Surface effect investigation for static bending of nanowires resting on elastic substrate using Timoshenko beam theory in tandem with the Laplace-Young equation

Abstract

In the present study, an enriched continuum mechanics framework is employed to study the surface effects on bending behavior of silver nanowires (NWs) resting on elastic substrate. The Timoshenko beam theory and the Laplace-Young equation are employed to investigate static behavior of silver NWs lying on Winkler-Pasternak elastic substrate. Three types of boundary conditions are considered as doubly simply supported (S-S), doubly clamped (C-C) and cantilevered (C-F). Analytical solutions are obtained for NWs with surface crystallographic orientation of [001] subjected to a concentrated external force. By defining different normalized contact stiffness, extensive numerical results are carried out to study the influence of effective parameters such as substrate, surface, aspect ratio (L/D) and diameter on the stiffness of NWs. According to the obtained results, the effect of surface and its rate of variation on stiffness of NWs lying on Winkler and Winkler-Pasternak elastic foundation models are more significant in (C-F) type of boundary condition compared to the NWs without foundation. By increasing the modulus of elastic substrate, the effect of shear deformation increases which it is more considerable in (C-C) and (S-S) NWs resting on the Winkler-Pasternak and Winkler substrate models, respectively.

A Levy-type solution for buckling analysis of micro-plates considering the small length scale

“…In the classical continuum theories as an assumption that material distribution is continuously throughout the body, mechanical behaviors of materials could not be precisely predicted due to the lack of material size-effects. The small length scale theories such as nonlocal elasticity theory [3,4], surface elasticity [5] and couple stress theory [6,7] have been developed to eliminate the lack of material size-effects in classical theories. In the classical couple stress theory two separate material length scale parameters exist and it is a very difficult task to experimentally determine two micro-structural material length scale parameters.…”