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Consistently atomistic understanding of the mechanism behind the intriguingbehavior of low-dimensional systems including monatomic chains, hollow tubes,surface skins, nanocavities, nanowires, and nanograins has long been a highchallenge. This article reports recent progress in this regard. A survey ispresented and then is followed by analytical approaches in terms of local bondaverage (LBA) from the perspective of bonding energetics and its functionaldependence on external stimuli of coordination environment and temperaturechange. It is shown that the measurable quantities of a specimen can befunctionally correlated to the identities of the representative bonds and theirresponses to the external stimuli. It is understood that the shortened andstrengthened bonds between the under-coordinated atoms and the associated localstrain and energy trapping dictate intrinsically the mechanical behavior ofsystems with large portion of under-coordinated atoms. The thermal softening ofa substance arises from thermally-induced bond expansion and lattice vibrationthat weakens the bonds through the internal energy increase. The competitionbetween the energy-density-gain and the residual atomic cohesive-energy in therelaxed surface skin determines intrinsically the mechanical performance of amesoscopic specimen, whereas competition between the activation and inhibitionof atomic dislocations dominates extrinsically the yield strength of thespecimen in plastic deformation.

The thermo-mechanical behavior of low-dimensional materials