  Mechanical instabilities can be exploited to design innovative structures,
able to change their shape in the presence of external stimuli. In this work,
we derive a mathematical model of an elastic beam subjected to an axial force
and constrained to smoothly slide along a rigid support, where the distance
between the rod midline and the constraint is fixed and finite. Using both
theoretical and computational techniques, we characterize the bifurcations of
such a mechanical system, in which the axial force and the natural curvature of
the beam are used as control parameters. We show that, in the presence of a
straight support, the rod can deform into shapes exhibiting helices and
perversions, namely transition zones connecting together two helices with
opposite chirality. The mathematical predictions of the proposed model are also
compared with some experiments, showing a good quantitative agreement. In
particular, we find that the buckled configurations may exhibit multiple
perversions and we propose a possible explanation for this phenomenon based on
the energy landscape of the mechanical system.
