H. Altendorf, 3D Morphological analysis and modeling of random fiber networks thesis; MINES-ParisTech, Ph.D, 2011.

P. R. Amestoy, I. S. Duff, and J. Y. L-'excellent, Multifrontal parallel distributed symmetric and unsymmetric solvers, Computer Methods in Applied Mechanics and Engineering, vol.184, issue.2-4, pp.501-520, 2000.
DOI : 10.1016/S0045-7825(99)00242-X
URL : https://hal.archives-ouvertes.fr/hal-00856651

J. L. Auriault, Heterogeneous medium. Is an equivalent macroscopic description possible?, International Journal of Engineering Science, vol.29, issue.7, pp.785-795, 1991.
DOI : 10.1016/0020-7225(91)90001-J

F. Barbe, L. Decker, D. Jeulin, and G. Cailletaud, Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model, International Journal of Plasticity, vol.17, issue.4, pp.513-536, 2001.
DOI : 10.1016/S0749-6419(00)00061-9

C. Barbier, R. Dendievel, and D. Rodney, Numerical study of 3D-compressions of entangled materials, Computational Materials Science, vol.45, issue.3, pp.593-596, 2009.
DOI : 10.1016/j.commatsci.2008.06.003
URL : https://hal.archives-ouvertes.fr/hal-00388904

C. Barbier, R. Dendievel, and D. Rodney, Role of friction in the mechanics of nonbonded fibrous materials, Physical Review E, vol.80, issue.1, p.16115, 2009.
DOI : 10.1038/nmat1810
URL : https://hal.archives-ouvertes.fr/hal-00436893

M. J. Beran, , 1968.

G. Cailletaud, S. Forest, D. Jeulin, F. Feyel, I. Galliet et al., Some elements of microstructural mechanics, Computational Materials Science, vol.27, issue.3, pp.351-374, 2003.
DOI : 10.1016/S0927-0256(03)00041-7

C. Chateau, L. Gélébart, M. Bornert, J. Crépin, and D. Caldemaison, Multiscale approach of mechanical behaviour of sic/sic composites: elastic behaviour at the scale of the tow, Technische Mechanik, vol.30, pp.1-3, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00490495

C. Delisée, D. Jeulin, and F. Michaud, Morphological characterization and porosity in 3D of cellulosic fibrous materials. Comptes-Rendus de l, Académie des Sciences ? Serie IIb: Mécanique, vol.329, issue.3, pp.179-185, 2001.

J. Dirrenberger, S. Forest, and D. Jeulin, Elastoplasticity of auxetic materials, Computational Materials Science, vol.64, pp.57-61, 2012.
DOI : 10.1016/j.commatsci.2012.03.036
URL : https://hal.archives-ouvertes.fr/hal-00732417

J. Dirrenberger, S. Forest, and D. Jeulin, Effective elastic properties of auxetic microstructures: anisotropy and structural applications, International Journal of Mechanics and Materials in Design, vol.46, issue.7, pp.21-33, 2013.
DOI : 10.1016/j.wavemoti.2009.04.002
URL : https://hal.archives-ouvertes.fr/hal-00790180

W. J. Drugan and J. R. Willis, A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, Journal of the Mechanics and Physics of Solids, vol.44, issue.4, pp.497-524, 1996.
DOI : 10.1016/0022-5096(96)00007-5

M. Faessel and D. Jeulin, 3D multiscale vectorial simulations of random models, Proceedings of ICS13, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00879688

P. J. Frey, YAMS: a fully automatic adaptive isotropic surface remeshing procedure, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00069922

L. Gélébart, C. Chateau, and M. Bornert, Conditions aux limites mixtes normales. In: 19ème Congrès Français de Mécanique, pp.24-28, 2009.

