Discontinuous Buckling of Wide Beams and Metabeams

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.

5 pages, 5 figures. See http://corentincoulais.wordpress.com/movies/metabeam-movies/ for movies. 2 pages of SI

References in corpus (3)

• Programmable Mechanical Metamaterials
• Unfolding the Sulcus
• The physics of antimatter induced fusion and thermonuclear explosions

Cited by in corpus (14)

• Combinatorial Design of Textured Mechanical Metamaterials
• Multi-step self-guided pathways for shape-changing metamaterials
• A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials
• Interfacial tension and a three-phase generalized self-consistent theory of non-dilute soft composite solids
• A Newton Solver for Micromorphic Computational Homogenization Enabling Multiscale Buckling Analysis of Pattern-Transforming Metamaterials
• Buckling of self-assembled colloidal structures
• Wang tiles enable combinatorial design and robot-assisted manufacturing of modular mechanical metamaterials
• Properties of compressible elastica from relativistic analogy
• Drop-on-coilable-fibre systems exhibit negative stiffness events and transitions in coiling morphology
• The Effects of Free Edge Interaction-Induced Knotting on the Buckling of Monolayer Graphene
• Emergent Nonlocal Combinatorial Design Rules for Multimodal Metamaterials
• Prospecting for Pluripotency in Metamaterial Design
• Inverted and programmable Poynting effects in metamaterials
• Growth of a viscoplastic blister underneath an elastic sheet