A review on the mechanics of functionally graded nanoscale and microscale structures

This article reviews, for the first time, the mechanical behaviour of functionally graded structures at small-scale levels. Functionally graded nanoscale and microscale structures are an advanced class of small-scale structures with promising applications in nanotechnology and microtechnology. Recent advancements in fabrication techniques such as the advent of powder metallurgy, made it possible to tailor the mechanical properties of structures at small-scale levels by fabricating them out of functionally layerwise mixture of two or more materials; this class of structures, called functionally graded (FG), can be used to improve the performance of many microelectromechanical and nanoelectromechanical systems due to their spatially varying mechanical and electrical properties. The increasing number of published papers on the mechanical behaviours of FG nanoscale and microscale structures, such as their buckling, vibration and static deformation, employing scale-dependent continuum-based models, has proved their importance in academia and industry. Generally, the nonlocal elasticity-based models have been used for FG nanostructures whereas modified versions of couple stress and strain gradient theories have been utilised for FG microstructures. In this review paper, first, various scale-dependent theories of elasticity for FG small-scale structures are explained. Then, available studies on the mechanical behaviours of FG nanostructures such as FG nanobeams and nanoplates are described. Moreover, available investigations on the mechanics of microstructures made of FG materials are reviewed. In addition, in each case, the most important findings of available studies are reviewed. Finally, further possible applications of advanced continuum mechanics to FG small-scale structures are inspired. (C) 2018 Elsevier Ltd. All rights reserved.