Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures

Internal Length Gradient (ILG) Material Mechanics Across Scales and Disciplines

“…A most recent excellent overview on the application of gradient theory to model a large number of mechanical characteristics of nanoscopic materials and objects can be found in [156] where an extensive list of references on the topic is also provided. It is interesting to note that in this overview -with a variety of new results and nanotechnology applications -both stress gradients and strain gradients in the form of Laplacians are used according to the author's earlier suggestion [6a].…”

“…For consistency, we are also assuming that ( ) = ( ) r r f r f e . Then, the governing differential equation for the radial displacement becomes [151][152][153][154][155][156]…”

On the solution of the purely nonlocal theory of beam elasticity as a limiting case of the two-phase theory

“…Since nonlocal elasticity naturally leads to integrodifferential equations whose solution is most often impractical, an equivalent differential nonlocal model (EDNM) was developed in [6]. In such form, nonlocal elasticity has been extensively applied to study elastodynamics of beams and shells as described in the recent review [4] and with special emphasis on the application to nanostructures [29]. Generally, EDNM leads to interesting mechanical effects, such as increased deflections and decreased buckling loads and natural frequencies (softening effect), when compared to classical elasticity.…”

Study of electric conduction mechanisms in bismuth silicate nanofibers

“…Different techniques have been adopted to synthesize bismuth silicate nanostructures such as solution phase synthesis 3 , hydrothermal, interfacial polymerization method and electrospinning 4,5 . Nanoscale materials have exclusive properties depending on their low dimensions and large surface area as compared to their bulk equivalents 6 . Among all reported nanostructured materials; one dimensional (1D) nanofibers are most common in electric device fabrications due to their large surface to volume ratio and relatively high crystallinity 7 .…”