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Colloque Promenade dans la physique d’aujourd’hui / A Stroll through Today’s Physics

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Crumpling a paper or a soft tissue
Martine Ben Amar (ENS)

29 juin 2007

(in collaboration with Julien Dervaux)
Ten years ago, Yves Pomeau and I investigated the existence of singularities in the solutions of Foppl-Von Karman equations of plates. We showed that the variationnal character of elasticity selects developable surfaces, the developable conic points and folds being the most commonly encountered in experiments. The Foppl-Von Karman equations include geometric non-linearities but maintain the linear hookean elasticity, an assumption which may be questionable for soft or living tissues. The first question we have considered concerns the validity of these equations for soft tissues and arbitrary elasticity. It is known that living tissues have non trivial behaviour to loadings due to nonlinear elastic response It turns out that the only hypothesis of small thickness compared to lateral size (the plate geometry) is sufficient to recover the standard Foppl-Von Karman equations. We extend this formalism to incorporate a growth process and show that growth may induce non trivial shapes which can been seen in nature like leaves and flowers.

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Martine Ben Amar Martine Ben Amar (ENS)
UMR 8550 Laboratoire de physique statistiques de l’ENS (LPS-ENS)