Post-buckling analysis of imperfect multi-phase nanocrystalline nanobeams considering nanograins and nanopores surface effects

In this paper, a size-dependent nonlinear higher order refined beam model is developed based on modified couple stress theory. Then, it is applied to investigate post-buckling behavior of multi-phase nanocrystalline silicon nanobeams with geometrical imperfection. Nanocrystalline materials (NcMs) are multi-phase composites with the contribution of nanopores, nanograins and interface phase. Because of experimental observation of strain gradients near interface phase, the nanobeam is modeled via strain gradient based couple stress theory. A micromechanical model based on Mori-Tanaka scheme is employed to incorporate the size of nanograins/nanopores and their surface energies. The post-buckling load-deflection relation is obtained by solving the governing equations having cubic nonlinearity applying Galerkin's method needless of any iteration process. New results show the importance of porosity percentage, nanograins size, geometrical imperfection, couple stress parameter, foundation parameters and surface phase of nanograins/nanopores on nonlinear buckling behavior of NcM nanoscale beams.