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, pp.761-784, 2001.

A. Acharya, Driving forces and boundary conditions in continuum dislocation mechanics, Proceedings of the Royal Society London A, vol.459, pp.1343-1363, 2003.

A. Acharya, Jump condition for gnd evolution as a constraint on slip transmission at grain boundaries, Philosophical Magazine, vol.87, pp.1349-1359, 2007.

A. Acharya, Microcanonical entropy and mesoscale dislocation mechanics and plasticity, Journal of Elasticity, vol.104, pp.23-44, 2011.

A. Acharya and J. L. Bassani, Lattice incompatibility and a gradient theory of crystal plasticity, Journal of the Mechanics and Physics of Solids, vol.48, issue.8, pp.1565-1595, 2000.

A. Acharya and A. J. Beaudoin, Grain size effect in viscoplastic polycristals at moderate strains, Journal of the Mechanics and Physics of Solids, vol.48, pp.2213-2230, 2000.

A. Acharya and A. Roy, Size effects and idealized dislocation microstructure at small scales : Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics : Part I, J. Mech. Phys. Solids, vol.54, pp.1687-1710, 2006.

A. Acharya, A. Roy, and A. Sawant, Continuum theory and methods for coarsegrained plasticity, Scripta Mater, vol.54, pp.705-710, 2006.

N. Allain-bonasso, F. Wagner, S. Berbenni, and D. P. Field, A study of the heterogeneity of plastic deformation in IF steel by EBSD, Materials Science Engineering A, vol.548, pp.56-63, 2012.

B. S. Anglin, R. A. Lebensohn, and A. D. Rollett, Validation of a numerical method based on fast Fourier transforms for heterogeneous thermoelastic materials by comparison with analytical solutions, Computational Materials Science, vol.87, pp.209-217, 2014.

R. Armstrong, I. Douthwaite, and N. J. Petch, The plastic deformation of polycrystalline aggregates, Philosophical Magazine, vol.7, pp.45-58, 1962.

R. Arora and A. Acharya, Dislocation pattern formation in finite deformation crystal plasticity, International Journal of Solids and Structures, 2019.

A. Arsenlis and D. M. Parks, Crystallographic aspects of geometrically necessary and statistically stored dislocation density, Acta Mater, vol.47, pp.1597-1611, 1999.

A. Arsenlis and D. M. Parks, Modeling the evolution of crystallographic dislocation density in crystal plasticity, Journal of the Mechanics and Physics of Solids, vol.50, pp.1979-2009, 2002.

M. F. Ashby, Deformation of plastically non-homogeneous materials, Philosophical Magazine, vol.21, pp.399-424, 1970.

D. S. Balint, V. S. Deshpande, A. Needleman, and E. Van-der-giessen, Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals, International Journal of Plasticity, vol.24, pp.2149-2172, 2010.

R. I. Barabash, G. E. Ice, and J. W. Pang, Gradients of geometrically necessary dislocations from white beam microdiffraction, Materials Science Engineering A, pp.125-131, 2005.

F. Barbe, L. Decker, D. Jeulin, and G. Cailletaud, Intergranular and intragranular behavior of polycrystalline aggregates. Part I. F.E. model, International Journal of Plasticity, vol.17, pp.513-536, 2001.
URL : https://hal.archives-ouvertes.fr/hal-02327393

F. Barbe, S. Forest, and G. Cailletaud, Intergranular and intragranular behavior of polycrystalline aggregates. Part II, Results. International Journal of Plasticity, vol.17, pp.537-563, 2001.
URL : https://hal.archives-ouvertes.fr/hal-02327393

B. Beausir, C. Fressengeas, N. P. Gurao, L. S. Toth, and S. Suwas, Spatial correlation in grain misorientation distribution, Acta Materialia, vol.57, issue.18, pp.5382-5395, 2009.

S. Berbenni, M. Berveiller, and T. Richeton, Intra-granular plastic slip heterogeneities: Discrete vs. Mean Field approaches, International Journal of Solids and Structures, vol.45, pp.4147-4172, 2008.

S. Berbenni, V. Favier, and M. Berveiller, Impact of the grain size distribution on the yield stress of heterogeneous materials, International Journal of Plasticity, vol.23, pp.114-142, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00128377

S. Berbenni and V. Taupin, Fast Fourier Transform-based micromechanics of interfacial line defects in crystalline materials, Journal of Micromechanics and Molecular Physics, vol.1840007, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02351498

S. Berbenni, V. Taupin, K. S. Djaka, and C. Fressengeas, A numerical spectral approach for solving elasto-static field dislocation and g-disclination mechanics, International Journal of Solids and Structures, 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

N. Bertin and L. Capolungo, A FFT-based formulation for discrete dislocation dynamics in heterogeneous media, Journal of Computational Physics, vol.355, pp.366-384, 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, p.65009, 2015.

M. Berveiller, Contributionà l'étude du comportement plastique des textures de déformation des polycristaux métalliques, 1978.

M. Berveiller and A. Zaoui, An extension of the self-consistent scheme to plastically-flowing polycrystals, Journal of the Mechanics and Physics of Solids, vol.26, pp.325-344, 1979.

S. B. Biner and J. R. Morris, A two-dimensional discrete dislocation simulation of the effect of grain size on strengthening behaviour, Modelling and Simulation in Materials Science and Engineering, vol.10, issue.6, pp.617-635, 2002.

