Supercritical and subcritical buckling bifurcations for a compressible hyperelastic slab subjected to compression |
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| Institution: | 1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, PR China;2. Department of Mathematics, Shaoxing University, Shaoxing 312000, Zhejiang, PR China;1. Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany;2. CNRS, UMR 7190, Institut Jean Le Rond d?Alembert, F-75005 Paris, France;3. UPMC Univ Paris 06, UMR 7190, Institut Jean Le Rond d?Alembert, F-75005 Paris, France;1. Université de Bretagne Sud, UBS – Institut Dupuy de Lôme, Centre de Recherche, Rue de Saint Maudé, BP92116, 56321 Lorient Cedex, France;2. Department of Mechanical Engineering, Texas A&M University, Forsyth Chair in Mechanical Engineering, TX 77843, USA;1. Department of Mechanical Engineering, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4L7;2. Aluminum Materials Consultants, 106 Nicholsons Point Road, Bath, Ontario, Canada K0H 1G0 |
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| Abstract: | We study the buckling bifurcation of a compressible hyperelastic slab under compression with sliding–sliding end conditions. The combined series-asymptotic expansions method is used to derive the simplified model equations. Linear bifurcation analysis yields the critical stress value of buckling, which gives a non-linear correction to the classical Euler buckling formula. The correction is due to the geometrical non-linearities coupled with the material non-linearities. Then through non-linear bifurcation analysis, the approximate analytical solutions for the post-buckling deformations are obtained. The amplitude of buckling is expressed explicitly in terms of the aspect ratio, the incremental dimensionless engineering stress, the mode of buckling and the material constants. Most importantly, we find that both supercritical and subcritical buckling could occur for compressible materials. The bifurcation type depends on the material constants, the geometry of the slab and the mode numbers. |
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| Keywords: | Buckling Bifurcation Compressible material Hyperelasticity |
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