A Fully Gradient Model for Euler-Bernoulli Nanobeams

A fully gradient elasticity model for bending of nanobeams is proposed by using a nonlocal thermodynamic approach. As a basic theoretical novelty, the proposed constitutive law is assumed to depend on the axial strain gradient, while existing gradient elasticity formulations for nanobeams contemplate only the derivative of the axial strain with respect to the axis of the structure. Variational equations governing the elastic equilibrium problem of bending of a fully gradient nanobeam and the corresponding differential and boundary conditions are thus provided. Analytical solutions for a nanocantilever are given and the results are compared with those predicted by other theories. As a relevant implication of applicative interest in the research field of nanobeams used in nanoelectromechanical systems (NEMS), it is shown that displacements obtained by the present model are quite different from those predicted by the known gradient elasticity treatments.