no. 19-20
Mathematical Problems in Mechanics
Modeling of rod-structures in nonlinear elasticity
[Modélisation des structures-poutres en élasticité non linéaire]

Présenté par : Philippe G. Ciarlet

Blanchard, Dominique1 ; Griso, Georges2
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, Tome 348 (2010) no. 19-20, pp. 1137-1141.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.09.008
Blanchard, Dominique 1 ; Griso, Georges 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 
@article{CRMATH_2010__348_19-20_1137_0,
     author = {Blanchard, Dominique and Griso, Georges},
     title = {Modeling of rod-structures in nonlinear elasticity},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1137--1141},
     publisher = {Elsevier},
     volume = {348},
     number = {19-20},
     year = {2010},
     doi = {10.1016/j.crma.2010.09.008},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2010.09.008/}
}
TY  - JOUR
AU  - Blanchard, Dominique
AU  - Griso, Georges
TI  - Modeling of rod-structures in nonlinear elasticity
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 1137
EP  - 1141
VL  - 348
IS  - 19-20
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2010.09.008/
DO  - 10.1016/j.crma.2010.09.008
LA  - en
ID  - CRMATH_2010__348_19-20_1137_0
ER  - 
%0 Journal Article
%A Blanchard, Dominique
%A Griso, Georges
%T Modeling of rod-structures in nonlinear elasticity
%J Comptes Rendus. Mathématique
%D 2010
%P 1137-1141
%V 348
%N 19-20
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2010.09.008/
%R 10.1016/j.crma.2010.09.008
%G en
%F CRMATH_2010__348_19-20_1137_0
Blanchard, Dominique; Griso, Georges. Modeling of rod-structures in nonlinear elasticity. Comptes Rendus. Mathématique, Tome 348 (2010) no. 19-20, pp. 1137-1141. doi : 10.1016/j.crma.2010.09.008. http://www.numdam.org/articles/10.1016/j.crma.2010.09.008/

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

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

[3] Ciarlet, P.G.; Mardare, C. Continuity of a deformation in H1 as a function of its Cauchy–Green tensor in L1, J. Nonlinear Sci., Volume 14 (2004), pp. 415-427

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

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

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

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

[8] Mora, M.G.; Müller, S. 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

Cité par Sources :