A Bending-Torsion Theory for Thin and Ultrathin Rods as a [math]-Limit of Atomistic Models

Multiscale Modeling &Simulation, Volume 21, Issue 4, Page 1717-1745, December 2023.
Abstract. The purpose of this note is to establish two continuum theories for the bending and torsion of inextensible rods as [math]-limits of three-dimensional atomistic models. In our derivation we study simultaneous limits of vanishing rod thickness [math] and interatomic distance [math]. First, we set up a novel theory for ultrathin rods composed of finitely many atomic fibers ([math]), which incorporates surface energy and new discrete terms in the limiting functional. This can be thought of as a contribution to the mechanical modelling of nanowires. Second, we treat the case where [math] and recover a nonlinear rod model—the modern version of Kirchhoff’s rod theory.