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. impact of discrete atomic structure on the critical load paramount interest, yet physics insufficiently understood. This study combines experiment and theory to solve that enigma: Phonon dispersion relations are at heart both continuous structures. insight will have an engineering solutions, from nanostructures molecular details prevail, medical stents naturally feature discretized polygonal symmetry.