Mechanical instabilities and snapping phenomena in helical rods with perversion

The mechanical instabilities of clamped helical elastic rods under controlled rotation and extension, featuring perversion, are studied experimentally, numerically and theoretically. Perversion appears at a winding lower than the intrinsic one. When the extension and winding are varied, the perversion is involved in three main instabilities. They can all be identified visually as abrupt qualitative modifications of the conformation. Singularities in the axial force and torque acting on the clamps are observed at critical winding and/or extension. (i) Transitioning from a pure helix to a configuration with perversion (and vice versa) is accompanied by a snapping instability. (ii) At zero net turns, the rod undergoes a writhing bifurcation from a straight to a writhed configuration. (iii) The perversion jumps to self-contact at critical extension. While the transitions (i) and (iii) are subcritical bifurcations, the writhing bifurcation is continuous and supercritical. The singularity at the creation of the perversion is reproduced numerically by incorporating clamping effects within path-following methods. A shooting technique, path-following method and finite element simulations are employed to assess the stability of the perversion and the associated snapping towards self-contact. An analogy with first-order phase transitions is discussed.