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The non-linear mechanics of slender deformable bodies

There are many examples of slender (quasi-one dimensional) bodies around us, including computer cables, human hair, sailing and climbing ropes. Being flexible, slender bodies can undergo large rotations. As a result, they often display complex and interesting behaviors, among which are buckling phenomena. Being effectively one-dimensional, slender bodies are governed by equations that are simpler to write down, more likely to have analytic solutions, and easier to solve numerically than the corresponding equations of 3D continuum mechanics : this allows one to address problems that would be much more difficult (or impossible) to tackle using 3D models. In this talk, I will discuss the derivation of 1D models by dimension reduction, and their analytic or numerical solution in the non-linear regime, based on three specific examples : the coiling of thin viscous threads, the buckling of thin rods with incompatible strain, and the phenomenon of necking localization in elastic bars.

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46