Necking of a hyperelastic solid cylinder under axial stretching: Evaluation of the infinite-length approximation

Fu

doi:10.1016/j.ijengsci.2020.103432

Necking of a hyperelastic solid cylinder under axial stretching: Evaluation of the infinite-length approximation

Fu

Authors

Yibin Fu y.fu@keele.ac.uk

Abstract

A weakly nonlinear analysis is conducted for localized necking of a hyperelastic solid cylinder under axial stretching based on the exact theory of nonlinear elasticity. The amplitude equation derived is shown to be consistent with the one-dimensional model recently proposed by Audoly and Hutchinson (J. Mech. Phys. Solids 97, 2016, 68–91). It is shown that results based on the infinite-length approximation are sufficiently accurate even for cylinders with very moderate length/diameter ratios. In contrast, a weakly nonlinear analysis based on the finite length is only valid for very stubby cylinders and for axial force much closer to its bifurcation value than anticipated.

Acceptance Date	Nov 14, 2020
Publication Date	Feb 1, 2021
Journal	International Journal of Engineering Science
Print ISSN	0020-7225
Publisher	Elsevier
DOI	https://doi.org/10.1016/j.ijengsci.2020.103432
Keywords	Localized necking, Hyperelasticity, Nonlinear analysis, Bifurcation, Stability
Publisher URL	https://www.sciencedirect.com/science/article/abs/pii/S0020722520302196?via%3Dihub