An analytic derivation of the bifurcation conditions for localization in hyperelastic tubes and sheets

We provide an analytic derivation of the bifurcation conditions for localized bulging in inflated hyperelastic tube arbitrary wall thickness and axisymmetric necking a sheet under equibiaxial stretching. It has previously been shown numerically that condition former problem is equivalent to vanishing Jacobian determinant internal pressure P resultant axial force N, with each them viewed as function azimuthal stretch on inner surface stretch. This equivalence established here analytically. For latter which it recently not given by equal zero, we explain why this case alternative interpretation.