Multiscale Modeling of Surface Effects on the Mechanical Behavior and Properties of Nanowires

Abstract

Surface effects have recently been recognized as having the dominant effect on the mechanical behavior and properties of nanowires. Understanding these effects will be critical, in particular for the accurate design and functionalization of future nanowire-based nanoelectromechanical systems, including sensors, resonators and actuators. The purpose of this chapter is therefore to overview a recently developed multiscale continuum model, the surface Cauchy-Born model, which was developed to study nanomaterials where surface effects such as surface stresses are expected to contribute significantly to the mechanical response. The approach is based upon a simple extension to Cauchy-Born theory, in which continuum properties such as stress and stiffness are obtained for a given material and crystal structure directly from an underlying atomistic potential. In particular, by explicitly accounting for differences in energy for both bulk and surface atoms, we develop a variational formulation that leads to a nanomechanical boundary value problem that can be solved using standard nonlinear finite element methods for displacements, stresses and strains while naturally accounting for the effects of atomistic surface stresses. Finite element calculations using the proposed surface Cauchy-Born model demonstrate how surface stresses cause variations in the resonant frequencies of silicon nanowires as compared to those expected from continuum beam theory, and emphasize the importance of nonlinear elasticity in understanding and capturing the resonant frequency variations