Surface effects at the nanoscale based on Gurtin’s theory: a review

Abstract

The fields of nanotechnology and nanoscience are full of opportunities and challenges. The needed modification of classical continuum mechanics to account for the dramatically novel characteristics and phenomena determining the mechanical response of nanomaterials/structures remains an ambitious goal pursued by mechanics researchers. The theory of surface elasticity proposed by Gurtin and Murdoch has been shown to be an important tool in theoretical nanomechanics. In this paper, we present an overview of recent advances in application of surface elasticity theory at the nanoscale. In particular, we focus on the elastic and plastic deformation, vibration and buckling, fracture and contact behavior of nanoscale solids from one dimension to three dimensions. We hope that this contribution can provide a valuable insight into nanomechanics analysis methods by taking surface effects into account. The results may help to bridge the gap between conventional mechanics and findings from simulation and experiment, in such areas as multifunctional material and micro-electro-mechanical systems.

Keywords

• nanomaterials
• nanomechanics
• nanostructures
• size effect
• surface effects
• surface elasticity
• surface stress