A. Acharya, A model of crystal plasticity based on the theory of continuously distributed dislocations, Journal of the Mechanics and Physics of Solids, vol.49, issue.4, pp.761-784, 2001.

P. M. Anderson, Crystal-based plasticity. Fundamentals of Metal Forming

R. H. Wagoner and J. Chenot, , pp.263-293, 1982.

B. S. Anglin, R. A. Lebensohn, and A. D. Rollett, Continuous distributions of dislocations : a new application of the methods of non-riemannian geometry, Proc. Roy. Soc. London A, vol.231, pp.263-273, 2014.

L. Balogh, L. Capolungo, and C. N. Tomé, On the measure of dislocation densities from diffraction line profiles : A comparison with discrete dislocation methods, Acta Materialia, vol.60, issue.4, pp.1467-1477, 2012.

B. W. Batterman and H. Cole, Dynamical diffraction of x rays by perfect crystals, Reviews of modern physics, vol.36, issue.3, p.681, 1964.

S. Berbenni, V. Taupin, K. S. Djaka, and C. Fressengeas, A numerical spectral approach for solving elasto-static Field Dislocation and G-Disclination Mechanics, Int. J. Solids Struct, vol.51, pp.4157-4175, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01515210

S. Berbenni, V. Taupin, C. Fressengeas, and L. Capolungo, A fast Fourier transform-based approach for generalized disclination mechanics within a couple stress theory. Generalized Continua as Models for Classical and Advanced Materials, Advanced Structured, pp.47-75, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02360511

S. Berbenni, V. Taupin, and R. A. Lebensohn, A fast fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals, Journal of the Mechanics and Physics of Solids, vol.135, 2020.
URL : https://hal.archives-ouvertes.fr/hal-02391955

E. F. Bertaut, Raies de debye-scherrer et repartition des dimensions des domaines de bragg dans les poudres polycristallines, Acta Crystallographica, vol.3, issue.1, pp.14-18, 1950.

F. Bertaut, Signification de la dimension cristalline mesuree dapres la largeur de raie debye-scherrer, Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences, vol.228, issue.2, pp.187-189, 1949.

N. Bertin and W. Cai, Computation of virtual x-ray diffraction patterns from discrete dislocation structures, Computational Materials Science, vol.146, pp.268-277, 2018.

N. Bertin, M. V. Upadhyay, C. Pradalier, and L. Capolungo, A fft-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics. Modelling and Simulation in, Materials Science and Engineering, vol.23, 2015.

A. Borbély and I. Groma, Variance method for the evaluation of particle size and dislocation density from x-ray bragg peaks, Applied Physics Letters, vol.79, issue.12, pp.1772-1774, 2001.

R. N. Bracewell, revised), The Fourier Transform and Its Applications, 1986.

R. Brenner, R. A. Lebensohn, and O. Castelnau, Elastic anisotropy and yield surface estimates of polycrystals, International Journal of Solids and Structures, vol.46, issue.16, pp.3018-3026, 2009.

S. Brisard and L. Dormieux, FFT-based methods for the mechanics of composites : A general variational framework, Comp. Mater. Sci, vol.49, pp.663-671, 2010.
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, Comp. Meth. Appl. Mech. Eng, pp.217-220, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00722361

S. Brisard and F. Legoll, Periodic homogenization using the lippmannschwinger formalism. archives ouvertes, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01080251

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.

Y. P. Chiu, Stress-field due to initial strains in a cuboid surrounded by an infinite elastic space, J. Appl. Mech. -Trans. ASME, vol.44, pp.587-590, 1977.

H. Cole, Bragg's law and energy sensitive detectors, Journal of Applied Crystallography, vol.3, issue.5, pp.405-406, 1970.

F. F. Csikor and I. Groma, Probability distribution of internal stress in relaxed dislocation systems, Physical Review B, vol.70, issue.6, p.64106, 2004.

