Application of an enhanced version of the Eringen differential model to nanotechnology

Nonlocal formulations are currently adopted to assess size effects in nanostructures. The Eringen differential constitutive model, due to its simplicity, is widely used to investigate the size-dependent behavior of beams at nanoscale. Nevertheless this theory provides vanishing size effects in nanobeams under point loads and exhibits stiffening phenomena in nanocantilevers for increasing values of the nonlocal factor. Accordingly, the analysis of structures like nanoactuators is commonly carried out by using more complex constitutive approaches, such as gradient or integral models. A new strategy is outlined in the present paper as a possibly convenient alternative, by equipping the Eringen differential law with an additional term involving the derivative of the axial stress. Effectiveness of the new methodology is tested with reference to simple case studies.