**Modified beam theories for bending properties of nanowires considering
surface/intrinsic effects and axial extension effect**

HF Zhan and YT Gu, JOURNAL OF APPLIED PHYSICS, 111, 084305 (2012).

DOI: 10.1063/1.3703673

Several studies of the surface effect on bending properties of a
nanowire (NW) have been conducted. However, these analyses are mainly
based on theoretical predictions, and there is seldom integration study
in combination between theoretical predictions and simulation results.
Thus, based on the molecular dynamics (MD) simulation and different
modified beam theories, a comprehensive theoretical and numerical study
for bending properties of nanowires considering surface/intrinsic stress
effects and axial extension effect is conducted in this work. The
discussion begins from the Euler-Bernoulli beam theory and Timoshenko
beam theory augmented with surface effect. It is found that when the NW
possesses a relatively small cross-sectional size, these two theories
cannot accurately interpret the true surface effect. The incorporation
of axial extension effect into Euler-Bernoulli beam theory provides a
nonlinear solution that agrees with the nonlinear-elastic experimental
and MD results. However, it is still found inaccurate when the NW cross-
sectional size is relatively small. Such inaccuracy is also observed for
the Euler-Bernoulli beam theory augmented with both contributions from
surface effect and axial extension effect. A comprehensive model for
completely considering influences from surface stress, intrinsic stress,
and axial extension is then proposed, which leads to good agreement with
MD simulation results. It is thus concluded that, for NWs with a
relatively small cross-sectional size, a simple consideration of surface
stress effect is inappropriate, and a comprehensive consideration of the
intrinsic stress effect is required. (C) 2012 American Institute of
Physics. **http://dx.doi.org/10.1063/1.3703673**

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