文献类型：期刊文献

英文题名：ANALYTICAL SOLUTIONS FOR THE POST-BUCKLING STATES OF AN INCOMPRESSIBLE HYPERELASTIC LAYER

作者：Dai, Hui-Hui[1,2];Wang, Fan-Fan[3]

机构：[1]City Univ Hong Kong, Dept Math, Kowloon Tong, Hong Kong, Peoples R China;[2]City Univ Hong Kong, Liu Bie Ju Ctr Math Sci, Kowloon Tong, Hong Kong, Peoples R China;[3]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2012

卷号：10

期号：1

起止页码：21

外文期刊名：ANALYSIS AND APPLICATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000300393300002)】；

基金：The authors would like to thank Professor Yibin Fu for pointing out the references [2, 16]. The work described in this paper was fully supported by a grant from the Research Grants Council of HKSAR, China (Project No.: CityU 100807).

语种：英文

外文关键词：Hyperelasticity; buckling; post-bifurcation; asymptotic analysis; analytical solutions

摘要：In this paper, we study the buckling of an incompressible hyperelastic rectangular layer due to compression with sliding end conditions. The combined series-asymptotic expansions method is used to derive two-coupled nonlinear ordinary differential equations (ODEs) governing the leading order of the axial strain W and shear strain G. Linear analysis yields the critical stress values of buckling. For the nonlinearly coupled system, by introducing a small parameter, the approximate analytical solutions for post-buckling deformations are obtained by using the method of multiple scales. The amplitude of buckling is expressed explicitly by the aspect ratio, the incremental dimensionless engineering stress and the mode of buckling. To the authors' best knowledge, it is the first time that such an analytical formula is obtained within the framework of two-dimensional field equations for nonlinearly elastic materials (including both geometric and material non-linearity). Numerical computations of the coupled system are also carried out. Good agreements between the numerical and analytical solutions are found when the amplitudes of buckling are moderate. Finally, some energy analysis regarding material failure is made.