In this Letter, we combine atomistic simulations and a continuum model, based on the Gurtin-Murdoch theory of surface elasticity, to explain the warp previously observed in $\langle 111\rangle$ gold nanowires. This phenomenon, which is characterized by the spontaneous formation of nonplanar cross sections, is primarily due to the crystallographic orientation of the surfaces that can form around a $\langle 111\rangle$ wire. As a result, the surface stress tensor expressed in the wire cylindrical coordinates basis presents a nondiagonal shear component denoted $S_{\mathrm{\Theta }Z}^S\left(\mathrm{\Theta }\right)$ whose anisotropy (its variation with azimuth $\mathrm{\Theta }$) induces bulk stress and warp in the wire. This result is demonstrated by computing $S_{\mathrm{\Theta }Z}^S$ as a function of $\mathrm{\Theta }$ and by integrating these atomistic inputs into the continuum model. By adopting this approach, the warp found in the atomistic simulations is well reproduced analytically for both Au and Cu nanowires having a circular cross section. This behavior is a fine example of the coupling between surface and bulk stress tensors involving nondiagonal components. An extension of this modeling to the case of nanowires with a hexagonal cross section is discussed.

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• Continuum mechanics
• Elasticity
• Stress
• Nanowires
• Molecular dynamics