%0 Journal Article
%T Selection of hexagonal buckling patterns by the elastic Rayleigh-Taylor instability
%+ Department of Chemical and Biomolecular Engineering
%+ Laboratoire de Mécanique et Génie Civil (LMGC)
%+ Physique et Mécanique des Milieux Divisés (PMMD)
%+ Laboratoire Charles Coulomb (L2C)
%+ Department of Mathematics [University of Arizona]
%+ California Institute of Technology (CALTECH)
%+ Laboratoire de mécanique des solides (LMS)
%A Chakrabarti, Aditi
%A Mora, Serge
%A Richard, Franck
%A Phou, Ty
%A Fromental, Jean-Marc
%A Pomeau, Yves
%A Audoly, Basile
%< avec comité de lecture
%@ 0022-5096
%J Journal of the Mechanics and Physics of Solids
%I Elsevier
%V 121
%P 234 - 257
%8 2018-07-30
%D 2018
%R 10.1016/j.jmps.2018.07.024
%K Plates
%K Stability and bifurcation
%K Elastic material
%K Finite strain
%K Buckling
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-01869797/document
%2 https://hal.science/hal-01869797/file/Art_Mora_al_J.Mech.Phys.Sol._2018.pdf
%L hal-01869797
%U https://hal.science/hal-01869797
%~ X
%~ INSTITUT-TELECOM
%~ CNRS
%~ LMGC
%~ X-LMS
%~ X-DEP
%~ X-DEP-MECA
%~ PARISTECH
%~ L2C
%~ UNIV-PARIS-SACLAY
%~ X-SACLAY
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021