Pitchfork and octopus bifurcations in a hyperelastic tube subjected to compression : Analytical post-bifurcation solutions and imperfection sensitivity

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)25-52
Journal / PublicationMathematics and Mechanics of Solids
Volume20
Issue number1
StatePublished - 16 Jan 2015

Abstract

This paper studies the axisymmetric deformations of a nonlinearly hyperelastic tube subjected to axial compression. We aim at investigating the critical buckling stresses and modes, deriving the analytical solutions for the post-bifurcation deformations and studying the imperfection sensitivity. For a general isotropic hyperelastic tube, a coupled series-asymptotic method is utilized to derive two simplified model equations with specified constraints on the tube geometry. Then, we specialize to the Blatz-Ko material. With greased end conditions, through linear bifurcation analysis, we obtain the critical stress values and the corresponding mode numbers. The analytical solutions for the post-bifurcation states are constructed by the multiple scales method. By examining the solution behavior in the post-bifurcation regime, it is found that a thick tube could be considerably softer than a thin one. The singularities theory is used to consider the imperfection sensitivity, which reveals the mechanism is the existence of two modes corresponding to the same critical stress. Numerical solutions are also obtained which confirm the validity of the analytical solutions.

Research Area(s)

  • asymptotic analysis, hyperelasticity, imperfection sensitivity, post-bifurcation solutions, Tube

Citation Format(s)

Pitchfork and octopus bifurcations in a hyperelastic tube subjected to compression : Analytical post-bifurcation solutions and imperfection sensitivity. / Dai, Hui-Hui; Wang, Fan-Fan; Wang, Jiong; Xu, Jian.

In: Mathematics and Mechanics of Solids, Vol. 20, No. 1, 16.01.2015, p. 25-52.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalNot applicablepeer-review