. Copyright-c-1, G. Papanicolaou, and S. Varadhan, Boundary value problems with rapidly oscillating random coefficients, Proceedings of the Conference on Random Fields, pp.835-873, 1981.

L. Tartar, The general theory of homogenization: a personalized introduction, Lecture notes of the Unione Matematica Italiana, 2009.
DOI : 10.1007/978-3-642-05195-1

S. Kozlov, AVERAGING OF RANDOM OPERATORS, Mathematics of the USSR-Sbornik, vol.37, issue.2, pp.167-18010, 1070.
DOI : 10.1070/SM1980v037n02ABEH001948

V. Zhikov, S. Kozlov, O. Oleinik, and K. Ngoan, Averaging and G-convergence of differential operators, Russian Math. Surv, vol.34, p.6910, 1070.

D. Maso, G. Modica, and L. , Nonlinear Stochastic Homogenization, Annali di Matematica Pura ed Applicata, vol.21, issue.1, pp.347-38910, 1986.
DOI : 10.1007/BF01760826

V. Yurinskii, Averaging elliptic equations with random coefficients. Siberian Math, J, vol.20, issue.4, pp.611-623, 1979.
DOI : 10.1007/bf00970374

V. Yurinskii, Averaging an elliptic boundary-value problem with random coefficients, Siberian Mathematical Journal, vol.12, issue.No. 10, pp.470-48210, 1980.
DOI : 10.1007/BF00968192

K. Sab, On the homogenization and the simulation of random materials, Europ. J. Mech. A/Solids, vol.11, issue.5, pp.585-607, 1992.

A. Bourgeat, A. Mikeli´cmikeli´c, and S. Wright, Stochastic two-scale convergence in the mean and applications, J. Reine Angewandte Math, issue.456, pp.19-52, 1994.

A. Bourgeat, S. Kozlov, and A. Mikeli´cmikeli´c, Effective equations of two-phase flow in random media, Calculus of Variations and Partial Differential Equations, vol.8, issue.3, pp.385-40610, 1995.
DOI : 10.1007/BF01189397

A. Lejay, Homogenization of divergence-form operators with lower-order terms in random media, Probability Theory and Related Fields, vol.120, issue.2, pp.255-27610, 2001.
DOI : 10.1007/PL00008783

URL : https://hal.archives-ouvertes.fr/inria-00001220

L. Caffarelli, P. Souganidis, and L. Wang, Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media, Communications on Pure and Applied Mathematics, vol.45, issue.3, pp.319-361, 2005.
DOI : 10.1002/cpa.20069

X. Blanc, L. Bris, C. Lions, and P. , Stochastic homogenization and random lattices, Journal de Math??matiques Pures et Appliqu??es, vol.88, issue.1, pp.34-63, 2007.
DOI : 10.1016/j.matpur.2007.04.006

URL : https://hal.archives-ouvertes.fr/hal-00140076

L. Bris and C. , Some Numerical Approaches for Weakly Random Homogenization, Numerical Mathematics and Advanced Applications, pp.29-4510, 2009.
DOI : 10.1007/978-3-642-11795-4_3

A. Bourgeat and A. Piatnitski, Approximations of effective coefficients in stochastic homogenization, Annales de l?Institut Henri Poincare (B) Probability and Statistics, vol.40, issue.2, pp.153-165, 2004.
DOI : 10.1016/j.anihpb.2003.07.003

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.3647-3679, 2003.
DOI : 10.1016/S0020-7683(03)00143-4

G. Povirk, Incorporation of microstructural information into models of two-phase materials, Acta Metallurgica et Materialia, vol.43, issue.8, pp.3199-320610, 1995.
DOI : 10.1016/0956-7151(94)00487-3

A. Gusev, Representative volume element size for elastic composites: A numerical study, Journal of the Mechanics and Physics of Solids, vol.45, issue.9, pp.1449-145910, 1997.
DOI : 10.1016/S0022-5096(97)00016-1

A. Roberts and E. Garboczi, Elastic Properties of Model Porous Ceramics, Journal of the American Ceramic Society, vol.60, issue.7-8, pp.3041-3048, 2000.
DOI : 10.1111/j.1151-2916.2000.tb01680.x

J. Zeman and M. Sejnoha, Numerical evaluation of effective elastic properties of graphite fiber tow impregnated by polymer matrix, Journal of the Mechanics and Physics of Solids, vol.49, issue.1, pp.69-9010, 2001.
DOI : 10.1016/S0022-5096(00)00027-2

S. Meille and E. Garboczi, Linear elastic properties of 2D and 3D models of porous materials made from elongated objects, Modelling and Simulation in Materials Science and Engineering, vol.9, issue.5, p.371, 2001.
DOI : 10.1088/0965-0393/9/5/303

