Comptes Rendus
Short paper
Distance to plane elasticity orthotropy by Euler–Lagrange method
Comptes Rendus. Mécanique, Volume 350 (2022), pp. 413-430.

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.

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.

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DOI: 10.5802/crmeca.122
Keywords: Anisotropy, Distance to a symmetry class, Orthotropy, Optimization, Plane elasticity
Mot clés : Anisotropie, Distance par rapport à une classe de symétrie, Orthotropie, Optimisation, Elasticité plane

Adrien Antonelli 1; Boris Desmorat 2, 3; Boris Kolev 1; Rodrigue Desmorat 1

1 Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS - Laboratoire de Mécanique Paris-Saclay, 91190, Gif-sur-Yvette, France
2 Sorbonne Université, UMPC Univ Paris 06, CNRS, UMR 7190, Institut d’Alembert, F-75252 Paris Cedex 05, France
3 Univ Paris Sud 11, F-91405 Orsay, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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