Continual approximation of the nanocantilever stain energy

Abstract

Unlike macromechanics, the elastic characteristics of nanoobjects cease to be constants in the usual sense, as volume-averaged coefficients of the constitutive relationships, and become dependent on its size. Therefore, these elastic moduli are called effective. An important aspect of continual nanomechanics is that these moduli are problematic to measure in a classical way, for example, on a nanostand. Instead, they resort to various types of atomistic modeling, in particular the simulation of nanocantilever bending under the absolute displacement of its free edge. As a result, using solid state physics, the displacement of its atoms and the energy change are determined. Verification of the obtained experimental data is important and is a necessary stage for their adequate mathematical description. In this work, the problem of continual description of the bending energy of a nanorod and of its deflection is considered taking into account surface elasticity. Experimental data on nanocantilever bending are approximated in two classes of transcendental functions and a cubic polynomial. The approximation error is estimated and the integral of the functional part of the potential energy of deformation is calculated.

Keywords:

nanocantilerver, surface elasticity, bending energy, effective elastic moduli