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The purpose of this note is to establish two continuum theories for thebending and torsion of inextensible rods as $\Gamma$-limits of 3D atomisticmodels. In our derivation we study simultaneous limits of vanishing rodthickness $h$ and interatomic distance $\varepsilon$. First, we set up a noveltheory for ultrathin rods composed of finitely many atomic fibres($\varepsilon\sim h$), which incorporates surface energy and new discrete termsin the limiting functional. This can be thought of as a contribution to themechanical modelling of nanowires. Second, we treat the case where$\varepsilon\ll h$ and recover a nonlinear rod model $-$ the modern version ofKirchhoff's rod theory.

A bending-torsion theory for thin and ultrathin rods as a $\Gamma$-limit of atomistic models