Softening of the Euler Buckling Criterion under Discretization of Compliance

The classical buckling problem, studied by Euler himself, is still important in many fields where macroscale or nanoscale structures may fail under compression. The impact of discrete or atomic structure on the critical buckling load is of paramount interest, yet the physics is still insufficiently understood. This study combines experiment and theory to solve that enigma: Phonon dispersion relations are at the heart of the physics of the buckling of both discrete and continuous structures. This insight will have an impact on engineering solutions, from nanostructures where molecular details prevail, to medical stents that naturally feature discretized polygonal symmetry.