T. W. Degeus, J. Vondrejc, J. Zeman, H. Peerlings, and G. D. Geers, Finite strain FFT-based non-linear solvers made simple, Comp. Meth. Appl. Mech. Eng, vol.318, pp.412-430, 2017.

F. Delaire, J. L. Raphanel, and C. Rey, Plastic heterogeneities of a copper multicrystal deformed in uniaxial tension : experimental study and finite element simulations, Acta Materialia, vol.48, issue.5, pp.1075-1087, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00111290

L. Dirand, Fluage à haute température d'un superalliage monocristallin : expérimentation in situ en rayonnement synchrotron, 2011.

L. Dirand, J. Cormier, A. Jacques, J. Chateau-cornu, T. Schenk et al., Measurement of the effective ?/? lattice mismatch during high temperature creep of ni-based single crystal superalloy, Materials Characterization, vol.77, pp.32-46, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01296899

L. Dirand, A. Jacques, J. P. Chateau-cornu, T. Schenk, O. Ferry et al., Phase-specific high temperature creep behaviour of a pre-rafted ni-based superalloy studied by x-ray synchrotron diffraction, Philosophical Magazine, vol.93, pp.1384-1412, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01344187

K. S. Djaka, S. Berbenni, V. Taupin, and R. A. Lebensohn, A fft-based numerical implementation of mesoscale field dislocation mechanics : Application to two-phase laminates, International Journal of Solids and Structures, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02352968

K. S. Djaka, V. Taupin, S. Berbenni, and C. Fressengeas, A numerical spectral approach to solve the dislocation density transport equation, Modell. Simul. Mater. Sci. Eng, vol.23, p.27, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01513871

K. S. Djaka, A. Villani, V. Taupin, L. Capolungo, and S. Berbenni, Field Dislocation Mechanics for heterogeneous elastic materials : A numerical spectral approach, Comp. Meth. Appl. Mech. Eng, vol.315, pp.921-942, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01947367

D. Komlan-sénam, Développement et applications dune technique de modélisation micromécanique de type" FFT" couplée à la mécanique des champs de dislocations, 2016.

S. P. Donegan and A. D. Rollett, Simulation of residual stress and elastic energy density in thermal barrier coatings using fast Fourier transforms, Acta Mater, vol.96, pp.212-228, 2015.

W. Dreyer, W. H. Muller, and J. Olschewski, An approximate analytical 2D-solution for the stresses and strains in eigenstrained cubic materials, Acta Mech, vol.136, issue.3-4, pp.171-192, 1999.

M. Dupraz, G. Beutier, D. Rodney, D. Mordehai, and M. Verdier, Signature of dislocations and stacking faults of face-centred cubic nanocrystals in coherent x-ray diffraction patterns : a numerical study, Journal of applied crystallography, vol.48, issue.3, pp.621-644, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01147801

J. N. Eastabrook and A. J. Wilson, The diffraction of x-rays by distortedcrystal aggregates iii : remarks on the interpretation of the fourier coefficients, Proceedings of the Physical Society. Section B, vol.65, issue.1, p.67, 1952.

P. Eisenlohr, M. Diehl, R. A. Lebensohn, and F. Roters, A spectral method solution to crystal elasto-viscoplasticity at finite strains, Int. J. Plast, vol.46, pp.37-53, 2013.

K. S. Eloh, A. Jacques, and S. Berbenni, Development of a new consistent discrete green operator for fft based methods to solve heterogeneous problems with eigenstrains, IJP, vol.11, p.1669, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01947206

K. S. Eloh, A. Jacques, G. Ribarik, and S. Berbenni, The effect of crystal defects on 3D high-resolution diffraction peaks : A FFT-based method, Materials, vol.11, p.1669, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02360465

D. J. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proceedings of the Royal Society A, vol.241, pp.376-396, 1957.

D. J. Eshelby, The elastic field outside an ellipsoidal inclusion, Proceedings of the Royal Society A, vol.252, pp.561-569, 1959.

P. P. Ewald, X-ray diffraction by finite and imperfect crystal lattices, Proceedings of the Physical Society, vol.52, p.167, 1940.

