Theoretical and experimental analysis of a thin elastic cylindrical tube acting as a non-Hookean spring

We analyze the deformation and energetics of a thin elastic cylindrical tube compressed between two plates which are parallel to the tube axis. The deformation is studied theoretically using exact numerical simulations and the variational approach. These results are used to interpret the experimental data obtained by pressing plastic-foil tubes in an apparatus specially designed for this purpose. A simplified variant of the physics that we present was used as a basis for one of the experimental problems posed on the 41st International Physics Olympiad held in Zagreb, Croatia in July 2010.