Poisson ratio effects on the mechanics of auxetic nanobeams

TL;DR

This paper investigates how Poisson ratio influences the mechanical behavior of auxetic and non-auxetic nanobeams using a general nonlocal theory that accounts for strain coupling effects.

Contribution

It introduces a parametric study on Poisson ratio effects on nanobeam mechanics employing a novel nonlocal theory with different attenuation functions for strains.

Findings

Poisson ratio significantly affects nanobeam mechanical behavior.

Auxetic and non-auxetic nanobeams exhibit softening or hardening depending on strain coupling.

The general nonlocal theory reveals Poisson ratio-nonlocal coupling effects.

Abstract

Poisson ratio is an important mechanical property that reveals the deformation patterns of materials. A positive Poisson ratio is a feature of the majority of materials. Some materials, however, display auxetic behaviors (i.e. possess negative Poisson ratios). Indeed, auxetic and non-auxetic materials display different deformation mechanisms. Revealing these differences and their effects on the mechanics of these materials is of a significant importance. In this study, effects of Poisson ratio on the mechanics of auxetic and non-auxetic nanobeams are revealed. A parametric study is provided on effects of Poisson ratio on the static bending and free vibration behaviors of auxetic nanobeams. The general nonlocal theory is employed to model the nonlocal effects. Unlike Eringen nonlocal theory, the general nonlocal theory uses different attenuation functions for the longitudinal and lateral strains. This theory can reveal the Poisson ratio-nonlocal coupling effects on the mechanics of nanomaterials. The obtained results showed that Poisson ratio is an essential parameter for determining mechanical behaviors of nanobeams. It is revealed that auxetic and non-auxetic nanobeams may reflect softening or hardening behaviors depending on the ratio of the nonlocal fields of the longitudinal and lateral strains of the beam.