Asymptotic modeling of thin linearly quasicrystalline plates

Thibaut Weller; Christian Licht

doi:10.1016/j.crme.2013.10.002

Asymptotic modeling of thin linearly quasicrystalline plates
[Analyse asymptotique de plaques minces quasicristallines linéaires]

Thibaut Weller ¹ ; Christian Licht ¹

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

Comptes Rendus. Mécanique, Volume 341 (2013) no. 11-12, pp. 793-798.

Résumé
Abstract

Lʼanalyse asymptotique, lorsque lʼépaisseur tend vers 0, de plaques minces quasicristallines linéaires montre que, selon le type de conditions aux limites considéré, il apparaît 26 modèles rendant compte de comportements différents. Ce nombre étonnamment élevé de modèles limites est essentiellement dû au couplage entre les déplacements élastiques et un type spécifique de réarrangement atomique appelé phason. On montre en particulier lʼinfluence de lʼordre icosahédral sur ces différents comportements limites.

We rigorously derive a theory of thin linearly quasicrystalline plates by studying the limit behavior of a three-dimensional flat body as its thickness tends to zero. We exhibit the existence of 26 different models, each of them linked to a specific set of boundary conditions. This stunning number of models is essentially the consequence of the coupling between displacements and a specific local rearrangement of matter at the microscopic scale that is called a phason. We exhibit the influence of the icosahedral order on the limit behavior.

Reçu le : 2013-09-16
Accepté le : 2013-10-02
Publié le : 2013-10-22

DOI : 10.1016/j.crme.2013.10.002

Keywords: Asymptotic modeling, Quasicrystals, Thin structures
Mot clés : Analyse asymptotique, Quasicristaux, Structures minces

Affiliations des auteurs :

Thibaut Weller ¹ ; Christian Licht ¹

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

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     title = {Asymptotic modeling of thin linearly quasicrystalline plates},
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     doi = {10.1016/j.crme.2013.10.002},
     language = {en},
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Thibaut Weller; Christian Licht. Asymptotic modeling of thin linearly quasicrystalline plates. Comptes Rendus. Mécanique, Volume 341 (2013) no. 11-12, pp. 793-798. doi : 10.1016/j.crme.2013.10.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.10.002/

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