[Conditions aux limites périodiques pour l'homogénéisation numérique de tubes composites]
Afin d'évaluer les contraintes et déformations au sein de matériaux composites périodiques, des simulations par élément-finis sont réalisées sur des cellules représentatives. Pour des composites « plans », les conditions aux limites périodiques sont bien établies et largement utilisées. L'objet de cette note est de détailler les conditions aux limites périodiques à appliquer dans le cas d'une cellule non « plane ». Deux procédures d'homogénéisation prenant en compte les simulations réalisées avec ce nouveau jeu de conditions aux limites sont par la suite proposées dans le but de discuter, en fonction du diamètre du tube, la validité d'une approximation « plane » de la cellule.
In order to evaluate the stress-strain fields within periodic composites, finite element simulations are commonly performed on representative unit-cells. For flat composites, periodic boundary conditions are well established and widely used. In the present paper, the definition of periodic boundary conditions is extended to non-flat unit-cells in order to account for the radius of the tube in the simulation. Two different homogenization procedures, based on the simulations performed with these new boundary conditions, are then proposed in order to discuss the validity, as a function of the tube diameter, of a flat unit-cell approximation.
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Mot clés : Solides et structures, Tube, Composites, Conditions aux limites, Homogénéisation, Élasticité
@article{CRMECA_2011__339_1_12_0,
author = {Lionel G\'el\'ebart},
title = {Periodic boundary conditions for the numerical homogenization of composite tubes},
journal = {Comptes Rendus. M\'ecanique},
pages = {12--19},
publisher = {Elsevier},
volume = {339},
number = {1},
year = {2011},
doi = {10.1016/j.crme.2010.12.010},
language = {en},
}
Lionel Gélébart. Periodic boundary conditions for the numerical homogenization of composite tubes. Comptes Rendus. Mécanique, Volume 339 (2011) no. 1, pp. 12-19. doi : 10.1016/j.crme.2010.12.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.12.010/
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