Mechanistic Models for Nanobeams with Surface Stress Effects

In this paper, a mechanistic model for nanobeams with surface energy effects is developed by using a variational formulation. This work is motivated by the unusual response of nanocantilevers predicted by models based on the Young-Laplace equation for surface stress. The governing equation and boundary conditions derived from the variational methods are compared with the governing equations and boundary conditions used in the Young-Laplace models and other formulations. A key difference in the shear force boundary condition is noted. Analytical solutions for simply supported, cantilevered, and fixed-fixed beams are reexamined. It is shown that the unusual behavior of nanocantilevers predicted by the Young-Laplace models is due to the shear force boundary condition used. The current formulation leads to consistent solutions for beams under different boundary conditions.