Discontinuous Buckling of Wide Beams and Metabeams

TL;DR

This paper investigates how nonlinearities cause discontinuous buckling in wide elastic beams and metabeams, revealing that increased nonlinearity leads to more negative post-buckling slopes and discontinuous buckling at very slender dimensions.

Contribution

It demonstrates experimentally and numerically that nonlinearities induce discontinuous buckling in wide beams and metabeams, a novel insight into nonlinear elastic stability.

Findings

Discontinuous buckling observed in wide elastic beams and metabeams.

Increased nonlinearity correlates with more negative post-buckling slopes.

Discontinuous buckling occurs in very slender beams, as small as 1-5% slenderness.

Abstract

We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams ---beams made from a mechanical metamaterial--- exhibit discontinuous buckling, an unstable form of buckling where the post-buckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit increasingly negative post-buckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as $1\%$ numerically and $5\%$ experimentally.