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Antonio DiCarlo (1) and Paola Nardinocchi (2)
(1) Universit`a degli Studi “Roma Tre”
(2) Universit`a degli Studi di Roma “La Sapienza”
“On the torsion of soft cylindrical shells”, Proceedings of the Symposium on Trends in Applications of Mathematics to Mechanics, 25-29 May 1998 (STAMM98); paper revised 17 June, 1999
PARTIAL INTRODUCTION: The experimental setup is rudimentary. Pick up a piece of a spongy sleeve, of the kind commonly used to fit over water pipes for insulation. You need a stub about one meter long, which is useless stuff for pipe installers, so you can easily get it for free. Hold the tube at both ends with your hands and twist energetically while pulling apart. If the tube is soft enough, you will be able to give several turns before it coils up, as shown in Figure 2. We expect you to observe the pattern of Figure 1, as long as you succeed in keeping the axis of the tube straight: its cross sections, circular when unstressed, flatten into a quasi-oval form, whose aspect ratio is essentially constant along the tube and increases with twist in a markedly nonlinear way; the principal axes of the oval seem to whorl at a uniform rate dictated by the twist (the parameter your hands control). This pattern is quite insensitive to the way you grab and squeeze each end of the tube, provided you apply suitable end torques and forces. In this paper, we aim at the simplest rational model that reproduces and explains this behaviour.
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