M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1964.
DOI : 10.1119/1.1972842

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, Symmetry characterization and measurement errors of elasticity tensors, GEOPHYSICS, vol.74, issue.5, pp.75-78, 2009.
DOI : 10.1190/1.3184013

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

I. Bucataru and M. A. Slawinski, Invariant Properties for Finding Distance in Space of??Elasticity Tensors, Journal of Elasticity, vol.391, issue.2, pp.97-114, 2009.
DOI : 10.1007/s10659-008-9186-9

P. Chadwick, M. Vianello, and S. C. Cowin, A new proof that the number of linear elastic symmetries is eight, Journal of the Mechanics and Physics of Solids, vol.49, issue.11, pp.2471-2492, 2001.
DOI : 10.1016/S0022-5096(01)00064-3

S. C. Cowin and M. M. Mehrabadi, ON THE IDENTIFICATION OF MATERIAL SYMMETRY FOR ANISOTROPIC ELASTIC MATERIALS, The Quarterly Journal of Mechanics and Applied Mathematics, vol.40, issue.4, pp.451-476, 1987.
DOI : 10.1093/qjmam/40.4.451

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

L. Devroye, Non-uniform random variate generation, 1986.
DOI : 10.1007/978-1-4613-8643-8

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.8896

F. I. Fedorov, Theory of Elastic Waves in Crystals, 1968.
DOI : 10.1007/978-1-4757-1275-9

S. Forte and M. Vianello, Symmetry classes for elasticity tensors, Journal of Elasticity, vol.31, issue.2, pp.81-108, 1996.
DOI : 10.1007/BF00042505

J. Guilleminot, C. Soize, and D. Kondo, Mesoscale probabilistic models for the elasticity tensor of fiber reinforced composites: Experimental identification and numerical aspects, Mechanics of Materials, vol.41, issue.12, pp.411309-1322, 2009.
DOI : 10.1016/j.mechmat.2009.08.004

URL : https://hal.archives-ouvertes.fr/hal-00684330

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

Y. Z. Huo and G. D. Piero, On the completeness of the crystallographic symmetries in the description of the symmetries of the elasticity tensor, Journal of Elasticity, vol.25, pp.203-246, 1991.

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. Kochetov and M. A. Slawinski, Estimating effective elasticity tensors from Christoffel equations, GEOPHYSICS, vol.74, issue.5, pp.67-73, 2009.
DOI : 10.1190/1.3155163

M. Kochetov and M. A. Slawinski, On obtaining effective orthotropic elasticity tensors, The Quarterly Journal of Mechanics and Applied Mathematics, vol.62, issue.2, pp.149-166, 2009.
DOI : 10.1093/qjmam/hbp001

URL : http://qjmam.oxfordjournals.org/cgi/content/short/62/2/149

M. Kochetov and M. A. Slawinski, On Obtaining Effective Transversely Isotropic Elasticity??Tensors, Journal of Elasticity, vol.40, issue.4, pp.1-13, 2009.
DOI : 10.1007/s10659-008-9180-2

M. M. Mehrabadi, S. C. Cowin, and J. Jaric, Six-dimensional orthogonal tensorrepresentation of the rotation about an axis in three dimensions, International Journal of Solids and Structures, vol.32, issue.3-4, pp.439-449, 1995.
DOI : 10.1016/0020-7683(94)00112-A

M. M. Mehrabadi and S. C. Cowin, EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS, The Quarterly Journal of Mechanics and Applied Mathematics, vol.43, issue.1, pp.15-41, 1990.
DOI : 10.1093/qjmam/43.1.15

M. L. Mehta, Random Matrices, 2004.

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

A. N. Norris, Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material, The Journal of the Acoustical Society of America, vol.119, issue.4, pp.2114-2121, 2006.
DOI : 10.1121/1.2173525

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

J. Rychlewski, On Hooke's law, Journal of Applied Mathematics and Mechanics, vol.48, issue.3, pp.303-314, 1984.
DOI : 10.1016/0021-8928(84)90137-0

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, Maximum entropy approach for modeling random uncertainties in transient elastodynamics, The Journal of the Acoustical Society of America, vol.109, issue.5, pp.1979-1996, 2001.
DOI : 10.1121/1.1360716

URL : https://hal.archives-ouvertes.fr/hal-00686287

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

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

H. F. Weber, Ueber die Integration der partiellen Differentialgleichung: $$\frac{{\partial ^2 u}}{{\partial x^2 }} + \frac{{\partial ^2 u}}{{\partial y^2 }} + k^2 u = 0.$$, Mathematische Annalen, vol.1, issue.1, pp.1-36, 1869.
DOI : 10.1007/BF01447384