R. Hill, Continuum micro-mechanics of elastoplastic polycrystals, Journal of the Mechanics and Physics of Solids, vol.13, issue.2, pp.89-101, 1965.
DOI : 10.1016/0022-5096(65)90023-2

J. R. Willis, The Overall Elastic Response of Composite Materials, Journal of Applied Mechanics, vol.50, issue.4b, pp.1202-1209, 1983.
DOI : 10.1115/1.3167202

G. J. Dvorak, Transformation field analysis of inelastic composite materials, Proc. R. Soc. Lond. A 437, pp.311-327, 1992.

Y. P. Qiu and G. J. Weng, A Theory of Plasticity for Porous Materials and Particle-Reinforced Composites, Journal of Applied Mechanics, vol.59, issue.2, pp.261-268, 1992.
DOI : 10.1115/1.2899515

P. Castañeda and P. , The effective mechanical properties of nonlinear isotropic composites, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.45-71, 1991.
DOI : 10.1016/0022-5096(91)90030-R

G. K. Hu, A method of plasticity for general aligned spheroidal void or fiber-reinforced composites, Int. J. Plasticity, vol.12, pp.439-449, 1996.

G. W. Milton and S. K. Serkov, Bounding the current in nonlinear conducting composites, Journal of the Mechanics and Physics of Solids, vol.48, issue.6-7, pp.1295-1324, 2000.
DOI : 10.1016/S0022-5096(99)00083-6

S. Nemat-nasser, Micromechanics: Overall Properties of Heterogeneous Solids, 1993.

S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Applied Mechanics Reviews, vol.55, issue.4, 2001.
DOI : 10.1115/1.1483342

G. W. Milton, Theory of Composites, 2002.
DOI : 10.1017/CBO9780511613357

T. Chu and Z. Hashin, Plastic behavior of composites and porous media under isotropic stress, International Journal of Engineering Science, vol.9, issue.10, pp.971-994, 1971.
DOI : 10.1016/0020-7225(71)90029-2

Q. He, Uniform strain fields and microstructure-independent relations in nonlinear elastic fibrous composites, Journal of the Mechanics and Physics of Solids, vol.47, issue.8, pp.1781-1793, 1999.
DOI : 10.1016/S0022-5096(98)00120-3

Q. He and B. Bary, Exact Relations for the Effective Properties of Nonlinearly Elastic Inhomogeneous Materials, International Journal for Multiscale Computational Engineering, vol.2, issue.1, pp.69-83, 2004.
DOI : 10.1615/IntJMultCompEng.v2.i1.50

Q. He, L. Quang, H. Feng, and Z. , Exact Results for the Homogenization of Elastic Fiber-Reinforced Solids at Finite Strain, Journal of Elasticity, vol.52, issue.2, pp.153-177, 2006.
DOI : 10.1007/s10659-006-9049-1

URL : https://hal.archives-ouvertes.fr/hal-01179043

L. Quang, H. He, and Q. , Effective pressure-sensitive elastoplastic behavior of particle-reinforced composites and porous media under isotropic loading, International Journal of Plasticity, vol.24, issue.2, pp.343-370, 2008.
DOI : 10.1016/j.ijplas.2007.08.006

URL : https://hal.archives-ouvertes.fr/hal-00733669

R. Smit, W. Brekelmans, and H. Meijer, Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling, Computer Methods in Applied Mechanics and Engineering, vol.155, issue.1-2, pp.181-192, 1998.
DOI : 10.1016/S0045-7825(97)00139-4

F. Feyel, Multiscale FE 2 elastoviscoplastic analysis of composite structure, Comput. Mater. Sci, vol.16, pp.1-4, 1999.

F. Feyel and J. Chaboche, FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Computer Methods in Applied Mechanics and Engineering, vol.183, issue.3-4, pp.309-330, 2000.
DOI : 10.1016/S0045-7825(99)00224-8

F. Feyel, A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.3233-3244, 2003.
DOI : 10.1016/S0045-7825(03)00348-7

K. Terada and N. Kikuchi, A class of general algorithms for multi-scale analyses of heterogeneous media, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.40-41, pp.5427-5464, 2001.
DOI : 10.1016/S0045-7825(01)00179-7

S. Ghosh, K. Lee, and P. Raghavan, A multi-level computational model for multi-scale damage analysis in composite and porous materials, International Journal of Solids and Structures, vol.38, issue.14, pp.2335-2385, 2001.
DOI : 10.1016/S0020-7683(00)00167-0

J. Yvonnet and Q. He, The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains, Journal of Computational Physics, vol.223, issue.1, pp.341-368, 2007.
DOI : 10.1016/j.jcp.2006.09.019

