Modeling of rod-structures in nonlinear elasticity

Dominique Blanchard; Georges Griso

doi:10.1016/j.crma.2010.09.008

Mathematical Problems in Mechanics

Modeling of rod-structures in nonlinear elasticity
[Modélisation des structures-poutres en élasticité non linéaire]

Présenté par : Philippe G. Ciarlet

Dominique Blanchard ¹ ; Georges Griso ²

¹ Université de Rouen, UMR 6085, laboratoire Raphaël-Salem, 76801 St Etienne du Rouvray cedex, France
² Laboratoire J.L. Lions, université P. et M. Curie, Case Courrier 187, 75252 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1137-1141.

Résumé
Abstract

Cette Note traite de la modélisation d'une structure formée de poutres droites élastiques. Nous montrons, après une normalisation convenable, que l'infimum de l'énergie élastique totale tend vers le minimum d'une fonctionnelle qui dépend de champs définis sur les axes des poutres.

This Note deals with the modeling of a structure made of straight elastic rods whose thickness tends to 0. We show that, upon an adequate scaling, the infimum of the total elastic energy tends to the minimum of a functional which depends on fields defined on the centerlines of the rods.

Reçu le : 2010-07-01
Accepté le : 2010-09-09
Publié le : 2010-09-22

DOI : 10.1016/j.crma.2010.09.008

Affiliations des auteurs :

Dominique Blanchard ¹ ; Georges Griso ²

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     author = {Dominique Blanchard and Georges Griso},
     title = {Modeling of rod-structures in nonlinear elasticity},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1137--1141},
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     year = {2010},
     doi = {10.1016/j.crma.2010.09.008},
     language = {en},
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Dominique Blanchard; Georges Griso. Modeling of rod-structures in nonlinear elasticity. Comptes Rendus. Mathématique, Volume 348 (2010) no. 19-20, pp. 1137-1141. doi : 10.1016/j.crma.2010.09.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.008/

Bibliographie
Cité par

[1] D. Blanchard; G. Griso Decomposition of deformations of thin rods. Application to nonlinear elasticity, Anal. Appl., Volume 7 (2009) no. 1, pp. 21-71

[2] P.G. Ciarlet Mathematical Elasticity, vol. I, North-Holland, Amsterdam, 1988

[3] P.G. Ciarlet; C. Mardare Continuity of a deformation in $H^{1}$ as a function of its Cauchy–Green tensor in $L^{1}$ , J. Nonlinear Sci., Volume 14 (2004), pp. 415-427

[4] G. Griso Asymptotic behavior of rods by the unfolding method, Math. Meth. Appl. Sci., Volume 27 (2004), pp. 2081-2110

[5] G. Griso Decomposition of displacements of thin structures, J. Math. Pures Appl., Volume 89 (2008), pp. 199-233

[6] G. Griso Asymptotic behavior of structures made of curved rods, Anal. Appl., Volume 6 (2008) no. 1, pp. 11-22

[7] H. Le Dret Modeling of the junction between two rods, J. Math. Pures Appl., Volume 68 (1989), pp. 365-397

[8] M.G. Mora; S. Müller A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 21 (2004) no. 3, pp. 271-293

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