D. J. Eyre and G. W. Milton, 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.

C. Fressengeas, V. Taupin, and L. Capolungo, An elasto-plastic theory of dislocation and disclination fields, International Journal of Solids and Structures, vol.48, pp.3499-3509, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01501431

M. Frigo and S. G. Johnson, An adaptive software architecture for the FFT, Proc. Int. Conf. Acoust. Speech Sig. Process, vol.3, pp.1381-1384, 1998.

. Gaal, De hass-van alphen effect in dislocated crystals, Acta Physica Academiae Scientiarum Hungaricae, vol.33, issue.3-4, pp.411-418, 1973.

. Gaal, Dissertation to the hungarian academy of sciences, 1976.

L. Gélébart and R. Mondon-cancel, Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials, Comp. Mater. Sci, vol.77, pp.430-439, 2013.

R. Glowinski and P. L. Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, vol.9, 1989.

J. T. Graham, A. D. Rollett, and R. Lesar, Fast fourier transform discrete dislocation dynamics, Modell. Simul. Mater. Sci. Eng, vol.8, p.85005, 2016.

F. Grennerat, M. Montagnat, O. Castelnau, P. Vacher, H. Moulinec et al., Experimental characterization of the intragranular strain field in columnar ice during transient creep, Acta Materialia, vol.60, issue.8, pp.3655-3666, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00690945

. Groma, X-ray line broadening due to an inhomogeneous dislocation distribution, Physical Review B, vol.57, issue.13, p.7535, 1998.

I. Groma, F. F. Csikor, and M. Zaiser, Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics, Acta Materialia, vol.51, issue.5, pp.1271-1281, 2003.

I. Groma and G. Monnet, Analysis of asymmetric broadening of x-ray diffraction peak profiles caused by randomly distributed polarized dislocation dipoles and dislocation walls, Journal of applied crystallography, vol.35, issue.5, pp.589-593, 2002.
URL : https://hal.archives-ouvertes.fr/hal-01830748

C. Hammond and C. Hammond, The Basics of Cristallography and Diffraction, vol.214, 2001.

S. Haouala, S. Lucarini, J. Llorca, and . Segurado, Simulation of the hall-petch effect in fcc polycrystals by means of strain gradient crystal plasticity and fft homogenization, Journal of the Mechanics and Physics of Solids, vol.134, p.103755, 2020.

E. Hewitt and R. E. Hewitt, The gibbs-wilbraham phenomenon : An episode in fourier analysis, Archive for History of Exact Sciences, vol.21, pp.129-160, 1979.

J. P. Hirth and J. Lothe, Theory of Dislocations, 1982.

F. Hofmann, S. Keegan, and A. M. Korsunsky, Diffraction post-processing of 3d dislocation dynamics simulations for direct comparison with micro-beam laue experiments, Materials Letters, vol.89, pp.66-69, 2012.

S. Y. Hu and L. Q. Chen, Solute segregation and coherent nucleation and growth near a dislocation : a Phase-Field Model integrating defect and phase microstructure, Acta Mater, vol.49, pp.463-472, 2001.

A. Jacques, From modelling of plasticity in single crystal superalloys to high resolution X-rays three-crystals diffractometer peaks simulation, Metall. Mater. Trans, vol.47, pp.5783-5805, 2016.

A. Jacques and P. Bastie, The evolution of the lattice parameter mismatch of a nickel-based superalloy during a high-temperature creep test, Philosophical Magazine, vol.83, issue.26, pp.3005-3027, 2003.

C. Jönsson, Elektroneninterferenzen an mehreren künstlich hergestellten feinspalten, Zeitschrift für Physik, vol.161, issue.4, pp.454-474, 1961.

C. Jönsson, Electron diffraction at multiple slits, American Journal of Physics, vol.42, issue.1, pp.4-11, 1974.

J. W. Ju and L. Z. Sun, Effective elastoplastic behavior of metal matrix composites containing randomly located aligned spheroidal inhomogeneities. Part i : micromechanics-based formulation, Int. J. Solids Struct, vol.38, pp.183-201, 2001.

