Semi-Continuum Model for Plate-Like Nanomaterials

Abstract

A semi-continuum model is presented for nano- structured materials possessing a plate-like geometry, such as ultra-thin films. In contrast to the classical continuum theory, the current model directly accounts for the discrete nature in the thickness direction. In- plane Young's modulus is investigated with this model and it is found that the value of the Young 's modulus depends on the number of atom layers in the thickness direction and approaches the asymptote of the bulk value. A nanoplate model is also developed based on this model. Cylindrical bending of a three-atom-layered nanoplate is analyzed with the nanoplate model, the lattice model, and the continuum Mindlin plate theory. It is found that the nanoplate model predicts the deflection with reasonable accuracy while the continuum plate theory with the bulk Young's modulus tends to under predict the deflection. This result indicates that, if the classical continuum theory is used to extract Young's modulus of a nanomaterial, the value will be significantly underestimated.