There has recently been a great deal of discussion on imechanica regarding the effects of surface stress on the resonant properties of nanostructures such as nanowires.  The controversy has revolved around the strain-independent part of the surface stress, which can be shown, i.e. by Gurtin et al. APL 1976, 529-530, or by Lu et al, PRB 2005, 085405, to have no effect on the resonant frequency of the nanobeam.  The reason is because in taking the moment, and differentiating the moment to get the beam equation of motion, the strain-independent part of the surface stress drops out as it is constant, while the strain-dependent (surface elastic) part survives the differentiation.

Abstract of paper recently accepted for publication in Journal of Applied Physics:

Nanoscale materials, including thin films, quantum dots, nanowires, nanobelts, etc – are all structurally unique because they have a relatively high ratio of surface area to volume ratio.  This increase in surface area to volume ratio is important for nanomaterials because wide and unexpected variations in mechanical and other physical properties, such as thermal, electrical and optical, have been found to scale in some proportion to increase in surface area to volume ratio. The critical impact of this is that standard continuum relations, which do not account for size-dependence or the discrete nature of atomistic surfaces, are no longer valid at the nanometer length scale.  

Hello All:

I'm interested in learning more about material instability, for example the localization criterions of Hill (1962) and Rudnicki and Rice (1975).  I also am aware of work by Rice (1976), in which a perturbation is made to the displacement field in the form of a plane harmonic wave, resulting in a strong ellipticity instability condition that looks like Det(Q), where Q = c_ijkl + Sigma_jk, i.e. a competition between material softening and stress increase determines the instability.  Furthermore, this stability criterion is developed assuming an infinite body.

We present atomistic simulations of the tensile and compressive loading of single crystal FCC nanowires with <100> and <110> orientations to study the propensity of the nanowires to deform via twinning or slip.  By studying the deformation characteristics of three FCC materials with disparate stacking fault energies (gold, copper and nickel), we find that the deformation mechanisms in

We present a surface Cauchy-Born approach to modeling FCC metals with nanometer scale dimensions for which surface stresses contribute significantly to the overall mechanical response. The model is based on an extension of the traditional Cauchy-Born theory in which a surface energy term that is obtained from the underlying crystal structure and governing interatomic potential is used to augment the bulk energy.