The two families of deformations for a thin elastic sheet are stretching and bending. The energy cost for those deformations is proportional to t for the stretching and proportional to t3 for the bending. Because t is small, it is reasonable to assume that a thin sheet might deform without stretching. This idea was already discussed by Lord Rayleigh in a paper from 1881 in which he states that, for a thin sheet “under ordinary circumstances, the deformation takes place [...] as if the sheet were inextensible”.

In this presentation, I will discuss some situations of extraordinary circumstances (in the words of Rayleigh) in which thin sheets cannot be considered inextensible. I will notably show that, in those situations, nonlinear regimes play a central role in the appearance of stretching in thin plates.