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

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 infinite-body 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.