Size effects of the bending stiffness of nanowires

This paper studies the size effect in the transverse deformation of nanowires or nanoropes subjected to flexural bending. Based on the classic strain-gradient theory, a continuum approach is proposed, in which the strain energy was expressed in terms of the linear strains and strain gradients, and two additional phenomenological internal parameters were introduced. The governing equation for the flexural deformation of the nanowires was derived according to the principle of minimum potential energy. In particular, the deformations of the nanowires under two support conditions were determined explicitly, i.e., a cantilever nanowire and a fixed nanowire. Numerical examples were demonstrated to indicate the dependence of the effective modulus and bending stiffness upon the nanowire diameter and aspect ratio. The predictions given by the present model are consistent very well with the experimental measurements reported in the recent literature. The proposed model can be further used to explain the size effect in other properties of nanowires such as dynamics and thermal properties, among others.