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

Fu

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.

Citation

Fu. (2021). Necking of a hyperelastic solid cylinder under axial stretching: Evaluation of the infinite-length approximation. International Journal of Engineering Science, https://doi.org/10.1016/j.ijengsci.2020.103432

• 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