J. L. Auriault, C. Boutin, and C. Geindreau, Homogenization of Coupled Phenomena in Heterogenous Media, ISTE, 2009.
DOI : 10.1002/9780470612033

A. Bensoussan, J. L. Lions, and P. George, Asymptotic Analysis for Periodic Structures, of Studies in Mathematics and its Applications, 1978.

S. Brisard and L. Dormieux, FFT-based methods for the mechanics of composites: A general variational framework, Computational Materials Science, vol.49, issue.3, pp.663-671, 2010.
DOI : 10.1016/j.commatsci.2010.06.009

URL : https://hal.archives-ouvertes.fr/hal-00722339

S. Brisard and L. Dormieux, Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites, Computer Methods in Applied Mechanics and Engineering, vol.217, issue.220, pp.217-220, 2012.
DOI : 10.1016/j.cma.2012.01.003

URL : https://hal.archives-ouvertes.fr/hal-00722361

S. Brisard and F. Legoll, Periodic homogenization using the Lippmann?Schwinger formalism. ArXiv e-prints 1411, p.330, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01080251

S. Brisard and P. Levitz, Small-angle scattering of dense, polydisperse granular porous media: Computation free of size effects, Physical Review E, vol.87, issue.1, p.13305, 2013.
DOI : 10.1103/PhysRevE.87.013305

URL : https://hal.archives-ouvertes.fr/hal-00779317

D. Cioranescu and P. Donato, An Introduction to Homogenization, of Oxford Lecture Series in Mathematics and Its Applications, 1999.

D. J. Eyre and G. W. Milton, A fast numerical scheme for computing the response of composites using grid refinement, Progress in Electromagnetics Research Symposium (PIERS 98), pp.41-47, 1998.
DOI : 10.1051/epjap:1999150

Z. Hashin and S. Shtrikman, On some variational principles in anisotropic and nonhomogeneous elasticity, Journal of the Mechanics and Physics of Solids, vol.10, issue.4, pp.335-342, 1962.
DOI : 10.1016/0022-5096(62)90004-2

V. V. Jikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals, 1994.
DOI : 10.1007/978-3-642-84659-5

J. Korringa, Theory of elastic constants of heterogeneous media, Journal of Mathematical Physics, vol.14, issue.4, pp.509-513, 1973.
DOI : 10.1063/1.1666346

E. Kröner, On the Physics and Mathematics of Self-Stresses, Topics in Applied Continuum Mechanics, pp.22-38, 1974.
DOI : 10.1007/978-3-7091-4188-5_2

R. Lebensohn, A. Rollett, and P. Suquet, Fast fourier transform-based modeling for the determination of micromechanical fields in polycrystals, JOM, vol.16, issue.12, pp.13-18, 2011.
DOI : 10.1007/s11837-011-0037-y

R. A. Lebensohn, A. K. Kanjarla, and P. Eisenlohr, An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials, International Journal of Plasticity, vol.32, issue.33, pp.32-33, 2012.
DOI : 10.1016/j.ijplas.2011.12.005

J. C. Michel, H. Moulinec, and P. Suquet, A computational scheme for linear and non???linear composites with arbitrary phase contrast, International Journal for Numerical Methods in Engineering, vol.58, issue.12, pp.139-160, 2001.
DOI : 10.1002/nme.275

G. W. Milton, The Theory of Composites, Cambridge Monographs on Applied and Computational Mathematics The Edinburgh Building, 2002.
DOI : 10.1017/CBO9780511613357

V. Monchiet and G. Bonnet, A polarization-based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast, International Journal for Numerical Methods in Engineering, vol.21, issue.3, pp.1419-1436, 2012.
DOI : 10.1002/nme.3295

URL : https://hal.archives-ouvertes.fr/hal-00687816

V. Monchiet and G. Bonnet, Numerical homogenization of nonlinear composites with a polarization-based FFT iterative scheme, Computational Materials Science, vol.79, pp.276-283, 2013.
DOI : 10.1016/j.commatsci.2013.04.035

URL : https://hal.archives-ouvertes.fr/hal-01165818

H. Moulinec and P. Suquet, A fast numerical method for computing the linear and nonlinear properties of composites. Comptes-rendus de l'Académie des sciences série II 318, pp.1417-1423, 1994.

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

S. Nemat-nasser, T. Iwakuma, and M. Hejazi, On composites with periodic structure, Mechanics of Materials, vol.1, issue.3, pp.239-267, 1982.
DOI : 10.1016/0167-6636(82)90017-5

S. Nemat-nasser, N. Yu, and M. Hori, Bounds and estimates of overall moduli of composites with periodic microstructure, Mechanics of Materials, vol.15, issue.3, pp.163-181, 1993.
DOI : 10.1016/0167-6636(93)90016-K

M. Schneider, Convergence of FFT-based homogenization for strongly heterogeneous media, Mathematical Methods in the Applied Sciences, vol.6, issue.5, 2014.
DOI : 10.1002/mma.3259

P. Suquet, A simplified method for the prediction of homogenized elastic properties of composites with a periodic structure. Comptes-rendus de l'Académie des sciences série II 311, pp.769-774, 1990.

J. Vond?ejc, J. Zeman, and I. Marek, An FFT-based Galerkin method for homogenization of periodic media, Computers & Mathematics with Applications, vol.68, issue.3, pp.156-173, 2014.
DOI : 10.1016/j.camwa.2014.05.014

V. Smilauer and Z. P. Ba?ant, Identification of viscoelastic C-S-H behavior in mature cement paste by FFT-based homogenization method, Cement and Concrete Research, vol.40, issue.2, pp.197-207, 2010.
DOI : 10.1016/j.cemconres.2009.10.003

F. Willot, Fourier-based schemes for computing the mechanical response of composites with accurate local fields, Comptes Rendus M??canique, vol.343, issue.3, 2015.
DOI : 10.1016/j.crme.2014.12.005

URL : https://hal.archives-ouvertes.fr/hal-01096757

F. Willot, B. Abdallah, and Y. P. Pellegrini, Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields, International Journal for Numerical Methods in Engineering, vol.94, issue.6, pp.518-533, 2014.
DOI : 10.1002/nme.4641

URL : https://hal.archives-ouvertes.fr/hal-00840986

J. Yvonnet, A fast method for solving microstructural problems defined by digital images: a space Lippmann-Schwinger scheme, International Journal for Numerical Methods in Engineering, vol.40, issue.1, pp.178-205, 2012.
DOI : 10.1002/nme.4334

URL : https://hal.archives-ouvertes.fr/hal-00822037

R. Zeller and P. H. Dederichs, Elastic Constants of Polycrystals, Physica Status Solidi (b), vol.241, issue.2, pp.831-842, 1973.
DOI : 10.1002/pssb.2220550241