  Consistently atomistic understanding of the mechanism behind the intriguing
behavior of low-dimensional systems including monatomic chains, hollow tubes,
surface skins, nanocavities, nanowires, and nanograins has long been a high
challenge. This article reports recent progress in this regard. A survey is
presented and then is followed by analytical approaches in terms of local bond
average (LBA) from the perspective of bonding energetics and its functional
dependence on external stimuli of coordination environment and temperature
change. It is shown that the measurable quantities of a specimen can be
functionally correlated to the identities of the representative bonds and their
responses to the external stimuli. It is understood that the shortened and
strengthened bonds between the under-coordinated atoms and the associated local
strain and energy trapping dictate intrinsically the mechanical behavior of
systems with large portion of under-coordinated atoms. The thermal softening of
a substance arises from thermally-induced bond expansion and lattice vibration
that weakens the bonds through the internal energy increase. The competition
between the energy-density-gain and the residual atomic cohesive-energy in the
relaxed surface skin determines intrinsically the mechanical performance of a
mesoscopic specimen, whereas competition between the activation and inhibition
of atomic dislocations dominates extrinsically the yield strength of the
specimen in plastic deformation.
