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

Softening of the Euler buckling criterion under discretisation of compliance