Basile Audoly
CNRS et Ecole polytechnique
http://www.lmm.jussieu.fr/~audoly/

” Localization phenomena in slender elastic structures “

Slender (i.e., quasi-one-dimensional) structures are found everywhere around us, and at very different scales: this includes flagella which bacteria use for propulsion, hair, suspension cables in bridges, piano strings, bridges, etc. Because of their geometry, slender structures tend to be flexible and highly deformable, and their elastic response rarely remains in the linear regime. Since Euler’s solution of the Elastica problem, the non-linear equilibria of slender structures have been extensively studied. This talk will focus specifically on localization phenomena in slender structures, such as the formation and propagation of bulges in cylindrical (party) balloons, the necking of metal bars, and the `collapse’ of a tape spring. Such phenomena cannot be addressed by the classical models for slender structures; we will show how their limitations can be overcome, and we will construct one-dimensional models that capture localization easily and accurately.