M. Kabel, T. Boehlke, and M. Schneider, Efficient fixed point and Newton-Krylov solvers for FFT-based homogenization of elasticity at large deformation, Comp. Mech, vol.6, pp.1497-1514, 2014.

M. Kabel, S. Fliegener, and M. Schneider, Mixed boundary conditions for FFT-based homogenization at finite strains, Comp. Mech, vol.57, pp.193-210, 2016.

M. Kabel, D. Merkert, and M. Schneider, Use of composite voxels in FFTbased homogenization, Comp. Meth. Appl. Mech. Eng, vol.294, pp.168-188, 2015.

S. Kassbohm, W. H. Muller, and R. Fessler, Improved approximations of Fourier coefficients for computing periodic structures with arbitrary stiffness distribution, Comp. Mater. Sci, vol.37, pp.90-93, 2006.

W. H. Kaßbohm, . Müller, and R. Feßler, Fourier series for computing the response of periodic structures with arbitrary stiffness distribution, Computational Materials Sciences, vol.32, pp.387-391, 2005.

M. A. Krivoglaz, Theory of x-ray and thermal-neutron scattering by real crystals, 1969.

M. A. Krivoglaz and K. P. Ryaboshapka, Theory of x-ray scattering by crystals containing dislocations, screw and edge dislocations randomly distributed throughout the crystal, Fiz. Metallov. Metalloved, vol.15, pp.18-31, 1963.

, Ekkehart Kröner. Statistical continuum mechanics. Number, vol.92, 1972.

R. Lebensohn, A. Kanjarla, and P. Eisenlohr, An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials, Int. J. Plast, pp.59-69, 2012.

R. Lebensohn, A. Rollett, and P. Suquet, Fast fourier transform-based modeling for the determination of micromechanical fields in polycrystals, J. Mater, vol.13, pp.13-18, 2011.

R. A. Lebensohn, N-site modeling of a 3d viscoplastic polycrystal using Fast Fourier Transform, Acta Mater, vol.49, pp.2723-2737, 2001.

R. A. Lebensohn, R. Brenner, O. Castelnau, and A. D. Rollet, Orientation image-based micromechanical modeling of subgrain texture evolution in polycrystalline copper, Acta Mater, vol.56, pp.3914-3926, 2008.

R. A. Lebensohn, O. Castelnau, R. Brenner, and P. Gilormini, 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.
URL : https://hal.archives-ouvertes.fr/hal-00096934

R. Lebensohn, J. Escobedo, E. Cerreta, D. Dennis-koller, C. Bronkhorst et al., Modeling void growth in polycrystalline materials, Acta Materialia, issue.18, pp.6918-6932, 2013.

R. A. Lebensohn and A. Needleman, Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms, J. Mech. Phys. Solids, vol.97, pp.333-351, 2016.

A. Leineweber and . Mittemeijer, Notes on the order-of-reflection dependence of microstrain broadening, Journal of Applied Crystallography, vol.43, issue.5, pp.981-989, 2010.

C. Lemarchand, L. P. Devincre, and . Kubin, Homogenization method for a discrete-continuum simulation of dislocation dynamics, Journal of the Mechanics and Physics of Solids, vol.49, issue.9, pp.1969-1982, 2001.

K. Levenberg, A method for the solution of certain non-linear problems in least squares, Quarterly of applied mathematics, vol.2, issue.2, pp.164-168, 1944.

J. Li, X. Tian, and R. Abdelmoula, A damage model for crack prediction in brittle and quasi-brittle materials solved by the fft method, International journal of fracture, vol.173, issue.2, pp.135-146, 2012.

Q. Li and P. M. Anderson, A compact solution for the stress field from a cuboidal region with a uniform transformation strain, J. Elasticity, vol.64, pp.237-245, 2001.

C. Licht and P. Suquet, Augmented lagrangian method applied to a problem of incompressible viscoplasticity arising in homogenization. Numerical Methods for Nonlinear Problems, pp.106-114, 1986.

