Weakly nonlinear analysis of localized bulging of an inflated hyperelastic tube of arbitrary wall thickness

Abstract

A weakly nonlinear analysis is conducted for localized bulging of an inflated hyperelastic cylindrical tube of arbitrary wall thickness. Analytical expressions are obtained for the coefficients in the amplitude equation despite the fact that the primary deformation is inhomogeneous and the incremental governing equations have variable coefficients. It is shown that for each value of wall thickness a localized bulging solution does indeed bifurcate sub-critically from the primary solution for almost all values of fixed axial force or fixed axial stretch for which the bifurcation condition is satisfied, as reported in all previous experimental studies, but there also exist extreme cases of fixed axial stretch for which localized bulging gives way to localized necking. Validation is carried out by comparing with results obtained under the membrane assumption and with fully numerical simulations based on Abaqus. It is shown that even for thin-walled tubes the membrane approximation becomes poorer and poorer as the tube is subjected to increasingly larger and larger axial stretch or force prior to inflation.