Comptes Rendus
Modeling the effective elastic behavior of composites: a mixed Finite Element and homogenisation approach
Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 275-282.

To make possible the Finite Element computation of Representative Volume Elements (RVE) of composites with a complex microstructure, we first propose to mesh the volume independently of the considered microstructure. Homogeneous elastic properties are then given to the elements whose behavior is ill-defined (different phases in the same element) while a polarization is homogeneously applied to these so-called ‘interphase elements’ to control the corresponding error. New bounds are derived by optimizing the polarisation. When interphase elements are given extreme elastic properties these bounds yield satisfying results in both cases of a unit cell as well as a concrete RVE.

Pour rendre possible les calculs (méthode des éléments finis) de Volumes Elémentaires Représentatifs (VER) de composites présentant une microstructure complexe, nous proposons de mailler indépendamment de la microstructure le volume considéré. Des propriétés élastiques homogènes sont ensuite affectées aux éléments dont le comportement est mal défini (éléments contenant des phases différentes), l'erreur commise étant contrôlée par l'application d'une polarisation, elle aussi homogène, dans ces éléments « interphases ». De nouvelles bornes sont finalement exhibées en optimisant cette polarisation. Lorsque les éléments interphases possèdent des propriétés élastiques extrêmes, ces bornes conduisent à des encadrements probants (calculs de cellule puis VER de béton).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2007.11.024
Keywords: Computational solid mechanics, Finite element, Homogenisation, Variational method, Sieve curves, Concrete, Microstructure, RVE
Mot clés : Mécanique des solides numérique, Eléments finis, Homogénéisation, Méthode variationnelle, Fuseau granulaire, Béton, Microstructure, VER

Charles Toulemonde 1; Renaud Masson 1; Joumana El Gharib 2

1 Materials and Mechanics of Components Department, EDF R&D, avenue des Renardières, 77818 Moret-sur-Loing cedex, France
2 Analysis in Mechanics and Acoustic Department, EDF R&D, 1, avenue du Général-de-Gaulle, 92141 Clamart cedex, France
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Charles Toulemonde; Renaud Masson; Joumana El Gharib. Modeling the effective elastic behavior of composites: a mixed Finite Element and homogenisation approach. Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 275-282. doi : 10.1016/j.crme.2007.11.024. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.024/

[1] R. Hill Elastic properties of reinforced solids: Some theoretical principles, J. Mech. Phys. Solids, Volume 11 (1963), pp. 357-372

[2] T.I. Zohdi; P. Wriggers Aspects of the computational testing of the mechanical properties of microheterogeneous material samples, Int. J. Numer. Meth. Eng., Volume 50 (2001), pp. 2573-2599

[3] C. Huet; P. Navi; P.E. Roelfstra A homogenization technique based on Hill's modification theorem (G.A. Maugin, ed.), Continuum Models and Discrete Systems, vol. 2, Longman, Harlow, 1991, pp. 135-143

[4] Z. Hashin; S. Shtrikman A variational approach to the theory of the elastic behaviour of multiphase materials, J. Mech. Phys. Solids, Volume 11 (1963), pp. 127-140

[5] Y. Le Pape, What can be learnt from the use of homogenization techniques to derive the mechanical properties of concrete in an industrial context?, in: G.Z. Voyiadis, R. Dorgan (Eds.), Proceedings of the Joint ASME/ASCE/SES Conference on Mechanics and Materials, Baton Rouge, Louisiana, USA, 2005

[6] Z.M. Wang; A.K.H. Kwan; H.C. Chan Mesoscopic study of concrete I: generation of random aggregate structure and finite element mesh, Comput. Struct., Volume 70 (1999) no. 5, pp. 533-544

[7] E. Schlangen; J.G.M. van Mier Simple lattice model for numerical simulation of fracture of concrete materials and structures, Mater. Struct., Volume 25 (1992) no. 153, pp. 534-542

[8] P. Wriggers; S.O. Moftah Mesoscale models for concrete: Homogenisation and damage behaviour, Finite Element Anal. Design, Volume 42 (2006), pp. 623-636

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