I. M. Gitman, H. Askes, and L. J. Sluys, Representative volume: Existence and size determination, Engineering Fracture Mechanics, vol.74, issue.16, pp.2518-2534, 2007.
DOI : 10.1016/j.engfracmech.2006.12.021

R. Glüge, M. Weber, and A. Bertram, Comparison of spherical and cubical statistical volume elements with respect to convergence, anisotropy, and localization behavior, Computational Materials Science, vol.63, pp.91-104, 2012.
DOI : 10.1016/j.commatsci.2012.05.063

Z. Hashin, Analysis of Composite Materials???A Survey, Journal of Applied Mechanics, vol.50, issue.3, pp.481-505, 1983.
DOI : 10.1115/1.3167081

H. Hatami-marbini and R. C. Picu, Heterogeneous long-range correlated deformation of semiflexible random fiber networks, Physical Review E, vol.271, issue.4, 2009.
DOI : 10.1002/nme.2191

S. Hazanov, Hill condition and overall properties of composites, Archive of Applied Mechanics (Ingenieur Archiv), vol.68, issue.6, pp.385-394, 1998.
DOI : 10.1007/s004190050173

S. Hazanov and M. Amieur, On overall properties of elastic heterogeneous bodies smaller than the representative volume, International Journal of Engineering Science, vol.33, issue.9, pp.1289-1301, 1995.
DOI : 10.1016/0020-7225(94)00129-8

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

R. Hill, Elastic properties of reinforced solids: Some theoretical principles, Journal of the Mechanics and Physics of Solids, vol.11, issue.5, pp.357-372, 1963.
DOI : 10.1016/0022-5096(63)90036-X

C. Huet, An integrated micromechanics and statistical continuum thermodynamics approach for studying the fracture behaviour of microcracked heterogeneous materials with delayed response, Engineering Fracture Mechanics, vol.58, issue.5-6, pp.5-6, 1997.
DOI : 10.1016/S0013-7944(97)00041-6

A. Jean, D. Jeulin, S. Forest, S. Cantournet, and F. N-'guyen, A multiscale microstructure model of carbon black distribution in rubber, Journal of Microscopy, vol.49, issue.21, pp.243-260, 2011.
DOI : 10.1016/S0022-5096(00)00027-2
URL : https://hal.archives-ouvertes.fr/hal-00585338

A. Jean, F. Willot, S. Cantournet, S. Forest, and D. Jeulin, LARGE-SCALE COMPUTATIONS OF EFFECTIVE ELASTIC PROPERTIES OF RUBBER WITH CARBON BLACK FILLERS, International Journal for Multiscale Computational Engineering, vol.9, issue.3, pp.271-303, 2011.
DOI : 10.1615/IntJMultCompEng.v9.i3.30
URL : https://hal.archives-ouvertes.fr/hal-00661612

D. Jeulin, Modèles de fonctions aléatoires multivariables, Sciences de la Terre, vol.30, pp.225-256, 1991.

D. Jeulin, Variance scaling of Boolean random varieties, MM, vol.11, issue.1, p.618967, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00618967

D. Jeulin, Morphology and effective properties of multi-scale random sets: A review, Comptes-Rendus de l'Académie des Sciences ? Serie IIb: Mécanique, pp.4-5, 2012.
DOI : 10.1016/j.crme.2012.02.004

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

C. Lantuéjoul, Ergodicity and integral range, Journal of Microscopy, vol.280, issue.3, pp.387-403, 1991.
DOI : 10.1007/978-3-642-48817-7

K. Madi, S. Forest, P. Cordier, and M. Boussuge, Numerical study of creep in two-phase aggregates with a large rheology contrast: Implications for the lower mantle, Earth and Planetary Science Letters, vol.237, issue.1-2, pp.223-238, 2005.
DOI : 10.1016/j.epsl.2005.06.027
URL : https://hal.archives-ouvertes.fr/hal-00146056

G. Matheron, The Theory of Regionalized Variables and its Applications, 1971.

G. Matheron, Estimating and Choosing, 1989.
DOI : 10.1007/978-3-642-48817-7

L. Mezeix, C. Bouvet, J. Huez, and D. Poquillon, Mechanical behavior of entangled fibers and entangled cross-linked fibers during compression, Journal of Materials Science, vol.50, issue.22, pp.3652-3661, 2009.
DOI : 10.1017/CBO9781139878326
URL : https://hal.archives-ouvertes.fr/hal-01853233

H. Moulinec and P. Suquet, A fast numerical method for computing the linear and nonlinear mechanical properties of composites, Comptes-Rendus de l'Académie des Sciences ? Serie IIb: Mécanique 318, pp.1417-1423, 1994.

