Size and surface effects on the mechanical behavior of nanotubes in first gradient elasticity

First gradient elasticity theory considering surface energy is employed to investigate the axisymmetric deformation of circular nanotubes, in which the microstructural and surface effects are taken into account. The governing equilibrium equation is derived and the corresponding analytical solutions are obtained. It is demonstrated that the total stress decreases with the increase of the intrinsic bulk size, while it increases with the increase of the directional surface energy length parameter. These parameters have strong influences on the mechanical behavior of the embedded nanotubes and thus should be considered in the practical analysis of nanostructures.