We show that when the Aubry transition occurs in incommensurately distorted structures, the amplitude of the distortions is not necessarily large as suggested by the standard Frenkel-Kontorova mechanical model. By modifying the shape of the potential in such a way that the mechanical force is locally stronger (i.e., increasing the nonlinearities), the transition may occur at a small amplitude of the potential with small distortions. A phason gap then opens, while the phonon spectrum resembles a standard undistorted spectrum at higher energies. This may explain the existence of pinned phases with very small distortions as experimentally observed in charge-density waves.
