  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.
