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Elasticité et géométrie : de la rigidité des surfaces à la délamination en fil de téléphone

Abstract : This thesis deals with the elasticity of thin, two dimensional bodies. We stress on the connection between the equations of elasticity and geometry. We first study the case of shells, that are defined as thin elastic bodies with natural curvature. It is known that the elastic behaviour of a shell is heavily determined by the infinitesimal rigidity of its mean surface: depending on whether it is possible or not to deform this surface while conserving the lengths of all curves drawn upon it, the shell is said to be isometrically bendable, or inhibited. We interpret the classification of surfaces of revolution by Cohn-Vossen, and extend it to more general surfaces. We point out rigidifying curves. Then, we consider the delamination of compressed thin films: under certain conditions, they detach from the substrate to which they were bound and lift it off. We study the crack of the film/substrate interface using a model of crack with Coulomb friction between the crack lips. Telephone-cord like delamination patterns have been observed in many situations. We interpret them as resulting from a secondary buckling instability using the Föppl-von Karman equations. Finally, we show that the structure of the Föppl-von Karman equations and the properties of the interfacial crack altogether explain the stability of delamination blisters.
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Contributor : Basile Audoly <>
Submitted on : Thursday, March 6, 2003 - 10:59:57 AM
Last modification on : Thursday, December 10, 2020 - 12:36:56 PM
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  • HAL Id : tel-00002515, version 1


Basile Audoly. Elasticité et géométrie : de la rigidité des surfaces à la délamination en fil de téléphone. Physique mathématique [math-ph]. Université Pierre et Marie Curie - Paris VI, 2000. Français. ⟨tel-00002515⟩



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