Warping caused by surface elasticity in a nanowire under torsion

By combining molecular statics simulations and continuum mechanics-based modeling, we show in this paper that the torsion of a $\ensuremath{\langle}001\ensuremath{\rangle}$ single-crystal copper nanowire with a circular cross section gives rise to a warp, i.e., to a displacement field along the wire axis that renders the cross section nonplanar. This behavior, which is in apparent contradiction with what is predicted by continuum mechanics for an isotropic cylinder, can be well explained if we take into account the elastic response of the wire lateral surface. The latter is characterized by the anisotropy of the surface elastic constants and, more specifically in the case of torsion, by the surface shear constant ${C}_{44}^{S}$ whose strength as a function of the local orientation of the lateral surface is estimated independently from atomistic calculations on slabs presenting different vicinal surfaces. The solution of the torsion problem is then obtained by adopting a semi-inverse method in the framework of the finite strain theory in linear elasticity with Gurtin-Murdoch boundary conditions linking surface stress and bulk stress. It is shown that such an approach is well suited to explain quantitatively the warp obtained in our atomistic simulations and to prove the preponderant role played by the surface elastic constant ${C}_{44}^{S}$.