A. A. Andrei, Representative volume element size for elastic composites: a numerical study, Journal of the Mechanics and Physics of Solids, vol.45, pp.1449-1459, 1997.

S. Berggren, D. Lukkassen, A. Meidell, L. Simula, and . Narvik, Some methods for calculating stiffness properties of periodic structures. Applications of mathematics, pp.97-110, 2003.

J. Berthelot, Matériaux composites, p.642, 1999.

A. Bhattacharyya and D. Lagoudas, Effective elastic moduli of two-phase transversely isotropic composites with aligned clustered fibers, Acta Mechanica, vol.29, issue.1-4, pp.65-95, 2000.
DOI : 10.1007/BF01453645

A. Bunsel and J. Renard, Fundamentals of fibre reinforcced composite materials, Series in Materials Science and Engineering IoP, p.398, 2005.

W. Drugan and J. Willis, A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, Journal of the Mechanics and Physics of Solids, vol.44, issue.4, pp.497-524, 1996.
DOI : 10.1016/0022-5096(96)00007-5

F. Xu, X. Chen, and X. , Stochastic homogenization of random elastic multi-phase composites and size quantification of representative volume element, Mechanics of Materials, vol.41, issue.2, pp.41-174, 2009.
DOI : 10.1016/j.mechmat.2008.09.002

I. Gitman, H. Askes, and L. J. Sluys, Representative volume: Existence and size determination, Engineering Fracture Mechanics, vol.74, issue.16, pp.2518-2534, 2007.
DOI : 10.1016/j.engfracmech.2006.12.021

C. Grufman and F. Ellyin, Determining a representative volume element capturing the morphology of fibre reinforced polymer composites, Composites Science and Technology, vol.67, issue.3-4, pp.766-775, 2007.
DOI : 10.1016/j.compscitech.2006.04.004

J. Guilleminot, C. Soize, D. Kondo, and C. Binetruy, Theoretical framework and experimental procedure for modeling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites, International Journal of Solids and Structures, pp.45-5567, 2008.

Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials, Journal of the Mechanics and Physics of Solids, vol.11, issue.2, pp.127-140, 1963.
DOI : 10.1016/0022-5096(63)90060-7

R. Hill, Elastic properties of reinforced solids: Some theoretical principles, Journal of the Mechanics and Physics of Solids, vol.11, issue.5, pp.357-372, 1963.
DOI : 10.1016/0022-5096(63)90036-X

G. Jan, Z. Jan, and S. Michal, Quantitative analysis of fiber composite microstructure: Influence of boundary conditions, Probabilistic Engineering Mechanics, vol.21, pp.317-329, 2006.

D. Jeulin, Modèles morphologiques de structures aléatoires et de changement d'échelle, p.800, 1991.

D. Jeulin and M. Ostoja-starzewski, Mechanics of random and multiscale microstructures. CISM Courses and lectures n° 430, p.267, 2001.

M. Jiang and K. Alzebdeh, Scale and boundary conditions effects in elastic properties of random composites, Acta Mechanica, vol.49, issue.3, pp.63-78, 2001.
DOI : 10.1007/BF01183669

M. Jiang, I. Jasiuk, and M. Ostoja-starzewski, Apparent thermal conductivity of periodic two-dimensional composites, Computational Materials Science, vol.25, issue.3, pp.329-338, 2002.
DOI : 10.1016/S0927-0256(02)00234-3

T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach, International Journal of Solids and Structures, vol.40, issue.13-14, pp.40-3647, 2003.
DOI : 10.1016/S0020-7683(03)00143-4

M. Knight, L. Wrobel, and J. Henshall, Micromechanical response of fibre-reinforced materials using the boundary element technique, Composite Structures, vol.62, issue.3-4, pp.341-352, 2003.
DOI : 10.1016/j.compstruct.2003.09.036

D. Lukkassen, L. Persson, and P. Wall, Some engineering and mathematical aspects on the homogenization method, Composites Engineering, vol.5, issue.5, pp.519-531, 1995.
DOI : 10.1016/0961-9526(95)00025-I

G. Matheron, The theory of regionalized variables and its applications. Publications Centre de morphologie mathématique, p.207, 1971.

