文献类型：期刊文献

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

作者：Dai, Hui-Hui[1];Wang, Fan-Fan[2];Wang, Jiong[3];Xu, Jian[4]

机构：[1]City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China;[2]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[3]Univ Erlangen Nurnberg, Chair Appl Mech, D-91054 Erlangen, Germany;[4]Tongji Univ, Sch Aerosp Engn & Appl Mech, Shanghai 200092, Peoples R China

年份：2015

卷号：20

期号：1

起止页码：25

外文期刊名：MATHEMATICS AND MECHANICS OF SOLIDS

收录：;EI(收录号：20145100341533);WOS:【SCI-EXPANDED(收录号:WOS:000346175900004)】；

基金：This work was supported by a grant from the Research Grants Council of the HKSAR, China (project number CityU 100911), the National Natural Science Foundation of China (project number 11102068) and the Fundamental Research Funds for the Central Universities (project number WM1214042).

语种：英文

外文关键词：Tube; post-bifurcation solutions; hyperelasticity; asymptotic analysis; imperfection sensitivity

摘要：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.