K. Liss, A. Bartels, A. Schreyer, and H. Clemens, High-energy x-rays : a tool for advanced bulk investigations in materials science and physics. Texture, Stress, and Microstructure, vol.35, pp.219-252, 2003.

K. Liss, T. Royer, P. Tschentscher, A. P. Suortti, and . Williams, On highresolution reciprocal-space mapping with a triple-crystal diffractometer for high-energy x-rays, Journal of Synchrotron Radiation, vol.5, issue.2, pp.82-89, 1998.

S. Liu, X. Jin, Z. Wang, L. M. Keer, and Q. Wang, Analytical solution for elastic fields caused by eigenstrains in a half-space and numerical implementation based on FFT, Int. J. Plast, vol.35, pp.135-154, 2012.

F. Livet, Diffraction with a coherent x-ray beam : dynamics and imaging, Acta Crystallographica Section A : Foundations of Crystallography, vol.63, issue.2, pp.87-107, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00142621

S. Lucarini and J. Segurado, On the accuracy of spectral solvers for micromechanics based fatigue modeling, Computational Mechanics, vol.63, issue.2, pp.365-382, 2019.

D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, Journal of the society for Industrial and Applied Mathematics, vol.11, issue.2, pp.431-441, 1963.

J. C. Michel, H. Moulinec, and P. Suquet, A computational scheme for linear and non-linear composites with arbitrary phase contrast, Int. J. Num. Meth. Eng, vol.52, pp.139-160, 2001.

D. P. Mika and P. R. Dawson, Effects of grain interaction on deformation in polycrystals, Materials Science and Engineering : A, vol.257, issue.1, pp.62-76, 1998.

G. W. Milton and K. Golden, Representations for the conductivity functions of multicomponent composites, Communications on Pure and Applied Mathematics, vol.43, issue.5, pp.647-671, 1990.

V. Monchiet and G. Bonnet, A polarization based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast, Int. J. Num. Meth. Eng, vol.89, pp.1419-1436, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00687816

V. Monchiet and G. Bonnet, Numerical homogenization of nonlinear composites with polization-based fft iterative scheme, Computational Materials Science, vol.79, pp.276-283, 2013.

H. Moulinec and F. Silva, Comparaison of three accelerated FFT-based schemes for computing the mechanical response of composite materials, Int. J. Num. Meth. Eng, vol.97, pp.960-985, 2014.

H. Moulinec and P. Suquet, A fast numerical method for computing the linear and non linear properties of composites, C. R. Acad. Sci. Paris II, vol.318, pp.1417-1423, 1994.

H. Moulinec and P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comp. Meth. Appl. Mech. Eng, vol.157, pp.69-94, 1998.
URL : https://hal.archives-ouvertes.fr/hal-01282728

H. Mughrabi, . Ungar, M. Kienle, and . Wilkens, Long-range internal stresses and asymmetric x-ray line-broadening in tensile-deformed [001]-orientated copper single crystals, Philosophical magazine A, vol.53, issue.6, pp.793-813, 1986.

W. Muller, Fourier transforms and their application to the formation of textures and changes of morphology in solids, Journal de Physique IV, vol.6, pp.139-148, 1997.

W. H. Muller, Mathematical vs. experimental stress analysis of inhomogeneities in solids, J. Phys. IV, vol.6, issue.C1, pp.139-148, 1996.
URL : https://hal.archives-ouvertes.fr/jpa-00254146

W. H. Müller and . Neumann, An approximate analytical 3-d solution for the stresses and strains in eigenstrained cubic materials, International journal of solids and structures, vol.35, issue.22, pp.2931-2958, 1998.

