[Distance à l’orthotropie élastique plane par la méthode d’Euler–Lagrange]
Les tenseurs constitutifs sont d’un usage courant en mécanique des matériaux. La détermination de la classe de symétrie pertinente d’un tenseur expérimental reste un problème difficile, qui nécessite des méthodes numériques en élasticité tridimensionnelle. Nous abordons ici le cas plus abordable de l’élasticité plane (bi-dimensionnelle), non encore complètement résolu. Nous rappelons d’abord la méthode de projection orthogonale de Vianello, valable pour les classes de symétrie isotrope et de symétrie du carré (tétragonale). Nous résolvons ensuite de manière analytique le problème de la distance à l’orthotropie de l’élasticité plane, grâce à la méthode d’Euler–Lagrange.
Constitutive tensors are of common use in mechanics of materials. Determining the relevant symmetry class of an experimental tensor is still a tedious problem. For instance, it requires numerical methods in three-dimensional elasticity. We address here the more affordable case of plane (2D) elasticity, which has not been fully solved yet. We recall first Vianello’s orthogonal projection method, valid for both the isotropic and the square symmetric (tetragonal) symmetry classes. We then solve in a closed-form, the problem of the distance to plane elasticity orthotropy, thanks to the Euler–Lagrange method.
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Mot clés : Anisotropie, Distance par rapport à une classe de symétrie, Orthotropie, Optimisation, Elasticité plane
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@article{CRMECA_2022__350_G2_413_0,
author = {Adrien Antonelli and Boris Desmorat and Boris Kolev and Rodrigue Desmorat},
title = {Distance to plane elasticity orthotropy by {Euler{\textendash}Lagrange} method},
journal = {Comptes Rendus. M\'ecanique},
pages = {413--430},
publisher = {Acad\'emie des sciences, Paris},
volume = {350},
year = {2022},
doi = {10.5802/crmeca.122},
language = {en},
}
TY - JOUR AU - Adrien Antonelli AU - Boris Desmorat AU - Boris Kolev AU - Rodrigue Desmorat TI - Distance to plane elasticity orthotropy by Euler–Lagrange method JO - Comptes Rendus. Mécanique PY - 2022 SP - 413 EP - 430 VL - 350 PB - Académie des sciences, Paris DO - 10.5802/crmeca.122 LA - en ID - CRMECA_2022__350_G2_413_0 ER -
%0 Journal Article %A Adrien Antonelli %A Boris Desmorat %A Boris Kolev %A Rodrigue Desmorat %T Distance to plane elasticity orthotropy by Euler–Lagrange method %J Comptes Rendus. Mécanique %D 2022 %P 413-430 %V 350 %I Académie des sciences, Paris %R 10.5802/crmeca.122 %G en %F CRMECA_2022__350_G2_413_0
Adrien Antonelli; Boris Desmorat; Boris Kolev; Rodrigue Desmorat. Distance to plane elasticity orthotropy by Euler–Lagrange method. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 413-430. doi : 10.5802/crmeca.122. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.122/
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