Elastic properties and pressure-induced structural transitions of single-walled carbon nanotubes

The mechanical properties and pressure-induced structural transitions of single-walled carbon nanotubes (SWCNTs) are studied in this paper in the theoretical scheme of the higher order gradient continuum. Both the first- and second-order deformation gradients are involved in the approximation of the deformations of microscale lattice vectors, and the continuum elastic potential is obtained by equating the deformation energy of a representative cell with that of an equivalent volume of the continuum, and thus, the established continuum constitutive model is more reasonable. By setting an appropriate equation as the deformation map from a graphite sheet to an initial undeformed SWCNT, the elastic constants of SWCNTs are obtained by minimizing the energy of a representative cell. The response of SWCNTs under axis-symmetrical loadings can also be obtained by changing the values of the set geometrical parameters. Based on the derived constitutive model, a computational method is developed to study the response of SWCNTs under hydrostatic pressure.