T. Mura, Micromechanics of defects in solids, 1987.

J. F. Nye, Some geometrical relations in dislocated crystals, Acta metallurgica, vol.1, issue.2, pp.153-162, 1953.

T. Otsuka, R. Brenner, and B. Bacroix, Fft-based modelling of transformation plasticity in polycrystalline materials during diffusive phase transformation, International Journal of Engineering Science, vol.127, pp.92-113, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01826587

A. Prakash and R. Lebensohn, Simulation of micromechanical behavior of polycrystals : finite elements versus fast Fourier transforms, Modell. Simul. Mater. Sci. Eng, vol.17, pp.64010-64016, 2009.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C++. The art of scientific computing, 2002.

S. Ravy, La diffraction cohérente des rayons x. Reflets physique, pp.60-64, 2013.

G. Ribárik, Modeling of diffraction patterns based on microstructural properties. Material Science and Solid State Physics Program, 2008.

G. Ribárik, Modeling of diffraction patterns based on microstructural properties. Material Science and Solid State Physics Program, 2008.

G. Ribárik, J. Gubicza, and T. Ungár, Correlation between strength and microstructure of ball-milled al-mg alloys determined by x-ray diffraction, Materials science and engineering : A, vol.387, pp.343-347, 2004.

G. Ribárik, T. Ungár, and J. Gubicza, Mwp-fit : a program for multiple wholeprofile fitting of diffraction peak profiles by ab initio theoretical functions, Journal of Applied Crystallography, vol.34, issue.5, pp.669-676, 2001.

A. W. Richards, R. A. Lebensohn, and K. Bhattacharya, Interplay of martensitic phase transformation and plastic slip in polycrystals, Acta Materialia, issue.12, pp.4384-4397, 2013.

. Ad-rollett, M. Ra-lebensohn, Y. Groeber, . Choi, G. S. Li et al., Stress hot spots in viscoplastic deformation of polycrystals. Modelling and Simulation in, Materials Science and Engineering, vol.18, issue.7, p.74005, 2010.

F. Roters, P. Eisenlohr, L. Hantcherli, D. D. Tjahjanto, T. R. Bieler et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling : Theory, experiments, applications, Acta Materialia, vol.58, issue.4, pp.1152-1211, 2010.

A. Rovinelli, Y. Guilhem, H. Proudhon, R. Lebensohn, W. Ludwig et al., Assessing reliability of fatigue indicator parameters for small crack growth via a probabilistic framework. Modelling and Simulation in Materials, Science and Engineering, vol.25, issue.4, p.45010, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01540936

A. Rovinelli, M. D. Sangid, H. Proudhon, Y. Guilhem, R. A. Lebensohn et al., Predicting the 3d fatigue crack growth rate of small cracks using multimodal data via bayesian networks : In-situ experiments and crystal plasticity simulations, Journal of the Mechanics and Physics of Solids, vol.115, pp.208-229, 2018.

M. Schneider, D. Merkert, and M. Kabel, Fft-based homogenization for microstructures discretized by linear hexahedral elements, Int. J. Num. Meth. Eng, vol.109, pp.1461-1489, 2017.

M. Schneider, F. Ospald, and M. Kabel, Computational homogenization of elasticity on a staggered grid, Int. J. Num. Meth. Eng, vol.105, pp.693-720, 2016.

C. Seitz, M. Weisser, R. Gomm, and . Hock, A high-energy tripleaxis x-ray diffractometer for the study of the structure of bulk crystals, Journal of applied crystallography, vol.37, issue.6, pp.901-910, 2004.

P. Shanthraj, P. Eisenlohr, M. Diehl, and F. Roters, Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials, Int. J. Plast, vol.66, pp.31-45, 2015.

L. Sharma, R. H. Peerlings, P. Shanthraj, F. Roters, and M. G. Geers, Fftbased interface decohesion modelling by a nonlocal interphase, Advanced Modeling and Simulation in Engineering Sciences, vol.5, issue.1, p.7, 2018.

D. Smilgies, D. R. Blasini, S. Hotta, and H. Yanagi, Reciprocal space mapping and single-crystal scattering rods, Journal of synchrotron radiation, vol.12, issue.6, pp.807-811, 2005.

