Nonlocal Modelling of Nanoscopic Structures

Abstract

Various types of nonlocal models have been proposed and extensively utilized to study the mechanical characteristics of nanoscopic structures with varied morphologies. These models are appropriate for describing the behaviour of ultra-small structures, as well as components embedded in nanoscale systems. Furthermore, they can accommodate the discrete nature of nanoscopic structures. The results obtained from the nonlocal models have been successfully compared with those obtained from both experimental and atomistic-based simulation studies. The nonlocal models that have been utilized include the nonlocal beam models, the nonlocal plate and shell models, and the nonlocal models for nanocrystals. The beam models are employed for computational modelling of one-dimensional nanoscopic structures such as nanowires, nanorods, nanofibers and nanotubes. The nonlocal plate models have been applied to study the mechanical characteristics of two-dimensional nanoscopic structures including thin films, nanoplates and nanosheets. The nonlocal shell model has been used to predict the behaviour of shell-like nanoscopic structures. In this chapter, we shall present the basic equations of all these highly complex models, and provide enough details in order to follow the current research materials and modelling future research problems.