Carbon-nanotube geometries: Analytical and numerical results

We investigate carbon-nanotubes under the perspective of geometry optimization. Nanotube geometries are assumed to correspond to atomic configurations which locally minimize Terso -type interaction energies. In the specific cases of so-called zigzag and armchair topologies, candidate optimal configurations are analytically identi ed and their local minimality is numerically checked. In particular, these optimal con gurations do not correspond neither to the classical Rolled-up model [5] nor to the more recent polyhedral model [3]. Eventually, the elastic response of the structure under uniaxial testing is numerically investigated and the validity of the Cauchy-Born rule is confirmed..