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Inextensible Elastic Ribbons : Models and Stability
We consider the deformation of elastic ribbons, i.e. solids whose thickness is much smaller than the width, and whose width is much smaller than the length. A ribbon can typically be obtained by cutting out a strip in a piece of paper. From a mechanical perspective, the ribbon lies halfway between a (one-dimensional) rod and a (two-dimensional) plate. Starting from a plate model, will first show that the equilibrium of a ribbon is governed by a one-dimensional model, which turns out to be a special type of elastic rod. Next, we will carry out stability analyses based on this model, and show that we can account for the shapes of paper models. This work has been done in collaboration with Marcelo Dias and Keith A. Seffen.