S. Baxter and L. Graham, Characterization of Random Composites Using Moving-Window Technique, Journal of Engineering Mechanics, vol.126, issue.4, pp.389-3970733, 2000.
DOI : 10.1061/(ASCE)0733-9399(2000)126:4(389)

S. Baxter, M. Hossain, and L. Graham, Micromechanics based random material property fields for particulate reinforced composites, International Journal of Solids and Structures, vol.38, issue.50-51, pp.20-768300076, 2001.
DOI : 10.1016/S0020-7683(01)00076-2

F. Bignonnet, K. Sab, L. Dormieux, S. Brisard, and A. Bisson, Macroscopically consistent non-local modeling of heterogeneous media, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.218-238, 2014.
DOI : 10.1016/j.cma.2014.05.014

S. Brisard and L. Dormieux, FFT-based methods for the mechanics of composites: A general variational framework, Computational Materials Science, vol.49, issue.3, pp.663-671, 2010.
DOI : 10.1016/j.commatsci.2010.06.009

URL : https://hal.archives-ouvertes.fr/hal-00722339

S. Brisard and L. Dormieux, Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites, Computer Methods in Applied Mechanics and Engineering, vol.217, issue.220, pp.197-212, 2012.
DOI : 10.1016/j.cma.2012.01.003

URL : https://hal.archives-ouvertes.fr/hal-00722361

E. Chow and Y. Saad, Preconditioned Krylov Subspace Methods for Sampling Multivariate Gaussian Distributions, SIAM Journal on Scientific Computing, vol.36, issue.2, pp.588-608, 2014.
DOI : 10.1137/130920587

C. L. Farmer, Upscaling: a review, International Journal for Numerical Methods in Fluids, vol.228, issue.1-2, pp.63-78, 2002.
DOI : 10.1002/fld.267

L. Graham and S. Baxter, Simulation of local material properties based on moving-window GMC, Probabilistic Engineering Mechanics, vol.16, issue.4, pp.295-305, 2001.
DOI : 10.1016/S0266-8920(01)00022-4

J. Guilleminot and C. Soize, Stochastic modeling of anisotropy in multiscale analysis of heterogeneous materials: A comprehensive overview on random matrix approaches, Mechanics of Materials, vol.44, pp.35-46, 2012.
DOI : 10.1016/j.mechmat.2011.06.003

URL : https://hal.archives-ouvertes.fr/hal-00684288

J. Guilleminot and C. Soize, On the Statistical Dependence for the Components of Random Elasticity Tensors Exhibiting Material Symmetry Properties, Journal of Elasticity, vol.21, issue.5, pp.109-130, 2013.
DOI : 10.1007/s10659-012-9396-z

URL : https://hal.archives-ouvertes.fr/hal-00724048

J. Guilleminot and C. Soize, Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media, Multiscale Modeling & Simulation, vol.11, issue.3, pp.840-870, 2013.
DOI : 10.1137/120898346

URL : https://hal.archives-ouvertes.fr/hal-00854121

T. Y. Hou and X. H. Wu, A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, Journal of Computational Physics, vol.134, issue.1, pp.169-189, 1997.
DOI : 10.1006/jcph.1997.5682

E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.106, issue.4, pp.620-630, 1957.
DOI : 10.1103/PhysRev.106.620

E. T. Jaynes, Information theory and statistical mechanics. ii. Phys. Rev, pp.171-190, 1957.

M. Moakher and A. N. Norris, The Closest Elastic Tensor of Arbitrary Symmetry to an Elasticity Tensor of Lower Symmetry, Journal of Elasticity, vol.40, issue.31???32, pp.215-263, 2006.
DOI : 10.1007/s10659-006-9082-0

H. Moulinec and P. Suquet, A fast numerical method for computing the linear and nonlinear properties of composites, C. R. Acad. Sci. IIb. Mec, vol.318, pp.1417-1423, 1994.

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

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

C. E. Rasmussen and C. K. Williams, Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning), 2005.

M. Sena, M. Ostoja-starzewski, and L. Costa, Stiffness tensor random fields through upscaling of planar random materials, Probabilistic Engineering Mechanics, vol.34, pp.131-156, 2013.
DOI : 10.1016/j.probengmech.2013.08.008

C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, vol.27, issue.3, pp.379-423, 1948.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

C. Soize, A nonparametric model of random uncertainties for reduced matrix models in structural dynamics, Probabilistic Engineering Mechanics, vol.15, issue.3, pp.277-294, 2000.
DOI : 10.1016/S0266-8920(99)00028-4

URL : https://hal.archives-ouvertes.fr/hal-00686293

C. Soize, Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.1-3, pp.26-64, 2006.
DOI : 10.1016/j.cma.2004.12.014

URL : https://hal.archives-ouvertes.fr/hal-00686157

Q. A. 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, 2010.
DOI : 10.3166/ejcm.19.241-253

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

S. Torquato, Random Heterogeneous Materials, 2002.
DOI : 10.1007/978-1-4757-6355-3

L. J. Walpole, Fourth-Rank Tensors of the Thirty-Two Crystal Classes: Multiplication Tables, Proc. R. Soc. Lond., A 391, pp.149-179, 1984.
DOI : 10.1098/rspa.1984.0008