A continuum model for brittle nanowires derived from an atomistic description by $Γ$-convergence

Bernd Schmidt, Jiří Zeman

Published 2022-08-08Version 1

Starting from a particle system with short-range interactions, we derive a continuum model for the bending, torsion, and brittle fracture of inextensible rods moving in three-dimensional space. As the number of particles tends to infinity, it is assumed that the rod's thickness is of the same order as the interatomic distance. Fracture energy in the $\Gamma$-limit is expressed by an implicit cell formula, which covers different modes of fracture, including (complete) cracks, folds and torsional cracks. Our approach applies e.g. to atomistic systems with Lennard-Jones-type potentials and is motivated by the research of ceramic nanowires.