Common nonlocal elastic constitutive relation and material-behavior modeling of nanostructures

Abstract

This article reviews conventional nonlocal elasticity constitutive relation which is frequently used for mechanical analyses of nanostructures. It is shown here that since this constitutive relation has been essentially derived based on infinitebody assumption, it cannot consider the nonlocal effects at all points of a nanoscale body accurately. Also, it is shown that although the nonlocal constitutive relations can potentially consider the surface effects, that constitutive relation has been obtained substantially by ignoring those effects. So, it cannot also consider the surface effects accurately. Therefore, the conventional nonlocal constitutive relation generally is not accurate for material-behavior modeling and consequently mechanical analysis of nanostructures. Furthermore, common nonlocal constitutive law is examined in buckling problem of Timoshenko beam-columns to show another limitation of that constitutive law. Finally, some special cases for which that constitutive relation can be used more accurately are proposed.

The nonlocal parameter for three-dimensional nonlocal elasticity analyses of square graphene sheets: An exact buckling analysis

“…They showed that for the Eigen value problem of buckling of rectangular plates based on the nonlocal elasticity, by increasing the half wave numbers, the magnitude of the Eigen value (buckling load) approach zero, which is not physically correct. 4 The same phenomenon was also reported by Naderi and Saidi 38 for the Eigen value buckling problem of nano-beams using the nonlocal Timoshenko beam theory. On the other hand, comparison of the nonlocal results with those of atomistic methods shows that there is an essential dependency between the nonlocal parameter as a material constant with the half wave numbers.…”

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force

“…They considered bilayer thin films in their analysis and used the Heisenberg model to describe the bilayer film structure. Naderi and Saidi 22 developed the nonlocal constitutive equations of nanostructures. They showed that nonlocal theories could not be used in the presence of surface effects.…”