no. 1-2
Mathematical Problems in Mechanics/Calculus of Variations
Homogenization of hexagonal lattices
[Homogénéisation d'un réseau hexagonal]
Présenté par : Philippe G. Ciarlet
Le Dret, Hervé1 ; Raoult, Annie2
1 UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005 France
2 Laboratoire MAP5, Université Paris Descartes, UMR CNRS 8145, 45, rue des Saints Pères, 75270 Paris cedex 06, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 111-114

We characterize the macroscopic effective behavior of a graphene sheet modeled by a hexagonal lattice of elastic bars, using Γ-convergence.

Nous identifions le comportement macroscopique d'une feuille de graphène modélisée par un réseau hexagonal de barres élastiques. Nous utilisons pour cela les techniques de la Γ-convergence.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.12.012

Le Dret, Hervé 1 ; Raoult, Annie 2

1 UPMC Univ Paris 06, UMR 7598 LJLL, Paris, F-75005 France
2 Laboratoire MAP5, Université Paris Descartes, UMR CNRS 8145, 45, rue des Saints Pères, 75270 Paris cedex 06, France 
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     pages = {111--114},
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Le Dret, Hervé; Raoult, Annie. Homogenization of hexagonal lattices. Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 111-114. doi: 10.1016/j.crma.2010.12.012

[1] Alicandro, R.; Cicalese, M. A general integral representation result for continuum limits of discrete energies with superlinear growth, SIAM J. Math. Anal., Volume 36 (2004) no. 1, pp. 1-37

[2] Braides, A.; Gelli, M.S. From Discrete to Continuum: A Variational Approach, Lecture Notes, SISSA, Trieste, 2000

[3] Caillerie, D.; Mourad, A.; Raoult, A. Discrete homogenization in graphene sheet modeling, J. Elasticity, Volume 84 (2006), pp. 33-68

[4] E, W.; Ming, P. Cauchy–Born rule and the stability of crystalline solids: Static problems, Arch. Rational Mech. Anal., Volume 183 (2007), pp. 241-297

[5] Engel, P. Geometric Crystallography, Kluwer Academic Publishers, 1986

[6] Friesecke, G.; Theil, F. Validity and failure of the Cauchy–Born hypothesis in a two-dimensional mass-spring lattice, J. Nonlinear Sci., Volume 12 (2002), pp. 445-478

[7] Marcellini, P. Periodic solutions and homogenization of nonlinear variational problems, Ann. Mat. Pura Appl., Volume IV (1978) no. CXVII, pp. 139-152

[8] Müller, S. Homogenization of nonconvex integral functionals and cellular elastic materials, Arch. Rational Mech. Anal., Volume 99 (1987) no. 3, pp. 189-212

[9] Raoult, A.; Caillerie, D.; Mourad, A. Elastic lattices: Equilibrium, invariant laws and homogenization, Ann. Univ. Ferrara, Volume 54 (2008), pp. 297-318

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