X. Song, F. Hofmann, and A. M. Korsunsky, Dislocation-based plasticity model and micro-beam laue diffraction analysis of polycrystalline ni foil : A forward prediction, Philosophical Magazine, vol.90, issue.30, pp.3999-4011, 2010.

A. R. Stokes and A. J. Wilson, The diffraction of x rays by distorted crystal aggregates-i, Proceedings of the Physical Society, vol.56, issue.3, p.174, 1944.

P. Suquet, H. Moulinec, O. Castelnau, M. Montagnat, N. Lahellec et al., Multi-scale modeling of the mechanical behavior of polycrystalline ice under transient creep, Proc. IUTAM, vol.3, pp.76-90, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00644773

T. Tran, V. Monchiet, and G. Bonnet, A micromechanics-based approach for derivation of constitutive coefficients of strain-gradient media, Int. J. Solids Struct, vol.5, pp.783-792, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00687822

R. Tréhorel, Comportement mécanique haute température du superalliage monocristallin AM1 : étude in situ par une nouvelle technique de diffraction en rayonnement synchrotron, 2018.

R. Tréhorel, G. Ribarik, T. Schenk, and A. Jacques, Real-time study of transients during high-temperature creep of an ni-base superalloy by far-field high-energy synchrotron x-ray diffraction, Journal of Applied Crystallography, vol.51, issue.5, 2018.

T. Ungár and . Borbély, The effect of dislocation contrast on x-ray line broadening : a new approach to line profile analysis, Applied Physics Letters, vol.69, issue.21, pp.3173-3175, 1996.

T. Ungár, . Dragomir, A. Révész, and . Borbély, The contrast factors of dislocations in cubic crystals : the dislocation model of strain anisotropy in practice, Journal of applied crystallography, vol.32, issue.5, pp.992-1002, 1999.

T. Ungár, J. Gubicza, G. Ribárik, and A. Borbély, Crystallite size distribution and dislocation structure determined by diffraction profile analysis : principles and practical application to cubic and hexagonal crystals, Journal of applied crystallography, vol.34, issue.3, pp.298-310, 2001.

T. Ungar, . Mughrabi, M. Rönnpagel, and . Wilkens, X-ray line-broadening study of the dislocation cell structure in deformed [001]-orientated copper single crystals, Acta Metallurgica, vol.32, issue.3, pp.333-342, 1984.

M. V. Upadhyay, L. Capolungo, and L. Balogh, On the computation of diffraction peaks from discrete defects in continuous media : comparison of displacement and strain-based methods, Journal of Applied Crystallography, vol.47, issue.3, pp.861-878, 2014.

M. V. Upadhyay, L. Capolungo, V. Taupin, and C. Fressengeas, Elastic constitutive laws for incompatible crystalline media : the contributions of dislocations, disclinations and g-disclinations, Philosophical Magazine, vol.93, issue.7, pp.794-832, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01501433

M. V. Upadhyay, L. Capolungo, V. Taupin, C. Fressengeas, and R. , Lebensohn. A higher order elasto-viscoplastic model using fast Fourier transforms : effects of lattice curvatures on mechanical response of nanocrystalline metals, Int. J. Plast, vol.83, pp.126-152, 2016.

A. Utkarsh, The ParaView Guide : A Parallel Visualization Application, ISBN 978-1930934306, 2015.

G. Vainikko, Fast solvers of the lippmann-schwinger equation, Direct and inverse problems of mathematical physics, pp.423-440, 2000.

J. G. Van-berkum, R. Delhez, T. H. De-keijser, and E. J. Mittemeijer, Diffraction-line broadening due to strain fields in materials ; fundamental aspects and methods of analysis, Acta Crystallographica Section A : Foundations of Crystallography, vol.52, issue.5, pp.730-747, 1996.

N. Vaxelaire, H. Proudhon, S. Labat, C. Kirchlechner, J. Keckes et al., Methodology for studying strain inhomogeneities in polycrystalline thin films during in situ thermal loading using coherent x-ray diffraction, New Journal of Physics, vol.12, issue.3, p.35018, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00491060

A. Vidyasagar, W. L. Tan, and D. M. Kochmann, Predicting the effective response of bulk polycrystalline ferroelectric ceramics via improved spectral phase field methods, J. Mech. Phys. Solids, vol.106, pp.133-151, 2017.

