%0 Journal Article
%T Buckling of a spinning elastic cylinder: linear, weakly nonlinear and post-buckling analyses
%+ Laboratoire de Mécanique et Génie Civil (LMGC)
%+ Laboratoire de mécanique des solides (LMS)
%+ California Institute of Technology (CALTECH)
%+ Department of Mathematics [University of Arizona]
%+ Physique et Mécanique des Milieux Divisés (PMMD)
%A Richard, Franck
%A Chakrabarti, Aditi
%A Audoly, Basile
%A Pomeau, Yves
%A Mora, Serge
%< avec comité de lecture
%@ 1364-5021
%J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
%I Royal Society, The
%V 474
%N 2216
%P 20180242
%8 2018-08-01
%D 2018
%R 10.1098/rspa.2018.0242
%K Stability and bifurcation
%K Asymptotic analysis
%K Beams and columns
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]Journal articles
%X An elastic cylinder spinning about a rigid axis buckles beyond a critical angular velocity, by an instability driven by the centrifugal force. This instability and the competition between the different buckling modes are investigated using analytical calculations in the linear and weakly nonlinear regimes, complemented by numerical simulations in the fully post-buckled regime. The weakly nonlinear analysis is carried out for a generic incompressible hyperelastic material. The key role played by the quadratic term in the expansion of the strain energy density is pointed out: this term has a strong effect on both the nature of the bifurcation, which can switch from supercritical to subcritical, and on the buckling amplitude. Given an arbitrary hyperelastic material, an equivalent shear modulus is proposed, allowing the main features of the instability to be captured by an equivalent neo-Hookean model.
%G English
%2 https://hal.science/hal-01869788/document
%2 https://hal.science/hal-01869788/file/Art_Mora_al_Proc.Roy.Soc.A_2018.pdf
%L hal-01869788
%U https://hal.science/hal-01869788
%~ X
%~ INSTITUT-TELECOM
%~ CNRS
%~ LMGC
%~ X-LMS
%~ X-DEP
%~ X-DEP-MECA
%~ PARISTECH
%~ UNIV-PARIS-SACLAY
%~ X-SACLAY
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021