Finite Deformation Effects of Residual and Strain-Dependent Parts of Surface Stress on Resonant Properties of Metal Nanowires

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.

However, the corresponding analysis has not been done, to-date, for finite deformation kinematics, which is critical in nanowires due to the large surface-stress-driven deformation that the nanowires undergo, particularly for sub-20 nm cross sections.  The attached paper, recently accepted in JMPS, addresses this issue for the first time.  As the paper is long, Section 5 of the paper is the relevant one, where we discuss the methodology we employ and the results; additional commentary is given in the conclusion.  

To summarize the key findings:  (1) The residual surface stress does impact the resonant properties of nanowires under finite deformation kinematics; in fact, the effect can be comparable to or larger than the effect of the strain-dependent part of the surface stress, depending on boundary condition.  (2) Knowledge of the state of deformation in the nanowires is not sufficient to predict their resonant frequencies.  

I should also note that ZP Huang and co-workers have recently shown analytically that the residual surface stress does impact the elastic properties of nanostructures if finite deformation kinematics are considered; portions of this discussion are also on iMechanica.

I certainly welcome any feedback and discussion from the imechanica community regarding the results, or the approach taken to obtain the results.