Atomic to continuum passage for nanotubes. Part II: error estimates

We consider deformations in R3 of an infinite general nanotube of atoms where each atom interacts with all the other through a two-body potential. We compute the effect of an external force applied to the nanotube. At the equilibrium, the positions of the atoms satisfy an Euler-Lagrange equation. For large classes of potentials (including Lennard-Jones potential) and under suitable stability assumptions, we prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting, but no bending. We establish an error estimate between the discrete and the continuous solution based on a Saint-Venant principle that the reader can find in the companion paper [25] (part I). AMS Classification: 35J15, 49M25, 65L70, 74A60, 74G15, 82B21.