The stress field in a pulled cork and some subtle points in the semi-inverse method of nonlinear elasticity

TL;DR

This paper investigates the stress field in a pulled cork modeled as an incompressible hyperelastic material, revealing secondary deformation fields and suggesting an optimal method for cork extraction involving combined axial and twisting forces.

Contribution

It introduces explicit examples of secondary deformation fields in nonlinear elasticity and analyzes their emergence under different strain-energy models, providing insights into cork-pulling mechanics.

Findings

Secondary deformation fields are activated by normal stress differences.

Combining axial force with a twisting moment improves cork removal.

Explicit solutions are provided for neo-Hookean, generalized neo-Hookean, and Mooney-Rivlin models.

Abstract

In an attempt to describe cork-pulling, we model a cork as an incompressible rubber-like material and consider that it is subject to a helical shear deformation superimposed onto a shrink fit and a simple torsion. It turns out that this deformation field provides an insight into the possible appearance of secondary deformation fields for special classes of materials. We also find that these latent deformation fields are woken up by normal stress differences. We present some explicit examples based on the neo-Hookean, the generalized neo-Hookean and the Mooney-Rivlin forms of the strain-energy density. Using the simple exact solution found in the neo-Hookean case, we conjecture that it is advantageous to accompany the usual vertical axial force by a twisting moment, in order to extrude a cork from the neck of a bottle efficiently. Then we analyse departures from the neo-Hookean behaviour by exact and asymptotic analyses. In that process, we are able to give an elegant and analytic example of secondary (or latent) deformations in the framework of nonlinear elasticity.