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

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