Postbuckling analysis of hyperelastic thick tube

In recent years, mechanical instabilities of soft materials have been substantially investigated and utilized. Though tube structures are widely used and instabilities of thin-walled tubes are well studied, postbuckling behavior of hyperelastic thick tubes is elusive. It is well known that exact solutions of postbuckling are hard to obtain, especially for structures under three-dimensional finite deformation. In this presentation, we conduct buckling and postbuckling analysis for hyperelastic thick tubes undergoing finite deformation. We will briefly introduce the asymptotic expansion method for buckling and weakly postbuckling of elastic bodies and apply this theory to thick tubes. Our analytical results are validated by finite element simulations. As a result, a long tube prefers the Euler buckling mode, while a short tube prefers the barreling mode. Depending on the geometry, three kinds of postbuckling paths, including increasing force, snap-through and snap-back, are discovered. We summarize our results in two phase diagrams of buckling and postbuckling with respect to geometric parameters, which provide guidelines for utilization of tube structures.