The stability of thin, stretched and twisted elastic rods

• Simple criterion for kinking of thin rubber bands is proposed.
• Good agreement with available experimental data.
• An alternative criterion based on the method of adjacent equilibria is also given.
• The two criteria are compared and contrasted for some simple models.

The stability of thin elastic rods that have been stretched and twisted is considered. Two general stability criteria are proposed. The first is appropriate when both the axial stretch and the torsional twist are prescribed and it is based on the elegant method of Gent for the formulation of a knot in twisting. The second criterion is valid when the axial force and the moment about the axis of the rod are prescribed. Both criteria are valid for all thin elastic rods, being independent of the modelling approach adopted. The criteria are illustrated with specific examples of the phenomenological approach to the modelling of thin, elastic, incompressible rods in tension and torsion.