Yu, X and Fu, Y ORCID: https://orcid.org/0000-0002-9617-0420 (2022) An analytic derivation of the bifurcation conditions for localization in hyperelastic tubes and sheets. Zeitschrift für angewandte Mathematik und Physik, 73 (3).

[img] Text
yu-fu-2022-zamp.pdf - Accepted Version
Restricted to Repository staff only until 7 May 2023.
Available under License Creative Commons Attribution Non-commercial.

Download (395kB)

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.

Item Type: Article
Additional Information: Copyright © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG The final version of this article and all relevant information related to it, including copyrights, can be found on the publisher website.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 25 May 2022 12:23
Last Modified: 25 May 2022 12:23
URI: https://eprints.keele.ac.uk/id/eprint/10957

Actions (login required)

View Item View Item