Thin linearly viscoelastic Kelvin–Voigt plates

Christian Licht

doi:10.1016/j.crme.2013.06.005

Thin linearly viscoelastic Kelvin–Voigt plates

Christian Licht ^1,²

¹ Laboratoire de mécanique et génie civil, UMR 5508 CNRS – UMII, université Montpellier-2, c.c. 048, place Eugène-Bataillon, 34095 Montpellier cedex 5, France
² Department of Mathematics, Mahidol University, Rama VI road, Bangkok 10400, Thailand

Comptes Rendus. Mécanique, Volume 341 (2013) no. 9-10, pp. 697-700.

Abstract
Résumé

A mathematical model for thin viscoelastic Kelvin–Voigt plates is derived through an asymptotic analysis when the thickness goes to zero. The model involves Kirchhoff–Love kinematics, but the mechanical behavior is no longer of Kelvin–Voigt type: an additional term of delayed memory appears like in homogenization.

On propose un modèle mathématique pour les plaques minces viscoélastiques linéaires de Kelvin–Voigt par une étude asymptotique lorsque lʼépaisseur tend vers zéro. Le modèle met en jeu une cinématique de Kirchhoff–Love, mais le comportement nʼest plus de type Kelvin–Voigt : comme en homogénéisation, un terme additionnel de mémoire longue apparaît.

Received: 2013-05-30
Accepted: 2013-06-27
Published online: 2013-08-09

DOI: 10.1016/j.crme.2013.06.005

Keywords: Asymptotic modeling, Thin viscoelastic plates, Kirchhoff–Love kinematics, Kelvin–Voigt viscoelasticity, Viscoelasticity with fading memory
Mot clés : Analyse asymptotique, Plaques minces viscoélastiques, Déplacements de Kirchhoff–Love, Viscoélasticité de Kelvin–Voigt, Viscoélasticité à mémoire

Author's affiliations:

Christian Licht ^{1, 2}

¹ Laboratoire de mécanique et génie civil, UMR 5508 CNRS – UMII, université Montpellier-2, c.c. 048, place Eugène-Bataillon, 34095 Montpellier cedex 5, France
² Department of Mathematics, Mahidol University, Rama VI road, Bangkok 10400, Thailand

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     title = {Thin linearly viscoelastic {Kelvin{\textendash}Voigt} plates},
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     pages = {697--700},
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     doi = {10.1016/j.crme.2013.06.005},
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Christian Licht. Thin linearly viscoelastic Kelvin–Voigt plates. Comptes Rendus. Mécanique, Volume 341 (2013) no. 9-10, pp. 697-700. doi : 10.1016/j.crme.2013.06.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.06.005/

References
Cited by

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