Three-dimensional postbuckling analysis of thick hyperelastic tubes

While the buckling of tubes under axial compression has been extensively studied, the post-buckling behavior of thick tubes remains elusive. In this paper, we conduct three-dimensional buckling and postbuckling analysis for thick hyperelastic tubes subjected to axial compression under finite deformation by the asymptotic expansion method. Our theoretical results successfully predict the deformation and stress-strain curves of buckled tubes near the critical loading, which are well validated by finite element analysis. Depending on the geometry, three kinds of post-buckling paths, including continuous buckling, snap-through and snap-back, are discovered. We summarize our results in two phase diagrams of the critical stretch for the onset of buckling and postbuckling paths with respect to the geometric parameters. In particular, we have observed that the postbuckling response can undergo a complex transition among different types of postbuck-ling paths, including continuous buckling, snap-through and snap-back, which is attributed to the competition between two modes of deformation, i.e., global deformation and local distortion. When a tube is long and thick, it prefers global deformation, and its cross section remains almost a plane after buckling, whereas when a tube is relatively short and relatively thin, it prefers local distortion and its cross section does not remain a plane any more after buckling. Our work provides understanding and insights into the buckling and postbuckling of thick tubes, and bridges the knowledge gap between postbuckling of thick columns and tubes.

Automated summary

In this paper, three-dimensional buckling and postbuckling analysis for thick hyperelastic tubes under axial compression and finite deformation are conducted using the asymptotic expansion method. The theoretical results successfully predict the deformation and stress-strain curves near critical loading, validated by finite element analysis. Three types of post-buckling paths, including continuous buckling, snap-through, and snap-back, are discovered, and phase diagrams summarizing the critical stretch for buckling onset and postbuckling paths are presented. The competition between global deformation and local distortion determines the complex transition among different types of postbuckling responses.