nanotubes—Molecular/structural mechanics and the finite element method

This paper discusses in details the relation between the bond bending stiffness used in molecular mechanics and the bending stiffness used in structural mechanics for zigzag carbon nanotubes (CNTs). Recent publications assumed the structural bending stiffness EI/a to be a constant and set it equal to the molecular bond bending stiffness C. By developing a closed form expression for the deformation of zigzag CNTs under simple tension, we suggest that the relation between EI/a and C is more complex. It actually depends on the bond bending stiffness C, the torsional angle u and the lattice translational index n. In the limit of an infinite tube radius, which represents a graphene sheet, EI/a tends to C/2. Numerical simulations are also presented that validate the results.