Selection of hexagonal buckling patterns by the elastic Rayleigh-Taylor instability

被引:27
作者
Chakrabarti, Aditi [1 ,2 ,3 ]
Mora, Serge [1 ,2 ]
Richard, Franck [1 ,2 ]
Phou, Ty [2 ,4 ]
Fromental, Jean-Marc [2 ,4 ]
Pomeau, Yves [5 ]
Audoly, Basile [6 ,7 ,8 ]
机构
[1] Univ Montpellier, Lab Mecan & Genie Civil, 163 Rue Auguste Broussonnet, F-34090 Montpellier, France
[2] CNRS, 163 Rue Auguste Broussonnet, F-34090 Montpellier, France
[3] Lehigh Univ, Dept Chem & Biomol Engn, Bethlehem, PA 18015 USA
[4] Univ Montpellier, Lab Charles Coulomb, 163 Rue Auguste Broussonnet, F-34090 Montpellier, France
[5] Univ Arizona, Dept Math, Tucson, AZ 85721 USA
[6] Ecole Polytech, Lab Mecan Solides, F-91128 Palaiseau, France
[7] CNRS, F-91128 Palaiseau, France
[8] CALTECH, Div Appl Sci & Engn, Pasadena, CA 91125 USA
关键词
Buckling; Elastic material; Finite strain; Plates; Stability and bifurcation; WEAKLY NONLINEAR-ANALYSIS; IMPERFECTION SENSITIVITY; THERMAL-CONVECTION; SPHERICAL-SHELLS; LAYER; STRAIN; BIFURCATION; TRANSITION; SUBSTRATE; BEHAVIOR;
D O I
10.1016/j.jmps.2018.07.024
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
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. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码:234 / 257
页数:24
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