The extraordinary circumstances of Lord Rayleigh: Can thin elastic sheets be always considered inextensible?
Thomas Barois  1@  
1 : Laboratoire Ondes et Matière dÁquitaine  (LOMA)  -  Website
Centre National de la Recherche Scientifique : UMR5798, Université de Bordeaux : UMR5798
Université de Bordeaux, PAC Talence, bât. A4N, 351 Cours de la Libération, 33405 TALENCE CEDEX -  France

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.


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