T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, vol.21, issue.5, pp.571-574, 1973.
DOI : 10.1016/0001-6160(73)90064-3

S. Nemat-nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials, Journal of Applied Mechanics, vol.63, issue.2, 1999.
DOI : 10.1115/1.2788912

M. Ostoja-starzewski, Micromechanics as a Basis of Stochastic Finite Elements and Differences: An Overview, Applied Mechanics Reviews, vol.46, issue.11S
DOI : 10.1115/1.3122629

M. Ostoja-starzewski, Random field models of heterogeneous materials, International Journal of Solids and Structures, vol.35, issue.19, pp.2429-2455, 1998.
DOI : 10.1016/S0020-7683(97)00144-3
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.572.440

M. Ostoja-starzewski, Microstructural Randomness Versus Representative Volume Element in Thermomechanics, Journal of Applied Mechanics, vol.69, issue.1, pp.25-35, 2002.
DOI : 10.1115/1.1410366

M. Ostoja-starzewski, Material spatial randomness: From statistical to representative volume element, Probabilistic Engineering Mechanics, vol.21, issue.2, pp.112-132, 2006.
DOI : 10.1016/j.probengmech.2005.07.007

M. Ostoja-starzewski, Microstructural ramdomness and scaling in mechanics of materials, CRC Series. Modern Mechanics And MathematicsCRC, p.471, 2007.

J. Segurado and J. Liorca, Computational micromechanics of composites: The effect of particle spatial distribution, Mechanics of Materials, vol.38, issue.8-10, pp.873-883, 2006.
DOI : 10.1016/j.mechmat.2005.06.026

J. Serra, Image Analysis and Mathematical Morphology, 1982.

Z. Shan and A. Gokhale, Representative volume element for non-uniform micro-structure, Computational Materials Science, vol.24, issue.3, pp.361-379, 2002.
DOI : 10.1016/S0927-0256(01)00257-9

C. Sun and R. Vaidya, Prediction of composite properties from a representative volume element, Composites Science and Technology, vol.56, issue.2, pp.171-179, 1996.
DOI : 10.1016/0266-3538(95)00141-7

C. Swan and I. Kosaka, Voigt-Reuss topology optimization for structures with linear elastic material behaviours, International Journal for Numerical Methods in Engineering, vol.93, issue.16, pp.3033-3057, 1997.
DOI : 10.1002/(SICI)1097-0207(19970830)40:16<3033::AID-NME196>3.0.CO;2-Z

M. Thomas, N. Boyard, L. Perez, Y. Jarny, and D. Delaunay, Representative volume element of anisotropic unidirectional carbon???epoxy composite with high-fibre volume fraction, Composites Science and Technology, vol.68, issue.15-16, pp.3184-3192, 2008.
DOI : 10.1016/j.compscitech.2008.07.015

S. Torquato, Random Heterogeneous Media: Microstructure and Improved Bounds on Effective Properties, Applied Mechanics Reviews, vol.44, issue.2, pp.37-76, 1991.
DOI : 10.1115/1.3119494

D. Trias, J. Costa, A. Turon, and J. Hurtado, Determination of the critical size of a statistical representative volume element (SRVE) for carbon reinforced polymers???, Acta Materialia, vol.54, issue.13, pp.3471-3484, 2006.
DOI : 10.1016/j.actamat.2006.03.042

J. Willis, Variational and related methods for the overall properties of composites Advances in Applied Mechanics, pp.1-78, 1981.

D. Xiangdong and M. Ostoja-starzewski, On the scaling from statistical to representative volume element in thermoelasticity of random materials. Networks and Heterogeneous Media, pp.259-274, 2006.

J. Zeman and M. Sejnoha, From random microstructures to representative volume elements. Modelling and Simulation in, Materials Science Engineering, vol.15, pp.325-335, 2007.

M. Mamane, Oumarou Ecole des Mines de Paris, Centre des matériaux, UMR CNRS 7633