Selection of hexagonal buckling patterns by the elastic Rayleigh-Taylor instability. (December 2018)

• Record Type: Journal Article
• Authors: Chakrabarti, Aditi; Mora, Serge; Richard, Franck; Phou, Ty; Fromental, Jean-Marc; Pomeau, Yves; Audoly, Basile
• Is Part Of: Journal of the mechanics and physics of solids. Volume 121(2018)
• Page Start: 234
• Page End: 257
• Publication Date: 2018-12
• Subjects: A. Buckling -- B. Elastic material -- B. Finite strain -- B. Plates -- C. Stability and bifurcation; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2018.07.024
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: We investigate the non-linear buckling patterns produced by the elastic Rayleigh-Taylor instability in a hyper-elastic slab hanging below a rigid horizontal plane, using a combination of experiments, weakly non-linear expansions and numerical simulations. Our experiments reveal the formation of hexagonal patterns through a discontinuous transition. As the unbuckled state is transversely isotropic, a continuum of linear modes become critical at the first bifurcation load: the critical wavevectors form a circle contained in a horizontal plane. Using a weakly non-linear post-bifurcation expansion, we investigate how these linear modes cooperate to produce buckling patterns: by a mechanism documented in other transversely isotropic structures, three-modes coupling make the unbuckled configuration unstable with respect to hexagonal patterns by a transcritical bifurcation. Stripe and square patterns are solutions of the post-bifurcation expansion as well but they are unstable near the threshold. These analytical results are confirmed and complemented by numerical simulations.