A. Vidyasagar, A. D. Tutcuoglu, and D. M. Kochmann, Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium, Comp. Meth. Appl. Mech. Eng, vol.335, pp.584-609, 2018.

V. Vinogradov and G. W. Milton, An accelerated FFT algorithm for thermoelastic and non-linear composites, Int. J. Num. Meth. Eng, vol.76, pp.1678-1695, 2008.

V. Volterra, Sur l'équilibre des corps élastiques multiplement connexes, Annales scientifiques de l'École normale supérieure, vol.24, pp.401-517, 1907.

J. Vond?ejc, J. Zeman, and I. Marek, An FFT-based Galerkin method for homogenization of periodic media, Comp. Math. Appl, vol.68, pp.156-173, 2015.

Z. Wang, H. Yu, and Q. Wang, Analytical solutions for elastic fields caused by eigenstrains in two joined and perfectly bonded half-spaces and related problems, Int. J. Plast, vol.76, pp.1-28, 2016.

B. E. Warren, X-ray studies of deformed metals, Progr. in Metal Phys, vol.8, 1959.

B. E. Warren, X-ray difiraction, vol.375, pp.379-388, 1969.

B. E. Warren, X-ray Diffraction. Courier Corporation, 1990.

B. E. Warren and B. L. Averbach, The separation of cold-work distortion and particle size broadening in x-ray patterns, Journal of applied physics, vol.23, issue.4, pp.497-497, 1952.

B. E. Warren, X-ray diffraction methods, Journal of applied physics, vol.12, issue.5, pp.375-384, 1941.

M. Wilkens, X-ray diffraction line broadening and crystal plasticity, Strength of Metals and Alloys (ICSMA 8), pp.125-130, 1989.

M. I. Wilkens, Theoretical aspects of kinematical x-ray diffraction profiles from crystals containing dislocation distributions(fourier transform of x ray diffraction line profiles from crystals with dislocations), NBS Fundamental Aspects of Dislocation Theory, vol.2, 1970.

G. K. Williamson and W. H. Hall, X-ray line broadening from filed aluminium and wolfram, Acta metallurgica, vol.1, issue.1, pp.22-31, 1953.

F. Willot, Fourier-based schemes for computing the mechanical response of composite with accurate local field, C. R. Mecanique, vol.343, pp.232-245, 2015.

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, Int. J. Num. Meth. Eng, vol.98, pp.518-533, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00840986

F. Willot and Y. P. Pellegrini, Fast Fourier transform computations and buildup of plastic deformation in 2D, elastic-perfectly plastic, pixelwise disordered porous media. Continuum Models and Discrete Systems, CMDS11, Presse Ecole des Mines Paris, pp.443-449, 2008.
URL : https://hal.archives-ouvertes.fr/cea-00412544

A. Wilson, The reflexion of x-rays from the anti-phase nuclei of aucu3, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol.181, issue.987, pp.360-368, 1943.

S. L. Wong, J. Park, M. P. Miller, and P. R. Dawson, A framework for generating synthetic diffraction images from deforming polycrystals using crystalbased finite element formulations, Computational Materials Science, vol.77, pp.456-466, 2013.

X. Wu, An efficient antialiasing technique, Acm Siggraph Computer Graphics, vol.25, pp.143-152, 1991.

G. Xiong, O. Moutanabbir, M. Reiche, R. Harder, and I. Robinson, Coherent x-ray diffraction imaging and characterization of strain in silicon-on-insulator nanostructures, Advanced Materials, vol.26, issue.46, pp.7747-7763, 2014.

J. Zeman, J. Vondrejc, J. Novak, and I. Marek, Accelerating a FFT-based solver for numerical homogenisation of periodic media by conjugate gradients, J. Comp. Phys, vol.229, pp.8065-8071, 2010.