An explicit solution for bending of nanowires lying on Winkler–Pasternak elastic substrate medium based on the Euler–Bernoulli beam theory

In the present work, we study the influence of both elastic substrate and surface effects due to nanoscale on the bending response of silver nanowires (NWs). For this purpose, the Euler–Bernoulli beam theory in tandem with the Laplace–Young equation is employed with a Winkler–Pasternak elastic type substrate medium. Corresponding analytical solutions are derived in this context for the first time when considering external concentrated forces and different types of boundary conditions. Extensive numerical applications are carried out to study the sensibility of different parameters related to the substrate, crystallographic directions ([0 0 1] and [1 1 1]) and diameters on the apparent rigidity of silver NWs. For NWs lying on Winkler and Pasternak elastic foundations, surface effect makes the NWs stiffer or softer as compared to the bulk material, depending on the type of boundary conditions.