Gradient Elasticity Formulations for Micro/Nanoshells

Abstract

Many unexpected applications were found due to superior thermochemomechanical and optoelectromagnetic material properties noted at the nanoscale. Nanoscale structures, such as nanobeams, nanoplates, and nanoshells, were used in many MEMS and NEMS applications. Therefore, understanding the static and dynamic behaviour of them is important for reliable design of micro- and nanodevices. Experimental studies are generally difficult at the nanoscale due to resolution limitation of available nanoprobes. Molecular dynamics (MD) experiments were therefore normally employed to understand nanoscale behavior. Unfortunately, MD studies are limited to small number of atoms and short time intervals. Continuum models were then proposed as an alternative solution method. For mechanical behaviour modelling of nanostructures, the classical continuum mechanics models are not adequate because these models only contain bulk material properties and cannot capture inhomogeneously evolving microstructures and related size effects. To simulate nanostructures, a number of continuum theories have been used to predict the influence of nanoscale effects, such as couple stress and Cosserat theories, nonlocal elasticity, and gradient elasticity. The gradient theory is an extension of classical theory to include additional higher-order spatial derivatives of strain and/or stress, as well as (internal) acceleration. It has been shown to be a powerful alternative tool for dealing with nanostructures without resorting to expensive MD computations.