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

Fu

doi:10.1007/s00033-022-01748-2

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

Fu

Authors

Yibin Fu y.fu@keele.ac.uk

Abstract

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

Acceptance Date	Apr 2, 2022
Publication Date	May 7, 2022
Journal	Zeitschrift für angewandte Mathematik und Physik
Print ISSN	0044-2275
Publisher	Springer Verlag
DOI	https://doi.org/10.1007/s00033-022-01748-2
Publisher URL	https://link.springer.com/article/10.1007/s00033-022-01748-2