A. Clément, C. Soize, and J. Yvonnet, Computational nonlinear stochastic homogenization using a nonconcurrent multiscale approach for hyperelastic heterogeneous microstructures analysis, International Journal for Numerical Methods in Engineering, vol.23, issue.4, pp.799-824, 2012.
DOI : 10.1002/nme.4293

D. Vogelaere and R. , Methods of integration which preserve the contact transformation property of the hamiltonian equations, 1956.

J. Guilleminot, A. Noshadravan, C. Soize, and R. G. Ghanem, A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.17-20, pp.1637-1648, 2011.
DOI : 10.1016/j.cma.2011.01.016
URL : https://hal.archives-ouvertes.fr/hal-00684305

J. Guilleminot and C. Soize, Non-Gaussian positive-definite matrix-valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries, International Journal for Numerical Methods in Engineering, vol.31, issue.3, pp.1128-1151, 2011.
DOI : 10.1002/nme.3212
URL : https://hal.archives-ouvertes.fr/hal-00684290

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

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01403326

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

P. Kree and C. Soize, Mathematics of Random Phenomena, 1986.
DOI : 10.1007/978-94-009-4770-2
URL : https://hal.archives-ouvertes.fr/hal-00770408

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

M. Salmi, F. Auslender, M. Bornert, and M. Fogli, Various estimates of Representative Volume Element sizes based on a statistical analysis of the apparent behavior of random linear composites, Comptes Rendus M??canique, vol.340, issue.4-5, pp.230-246, 2012.
DOI : 10.1016/j.crme.2012.02.007
URL : https://hal.archives-ouvertes.fr/hal-01157361

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

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, Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices, International Journal for Numerical Methods in Engineering, vol.195, issue.4, pp.1583-1611, 2008.
DOI : 10.1002/nme.2385
URL : https://hal.archives-ouvertes.fr/hal-00684517

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

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

S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Applied Mechanics Reviews, vol.55, issue.4, 2002.
DOI : 10.1115/1.1483342

M. Tootkaboni and L. L. Graham-brady, A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties, International Journal for Numerical Methods in Engineering, vol.196, issue.2, pp.59-90, 2010.
DOI : 10.1002/nme.2829

L. Verlet, Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Physical Review, vol.159, issue.1, pp.98-103, 1967.
DOI : 10.1103/PhysRev.159.98

L. J. Walpole, Fourth-Rank Tensors of the Thirty-Two Crystal Classes: Multiplication Tables, Proc. R. Soc
DOI : 10.1098/rspa.1984.0008

T. I. Zohdi and P. Wriggers, Introduction To Computational Micromechanics, 2005.
DOI : 10.1007/978-3-540-32360-0