URL : https://hal.archives-ouvertes.fr/hal-00693621

E. Monteiro, J. Yvonnet, and Q. He, Computational homogenization for nonlinear conduction in heterogeneous materials using model reduction, Computational Materials Science, vol.42, issue.4, pp.704-712, 2008.
DOI : 10.1016/j.commatsci.2007.11.001

URL : https://hal.archives-ouvertes.fr/hal-00692239

V. G. Kouznetsova, M. G. Geers, and W. A. Brekelmans, Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.48-51, pp.5525-5550, 2004.
DOI : 10.1016/j.cma.2003.12.073

C. Mcveigh, F. Vernerey, W. K. Liu, and C. Brinson, Multiresolution analysis for material design, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.37-40, pp.5525-5550, 2006.
DOI : 10.1016/j.cma.2005.07.027

P. Castañeda, P. Willis, and J. R. , On the Overall Properties of Nonlinearly Viscous Composites, Proc. R. Soc. Lond. A 416, pp.217-244, 1988.
DOI : 10.1098/rspa.1988.0035

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. Habermann and F. Kindermann, Multidimensional Spline Interpolation: Theory and Applications, Computational Economics, vol.113, issue.1, pp.153-169, 2007.
DOI : 10.1007/s10614-007-9092-4

R. K. Beatson, On the Convergence of Some Cubic Spline Interpolation Schemes, SIAM Journal on Numerical Analysis, vol.23, issue.4, pp.903-912, 1986.
DOI : 10.1137/0723058

F. L. Hitchkock, The Expression of a Tensor or a Polyadic as a Sum of Products, Journal of Mathematics and Physics, vol.6, issue.1-4, pp.164-189, 1927.
DOI : 10.1002/sapm192761164

A. Harshman, Foundations of the PARAFAC procedure: Models and conditions for an " explanatory " multi-modal factor analysis. UCLA working papers in phonetics, 1970.

J. D. Carol and J. J. Chang, Analysis of individual differences in multidimensional scaling via an n-way generalization of ???Eckart-Young??? decomposition, Psychometrika, vol.12, issue.3, pp.283-319, 1970.
DOI : 10.1007/BF02310791

J. Möcks, Topographic components model for event-related potentials and some biophysical considerations, IEEE Transactions on Biomedical Engineering, vol.35, issue.6, pp.482-484, 1988.
DOI : 10.1109/10.2119

H. A. Kiers, Towards a standardized notation and terminology in multiway analysis, Journal of Chemometrics, vol.56, issue.3, pp.105-122, 2000.
DOI : 10.1002/1099-128X(200005/06)14:3<105::AID-CEM582>3.0.CO;2-I

D. Lathauwer, L. De-moor, B. Vandewalle, and J. , A Multilinear Singular Value Decomposition, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.4, pp.1253-1278, 2000.
DOI : 10.1137/S0895479896305696

A. Kapteyn, H. Neudecker, and T. Wansbeek, An approach ton-mode components analysis, Psychometrika, vol.31, issue.2, pp.269-275, 1986.
DOI : 10.1007/BF02293984

L. R. Tucker, Some mathematical notes on three-mode factor analysis, Psychometrika, vol.64, issue.3, pp.279-311, 1966.
DOI : 10.1007/BF02289464

D. Muti and S. Bourennane, Multidimensional filtering based on a tensor approach. Signal Process, pp.2338-2353, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00082677

G. Beylkin and J. Mohlenkamp, Algorithms for Numerical Analysis in High Dimensions, SIAM Journal on Scientific Computing, vol.26, issue.6, pp.2133-2159, 2005.
DOI : 10.1137/040604959

T. Zhang and G. H. Golub, Rank-One Approximation to High Order Tensors, SIAM Journal on Matrix Analysis and Applications, vol.23, issue.2, pp.534-550, 2001.
DOI : 10.1137/S0895479899352045

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

N. Moës, M. Cloirec, P. Cartraud, and J. Remacle, A computational approach to handle complex microstructure geometries, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.3163-3177, 2003.
DOI : 10.1016/S0045-7825(03)00346-3

G. Debotton and I. Hariton, High-rank nonlinear sequentially laminated composites and their possible tendency towards isotropic behavior, Journal of the Mechanics and Physics of Solids, vol.50, issue.12, pp.2577-2595, 2002.
DOI : 10.1016/S0022-5096(02)00049-2

M. I. Idiart, P. Castañeda, and P. , Fields in nonlinear composites. I. theory, Proc. R. Soc. Lond. A 463, pp.183-202, 2007.