  Euler solved the problem of the collapse of tall thin columns under
unexpectedly small loads in 1744. The analogous problem of the collapse of
circular elastic rings or tubes under external pressure was mathematically
intractable and only fully solved recently. In the context of carbon nanotubes,
an additional phenomenon was found experimentally and in atomistic simulations
but not explained: the collapse pressure of smaller diameter tubes deviates
below the continuum mechanics solution [Torres-Dias et al., Carbon 123, 145
(2017)]. Here, this deviation is shown to occur in discretized straight columns
and it is fully explained in terms of the phonon dispersion curve. This reveals
an unexpected link between the static mechanical properties of discrete systems
and their dynamics described through dispersion curves.