URL : https://hal.archives-ouvertes.fr/hal-00587075

R. Costaouec, L. Bris, C. Legoll, and F. , Variance reduction in stochastic homogenization: proof of concept, using antithetic variables, SeMA Journal, vol.27, issue.4, pp.9-27, 2010.
DOI : 10.1007/BF03322539

URL : https://hal.archives-ouvertes.fr/inria-00457946

S. Héraud, L. Allais, H. Haddadi, B. Marini, C. Teodosiu et al., Du polycristal au multicristal : vers un m??soscope num??rique, Le Journal de Physique IV, vol.08, issue.PR4, pp.27-3210, 1998.
DOI : 10.1051/jp4:1998403

H. Haddadi, C. Teodosiu, S. Héraud, L. Allais, and A. Zaoui, A ???Numerical Mesoscope??? for the Investigation of Local Fields in Rate-Dependent Elastoplastic Materials at Finite Strain, IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains, Miehe C, pp.311-320, 2003.
DOI : 10.1007/978-94-017-0297-3_28

R. Cottereau, B. Dhia, H. Clouteau, and D. , Localized modeling of uncertainty in the Arlequin framework. IUTAM Symposium on the Vibration Analysis of Structures with uncertainties, IUTAM Bookseries, pp.477-488, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00751473

R. Cottereau, D. Clouteau, B. Dhia, H. Zaccardi, and C. , A stochastic-deterministic coupling method for continuum mechanics, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.47-48, pp.47-483280, 2011.
DOI : 10.1016/j.cma.2011.07.010

URL : https://hal.archives-ouvertes.fr/hal-00709540

C. Huet, Application of variational concepts to size effects in elastic heterogeneous bodies, Journal of the Mechanics and Physics of Solids, vol.38, issue.6, pp.813-84110, 1990.
DOI : 10.1016/0022-5096(90)90041-2

K. Sab and B. Nedjar, Periodization of random media and representative volume element size for linear composites, Comptes Rendus M??canique, vol.333, issue.2, pp.187-195, 2005.
DOI : 10.1016/j.crme.2004.10.003

URL : https://hal.archives-ouvertes.fr/hal-00121487

H. Moulinec and P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2, pp.69-94, 1998.
DOI : 10.1016/S0045-7825(97)00218-1

URL : https://hal.archives-ouvertes.fr/hal-01282728

G. Milton, The theory of composites. Cambridge Monographs on Applied and Computational Mechanics, 2002.

B. Dhia and H. , Multiscale mechanical problems: the Arlequin method Comptes Rendus de l'Académie des, Sciences -Series IIB, vol.326, issue.12, pp.899-904, 1998.

B. Dhia, H. Rateau, and G. , Mathematical analysis of the mixed Arlequin method, Comptes Rendus Acad. Sci. -Series I -Math, vol.332, issue.701, pp.649-65410, 2001.

B. Dhia, H. Rateau, and G. , The Arlequin method as a flexible engineering design tool, International Journal for Numerical Methods in Engineering, vol.193, issue.11, pp.1442-1462, 2005.
DOI : 10.1002/nme.1229

URL : https://hal.archives-ouvertes.fr/hal-00018915

B. Dhia and H. , Further Insights by Theoretical Investigations of the Multiscale Arlequin Method, International Journal for Multiscale Computational Engineering, vol.6, issue.3, pp.215-232, 2008.
DOI : 10.1615/IntJMultCompEng.v6.i3.30

URL : https://hal.archives-ouvertes.fr/hal-00751336

S. Prudhomme, L. Chamoin, B. Dhia, H. Bauman, and P. , An adaptive strategy for the control of modeling error in two-dimensional atomistic-to-continuum coupling simulations, Comp. Meth. Appl. Mech. Engrg, vol.198, pp.21-261887, 2009.

J. Lagarias, J. Reeds, M. Wright, and P. Wright, Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions, SIAM Journal on Optimization, vol.9, issue.1, pp.112-147, 1998.
DOI : 10.1137/S1052623496303470

M. Shinozuka and G. Deodatis, Simulation of Stochastic Processes by Spectral Representation, Applied Mechanics Reviews, vol.44, issue.4, pp.191-205, 1991.
DOI : 10.1115/1.3119501

L. Ryzhik, G. Papanicolaou, and J. Keller, Transport equations for elastic and other waves in random media, Wave Motion, vol.24, issue.4, pp.327-370, 1996.
DOI : 10.1016/S0165-2125(96)00021-2

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=

Q. Ta, D. Clouteau, and R. Cottereau, Modeling of random anisotropic elastic media and impact on wave propagation, Revue europ??enne de m??canique num??rique, vol.19, issue.1-3, pp.241-253, 2010.
DOI : 10.3166/ejcm.19.241-253

URL : https://hal.archives-ouvertes.fr/hal-00709537