M. Ostoja-starzewski, Microstructural Randomness Versus Representative Volume Element in Thermomechanics, Journal of Applied Mechanics, vol.455, issue.1, pp.25-35, 2002.
DOI : 10.1098/rspa.1999.0418

M. Oumarou, D. Jeulin, J. Renard, and P. Castaing, Multi-scale statistical approach of the elastic and thermal behavior of a thermoplastic polyamidglass fiber composite, Technische Mechanik, vol.32, pp.2-5, 2012.

D. H. Pahr and P. K. Zysset, Influence of boundary conditions on computed apparent elastic properties of cancellous bone, Biomechanics and Modeling in Mechanobiology, vol.120, issue.5, pp.463-476, 2008.
DOI : 10.1098/rspa.1984.0008

C. Pelissou, J. Baccou, Y. Monerie, and F. Perales, Determination of the size of the representative volume element for random quasi-brittle composites, International Journal of Solids and Structures, vol.46, issue.14-15, pp.2842-2855, 2009.
DOI : 10.1016/j.ijsolstr.2009.03.015
URL : https://hal.archives-ouvertes.fr/hal-02095427

C. Peyrega, D. Jeulin, C. Delisée, and J. Malvestio, 3D MORPHOLOGICAL MODELLING OF A RANDOM FIBROUS NETWORK, Image Analysis & Stereology, vol.28, issue.3, pp.129-141, 2009.
DOI : 10.5566/ias.v28.p129-141
URL : https://hal.archives-ouvertes.fr/hal-00906502

R. C. Picu, Mechanics of random fiber networks???a review, Soft Matter, vol.306, issue.15, pp.6768-6785, 2011.
DOI : 10.1016/S0370-1573(98)00024-6

R. C. Picu and H. Hatami-marbini, Long-range correlations of elastic fields in semi-flexible fiber networks, Computational Mechanics, vol.37, issue.4, pp.635-640, 2010.
DOI : 10.1007/s00466-010-0500-6

S. D. Poisson, Recherches sur la Probabilité des Jugements en Matière Criminelle et en Matière Civile, 1837.

P. Raghavan, DSCPACK: domain-separator codes for solving sparse linear systems, 2002.

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.

K. Sab and B. Nedjar, Periodization of random media and representative volume element size for linear composites, Comptes-Rendus de l'Académie des Sciences ? Serie IIb: Mécanique, pp.187-195, 2005.
DOI : 10.1016/j.crme.2004.10.003
URL : https://hal.archives-ouvertes.fr/hal-00121487

M. Salmi, F. Auslender, M. Bornert, and M. Fogli, Apparent and effective mechanical properties of linear matrix-inclusion random composites: Improved bounds for the effective behavior, International Journal of Solids and Structures, vol.49, issue.10, pp.1195-1211, 2012.
DOI : 10.1016/j.ijsolstr.2012.01.018
URL : https://hal.archives-ouvertes.fr/hal-01157362

K. Schladitz, S. Peters, D. Reinel-bitzer, A. Wiegmann, and J. Ohser, Design of acoustic trim based on geometric modeling and flow simulation for non-woven, Computational Materials Science, vol.38, issue.1, pp.56-66, 2006.
DOI : 10.1016/j.commatsci.2006.01.018

W. Schroeder, K. Martin, and B. Lorensen, The Visualization Toolkit, 2006.
DOI : 10.1016/B978-012387582-2/50032-0

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

A. S. Shahsavari and R. C. Picu, Size effect on mechanical behavior of random fiber networks, International Journal of Solids and Structures, vol.50, issue.20-21, pp.3332-3338, 2013.
DOI : 10.1016/j.ijsolstr.2013.06.004

S. , TetMesh-GHS3D User's Manual, 2003.

M. A. Soare and R. C. Picu, An approach to solving mechanics problems for materials with multiscale self-similar microstructure, International Journal of Solids and Structures, vol.44, issue.24, pp.7877-7890, 2007.
DOI : 10.1016/j.ijsolstr.2007.05.015
URL : https://doi.org/10.1016/j.ijsolstr.2007.05.015

K. Terada, M. Hori, T. Kyoya, and N. Kikuchi, Simulation of the multi-scale convergence in computational homogenization approaches, International Journal of Solids and Structures, vol.37, issue.16, pp.2285-2311, 2000.
DOI : 10.1016/S0020-7683(98)00341-2