V. Arsigny, P. Fillard, X. Pennec, and N. Ayache, Log-Euclidean metrics for fast and simple calculus on diffusion tensors, Magnetic Resonance in Medicine, vol.52, issue.2, pp.411-421, 2006.
DOI : 10.1002/mrm.20965

URL : https://hal.archives-ouvertes.fr/inria-00502678

A. Bóna, I. Bucataru, and M. A. Slawinski, Coordinate-free Characterization of the Symmetry Classes of Elasticity Tensors, Journal of Elasticity, vol.25, issue.4,5, pp.109-132, 2007.
DOI : 10.1007/s10659-007-9099-z

J. T. Browaeys and S. Chevrot, Decomposition of the elastic tensor and geophysical applications, Geophysical Journal International, vol.159, issue.2, pp.667-678, 2004.
DOI : 10.1111/j.1365-246X.2004.02415.x

S. Das and R. Ghanem, A Bounded Random Matrix Approach for Stochastic Upscaling, Multiscale Modeling & Simulation, vol.8, issue.1, pp.296-325, 2009.
DOI : 10.1137/090747713

S. Das, R. Ghanem, and J. Spall, Asymptotic Sampling Distribution for Polynomial Chaos Representation from Data: A Maximum Entropy and Fisher Information Approach, SIAM Journal on Scientific Computing, vol.30, issue.5, pp.2207-2234, 2008.
DOI : 10.1137/060652105

C. Desceliers, R. Ghanem, and C. Soize, Maximum likelihood estimation of stochastic chaos representations from experimental data, International Journal for Numerical Methods in Engineering, vol.11, issue.6, pp.978-1001, 2006.
DOI : 10.1002/nme.1576

URL : https://hal.archives-ouvertes.fr/hal-00686154

R. Ghanem and P. Spanos, Stochastic finite elements: a Spectral Approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

J. Guilleminot and C. Soize, A stochastic model for elasticity tensors with uncertain material symmetries, International Journal of Solids and Structures, vol.47, issue.22-23, pp.22-233121, 2010.
DOI : 10.1016/j.ijsolstr.2010.07.013

URL : https://hal.archives-ouvertes.fr/hal-00684310

S. Hazanov and C. Huet, Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume, Journal of the Mechanics and Physics of Solids, vol.42, issue.12, pp.1995-2011, 1994.
DOI : 10.1016/0022-5096(94)90022-1

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.813-841, 1990.
DOI : 10.1016/0022-5096(90)90041-2

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, Physical Review, vol.106, issue.4, pp.171-190, 1957.
DOI : 10.1103/PhysRev.106.620

M. P. Mignolet and C. Soize, Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies, Probabilistic Engineering Mechanics, vol.23, issue.2-3, pp.267-278, 2008.
DOI : 10.1016/j.probengmech.2007.12.027

URL : https://hal.archives-ouvertes.fr/hal-00685147

M. Moakher, On the Averaging of Symmetric Positive-Definite Tensors, Journal of Elasticity, vol.38, issue.1, pp.273-296, 2006.
DOI : 10.1007/s10659-005-9035-z

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

R. M. Neal, Slice sampling, The Annals of Statistics, vol.31, issue.3, pp.705-767, 2003.
DOI : 10.1214/aos/1056562461

S. Nemat-nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials, Journal of Applied Mechanics, vol.63, issue.2, 1993.
DOI : 10.1115/1.2788912

M. Ostoja-starzewski, Microstructural Randomness and Scaling in Mechanics of Materials, 2008.
DOI : 10.1201/9781420010275

M. Rosenblatt, Remarks on a Multivariate Transformation, The Annals of Mathematical Statistics, vol.23, issue.3, p.470472, 1952.
DOI : 10.1214/aoms/1177729394

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

R. J. Serfling, Approximation Theorems of Mathematical Statistics, 1980.

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

C. Soize, Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size, Probabilistic Engineering Mechanics, vol.23, issue.2-3, pp.307-323, 2008.
DOI : 10.1016/j.probengmech.2007.12.019

URL : https://hal.archives-ouvertes.fr/hal-00685154

C. Soize, Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions, International Journal for Numerical Methods in Engineering, vol.80, issue.21-26, pp.939-970, 2010.
DOI : 10.1002/nme.2712

URL : https://hal.archives-ouvertes.fr/hal-00684322

C. Soize, Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.33-36, pp.2150-2164, 2010.
DOI : 10.1016/j.cma.2010.03.013

URL : https://hal.archives-ouvertes.fr/hal-00684324

C. Soize, E. Capiez-lernout, J. Durand, C. Fernandez, and L. Gagliardini, Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.1, pp.150-163, 2008.
DOI : 10.1016/j.cma.2008.04.007

URL : https://hal.archives-ouvertes.fr/hal-00686138

C. Soize and R. Ghanem, Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure, SIAM Journal on Scientific Computing, vol.26, issue.2, pp.395-410, 2004.
DOI : 10.1137/S1064827503424505

URL : https://hal.archives-ouvertes.fr/hal-00686211

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, pp.241-253, 2010.
DOI : 10.3166/ejcm.19.241-253

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

N. Wiener, The Homogeneous Chaos, American Journal of Mathematics, vol.60, issue.4, pp.897-936, 1938.
DOI : 10.2307/2371268

X. Yina, W. Chen, A. To, C. Mcveigh, and W. K. Liu, Statistical volume element method for predicting microstructure???constitutive property relations, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.43-44, pp.43-443516, 2008.
DOI : 10.1016/j.cma.2008.01.008