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

Fu

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.

Citation

Fu. (2022). An analytic derivation of the bifurcation conditions for localization in hyperelastic tubes and sheets. Zeitschrift für Angewandte Mathematik und Physik, https://doi.org/10.1007/s00033-022-01748-2

• Acceptance Date: Apr 2, 2022
• Publication Date: May 7, 2022
• Publicly Available Date: May 30, 2023
• Journal: Zeitschrift für angewandte Mathematik und Physik
• Print ISSN: 0044-2275
• Publisher: Springer Verlag
• DOI: https://doi.org/10.1007/s00033-022-01748-2
• Public URL: https://keele-repository.worktribe.com/output/423244
• Publisher URL: https://link.springer.com/article/10.1007/s00033-022-01748-2