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On the modeling of thin plates in nonlinear elasticity

Abstract : This PhD thesis is dedicated to the mathematical modelling of nonlinearly elastic thin plates. Namely, nonlinear two-dimensional models of plates are derived from three-dimensional elasticity via two methods: the formal asymptotic expansions and Gamma-convergence. Two classes of realistic hyperelastic materials with singular stored energy function are considered. For the first class of materials, the energy tends to infinity as the determinant of the deformation gradient tends to zero hence preventing the annihilation of volumes. Here, using the first method, we draw a new nonlinear membrane model that precludes the formation of \textit(folds) and that approximates the classical model for small deformations. The classical nonlinear inextensional model is also retrieved. Then incompressible materials are considered i.e. stored energy functions are infinite whenever the determinant of the deformation gradient is different from one. A nonlinear membrane model is produced using the second method. Finally, we show the non-existence of minimizers for membranes under compression and make some general remarks on the topic.
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https://tel.archives-ouvertes.fr/tel-00008991
Contributor : Karim Trabelsi <>
Submitted on : Monday, April 11, 2005 - 7:18:04 PM
Last modification on : Tuesday, January 5, 2021 - 6:22:04 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:58:18 PM

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  • HAL Id : tel-00008991, version 1

Citation

Karim Trabelsi. On the modeling of thin plates in nonlinear elasticity. Mechanics [physics.med-ph]. Université Pierre et Marie Curie - Paris VI, 2004. English. ⟨tel-00008991⟩

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