, A fast numerical method for computing the linear and non linear mechanical properties of the composites. Comptes rendus de l'Académie des Sciences, Série II, vol.318, issue.11, pp.1417-1423, 1994.
, Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: Dilute limit and crossover behavior, Physical Review B, vol.78, issue.10, p.104111, 2008.
DOI : 10.1103/PhysRevB.78.104111
, N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform, Acta Materialia, vol.49, issue.14, pp.2723-2737, 2001.
DOI : 10.1016/S1359-6454(01)00172-0
, A non-local fracture model for composite laminates and numerical simulations by using the FFT method, Composites Part B: Engineering, vol.43, issue.3, pp.961-971, 2011.
DOI : 10.1016/j.compositesb.2011.08.055
, Microstructure-induced hotspots in the thermal and elastic responses of granular media, International Journal of Solids and Structures, vol.50, issue.10, pp.1699-1709, 2013.
DOI : 10.1016/j.ijsolstr.2013.01.040
URL : https://hal.archives-ouvertes.fr/hal-00728155
, Elastic and electrical behavior of some random multiscale highly-contrasted composites, International Journal for Multiscale Computational Enginneering: special issue on Multiscale Modeling and Uncertainty Quantification of Heterogeneous Materials, vol.9, issue.3, pp.305-326, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00553376
, Optical properties of deposit models for paints: full-fields FFT computations and representative volume element, Journal of Modern Optics, vol.32, issue.7, pp.519-528, 2013.
DOI : 10.1017/CBO9780511613357
URL : https://hal.archives-ouvertes.fr/hal-00836118
, 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
, Predictionoftheoverallbehaviorofa3DmicrostructureofausteniticsteelbyusingFFTnumericalscheme, Procedia Engineering, vol.10, pp.1883-1888, 2011.
DOI : 10.1016/j.proeng.2011.04.313
URL : http://doi.org/10.1016/j.proeng.2011.04.313
, Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms, Modelling and Simulation in Materials Science and Engineering, vol.17, issue.6, p.64010, 2009.
DOI : 10.1088/0965-0393/17/6/064010
, Stress hot spots in viscoplastic deformation of polycrystals, Modelling and Simulation in Materials Science and Engineering, vol.18, issue.7, p.74005, 2010.
DOI : 10.1088/0965-0393/18/7/074005
, Study of the antiplane deformation of linear 2-D polycrystals with different microstructures, International Journal of Solids and Structures, vol.42, issue.20, pp.5441-5459, 2005.
DOI : 10.1016/j.ijsolstr.2005.02.051
URL : https://hal.archives-ouvertes.fr/hal-00096934
, A critical comparison of several numerical methods for computing effective properties of highly heterogeneous materials, Advances in Engineering Software, vol.58, pp.1-12, 2013.
DOI : 10.1016/j.advengsoft.2012.12.002
URL : https://hal.archives-ouvertes.fr/hal-00804043
, 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
, 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.13-143647, 2003.
DOI : 10.1016/S0020-7683(03)00143-4
, The Theory of Composites, 2002.
DOI : 10.1017/CBO9780511613357
, A fast numerical scheme for computing the response of composites using grid refinement, The European Physical Journal Applied Physics, vol.6, issue.1, pp.41-47, 1999.
DOI : 10.1051/epjap:1999150
, 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
, 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.1410-1436, 2012.
DOI : 10.1002/nme.3295
URL : https://hal.archives-ouvertes.fr/hal-00687816
, Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials, International Journal for Numerical Methods in Engineering, vol.42, issue.2, pp.960-985, 2014.
DOI : 10.1002/nme.4614
URL : https://hal.archives-ouvertes.fr/hal-00787089
, 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.197-212, 2012.
DOI : 10.1016/j.cma.2012.01.003
URL : https://hal.archives-ouvertes.fr/hal-00722361
, Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients, Journal of Computational Physics, vol.229, issue.21, pp.8065-8071, 2010.
DOI : 10.1016/j.jcp.2010.07.010
, Analysis of a Fast Fourier Transform Based Method for Modeling of Heterogeneous Materials, Large-Scale Scientific Computing, vol.7116, pp.515-522, 2012.
DOI : 10.1007/978-3-642-29843-1_58
, 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
, 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
, Mathematical vs. Experimental Stress Analysis of Inhomogeneities in Solids, Le Journal de Physique IV, vol.06, issue.C1, pp.139-148, 1996.
DOI : 10.1051/jp4:1996114
, Fast Fourier transform computations and build-up of plastic deformation in 2D, elastic-perfectly plastic, pixelwise-disordered porous media, Continuum Models and Discrete Systems CMDS 11, pp.443-449, 2008.
URL : https://hal.archives-ouvertes.fr/cea-00412544
, Conductivity of random resistor networks: An investigation of the accuracy of the effective-medium approximation, Physical Review B, vol.43, issue.5, pp.3933-3944, 1991.
DOI : 10.1103/PhysRevB.43.3933
, Four-Phase Checkerboard Composites, SIAM Journal on Applied Mathematics, vol.61, issue.6, pp.1839-1856, 2001.
DOI : 10.1137/S0036139900371825
, Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials, Computational Materials Science, vol.77, pp.430-439, 2013.
DOI : 10.1016/j.commatsci.2013.04.046
, Available from: http://craft.lma.cnrs-mrs.fr), [accessed on 30, 2013.
, EJ-HEAT: A fast explicit jump harmonic averaging solver for the effective heat conductivity of composite materials, Berichte des Fraunhofer ITWM, vol.94, pp.1-21, 2006.