Mechanics of carbon-coated silicon nanowire via second strain gradient theory

Abstract

The phenomena of surface, interface, and size effects are the determinative factors in the prediction of the mechanical behavior of multiphase nanowires. The interatomic bond lengths and charge density distribution associated with the surface and interface layers of the relaxed configuration of such nanostructures, in the absence of any external loadings, differ from those of the bulk remarkably. Second strain gradient theory due to its competency in capturing the above mentioned effects will be employed to examine the relaxation of carbon-coated silicon nanowire, carbon nanoshell, and silicon nanowire. Using this theory their effective Young’s modulus will also be estimated. To this end, the mathematical framework of second strain gradient theory will be presented in cylindrical coordinate system. For further illustrations, the Lamé type problem for a carbon nanotube where its inner and outer surfaces have strong, weak, and no interactions will be considered. Moreover, the size-dependent stress concentration phenomenon associated with an unbounded carbon plate weakened by a circular hole under remote biaxial loading is addressed. For verification of the theoretical treatment, the relaxation problems will be reexamined by employing atomistic simulation using LAMMPS and some suitable potentials.