Torsion instability of soft solid cylinders

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.