Torsion instability of soft solid cylinders

TL;DR

This paper investigates the torsion instability in soft cylinders under combined axial stretch and torsion, using incremental elastic theory and numerical methods to analyze stability and surface wrinkling phenomena.

Contribution

It introduces a comprehensive theoretical and numerical framework for analyzing torsion instability in soft cylinders with finite strains and axial stretch.

Findings

Identifies critical conditions for surface wrinkling under torsion.

Shows influence of material parameters on stability thresholds.

Develops a robust numerical method for stability analysis.

Abstract

The application of pure torsion to a long and thin cylindrical rod is known to provoke a twisting instability, evolving from an initial kink to a knot. In the torsional parallel-plate rheometry of stubby cylinders, the geometrical constraints impose zero displacement of the axis of the cylinder, preventing the occurrence of such twisting instability. Under these experimental conditions, wrinkles occur on the cylinder's surface at a given critical angle of torsion. Here we investigate this subclass of elastic instability--which we call torsion instability--of soft cylinders subject to a combined finite axial stretch and torsion, by applying the theory of incremental elastic deformation superimposed on finite strains. We formulate the incremental boundary elastic problem in the Stroh differential form, and use the surface impedance method to build a robust numerical procedure for deriving the marginal stability curves. We present the results for a Mooney-Rivlin material and study the influence of the material parameters on the elastic bifurcation.