Nonlinear finite element modeling of large deformation of nanobeams

Abstract

In this article, the finite element method is utilized to understand the bending response of both straight and tapered nanowires under large deformation. The force field caused by the residual surface stress is applied in the nanowire longitudinal direction and is formulated accordingly. Then, a finite element code is developed to analyze the large bending responses of the nanobeam in three different boundary conditions. As expected, the cantilever nanowire behaves softly under the positive surface stress and rigidly when the surface stress is negative. However, the simply supported and fixed–fixed nanobeams act like a more rigid beam for $$\sigma _0 >0$$ and present softer behavior for $$\sigma _0 <0$$ . In addition, in the high value of forces in the cantilever beam, for which the deformation becomes large, the curvature tends to significantly increase, and the effect of surface stress disappears. Bending of tapered nanobeams is also analyzed the same way.