R. Brenner, A. J. Beaudoin, P. Suquet, and A. Acharya, Numerical implementation of static Field Dislocation Mechanics theory for periodic media, Philosophical Magazine, pp.1-24, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00918607

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

B. Budiansky and T. T. Wu, Theoretical prediction of plastic strains of polycrystals, Proceedings of the 4th US National Congress of Applied Mechanics. Transactions of AIME, pp.1175-1185, 1962.

E. P. Busso, F. T. Meisonnier, and N. P. O'dowd, Gradient-dependent deformation of two-phase single crystals, Journal of the Mechanics and Physics of Solids, vol.48, pp.2333-2361, 2000.

M. Calcagnotto, D. Ponge, E. Demir, and D. Raabe, Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD, Materials Science Engineering A, vol.527, pp.2738-2746, 2010.

K. S. Cheong, E. P. Busso, and A. Arsenlis, A study of microstructural length scale effects on the behaviour of FCC polycrystals using strain gradient concepts, International Journal of Plasticity, vol.21, pp.1797-1814, 2005.

C. Collard, V. Favier, S. Berbenni, and M. Berveiller, Role of discrete intragranular slip bands on the strain-hardening of polycrystals, International Journal of Plasticity, vol.26, pp.310-328, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01768250

N. M. Cordero, S. Forest, E. P. Busso, S. Berbenni, and M. Cherkaoui, Grain size effects on plastic strain and dislocation density tensor fields in metal polycrystals, Computational Materials Science, vol.52, pp.7-13, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00658644

N. M. Cordero, A. Gaubert, S. Forest, E. P. Busso, F. Galerneau et al., Size effects in generalised continuum crystal plasticity for two-phase laminates, Journal of the Mechanics and Physics of Solids, vol.58, pp.1963-1994, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00542418

Z. C. Cordero, B. E. Knight, and C. A. Schuh, Six decades of the Hall-Petch effect: a survey of grain size strengthening studies on pure metals, International Materials Reviews, vol.61, issue.8, pp.495-512, 2016.

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, pp.1075-1087, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00111290

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. Modelling and Simulation in, Materials Science and Engineering, vol.23, issue.27pp, p.65008, 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, Computer Methods in Applied Mechanics and Engineering, vol.315, pp.921-942, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01947367

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

W. Dreyer, W. H. Müller, 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.

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.

S. A. El-naaman, K. L. Nielsen, and C. F. Niordson, An investigation of back stress formulations under cyclic loading, Mechanics of Materials, vol.130, pp.76-87, 2019.

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, International Journal of Plasticity, vol.116, pp.1-23, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01947206

H. Espinosa, S. Berbenni, M. Panico, and K. Schwarz, An interpretation of size scale plasticity in geometrically confined systems, Proceedings of the National Academy of Sciences USA, vol.102, issue.47, pp.16933-16938, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00128374

H. Espinosa, M. Panico, S. Berbenni, and K. Schwarz, Discrete dislocation dynamics simulations to interpret plasticity size and surface effects in freestanding FCC thin films, International Journal of Plasticity, vol.22, issue.11, pp.2091-2117, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00128371

L. P. Evers, W. A. Brekelmans, and M. G. Geers, Non-local crystal plasticity model with intrinsic SSD and GND effects, Journal of the Mechanics and Physics of Solids, vol.52, pp.2379-2401, 2004.

L. P. Evers, D. M. Parks, W. A. Brekelmans, and M. G. Geers, Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation, Journal of the Mechanics and Physics of Solids, vol.50, pp.2403-2424, 2002.

D. J. Eyre and G. W. Milton, A fast numerical scheme for computing the response of composite using grid refinement, European Physical Journal -Applied Physics, vol.6, pp.41-47, 1999.

N. A. Fleck and J. W. Hutchinson, A phenomenological theory of strain gradient plasticity, J. Mech. Phys. Solids, vol.41, pp.1825-1857, 1993.

N. A. Fleck and J. W. Hutchinson, Reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, vol.48, pp.2245-2271, 2001.

N. A. Fleck, J. W. Hutchinson, and J. R. Willis, Guidelines for constructing strain gradient plasticity theories, Trans. ASME Journal of Applied Mechanics, vol.82, pp.71002-71012, 2015.

N. A. Fleck and J. R. Willis, A mathematical basis for strain-gradient plasticity theory-Part I: scalar plastic multiplier, Journal of the Mechanics and Physics of Solids, vol.57, pp.161-177, 2009.

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 Mater, vol.60, pp.3655-3666, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00690945

P. Gudmundson, A unified treatment of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, vol.52, pp.1379-1406, 2004.

S. Gupta, A. J. Beaudoin, and J. Chevy, Strain rate jump induced negative strain rate sensitivity (nsrs) in aluminium alloy 2024: Experiments and constitutive modeling, Materials Science Engineering A, vol.683, pp.143-152, 2017.

M. Gurtin, A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations, Journal of the Mechanics and Physics of Solids, vol.50, pp.5-32, 2002.

M. E. Gurtin and L. Anand, Thermodynamics applied to gradient theories involving accumulated plastic strain: The theories of Aifantis and Fleck and Hutchinson and their generalization, Journal of the Mechanics and Physics of Solids, vol.57, pp.405-421, 2009.

M. E. Gurtin, L. Anand, and S. P. Lele, Gradient single-crystal plasticity with free energy dependent on dislocation densities, Journal of the Mechanics and Physics of Solids, vol.55, pp.1853-1878, 2007.

P. J. Guruprasad, W. J. Carter, and A. A. Benzerga, A discrete dislocation analysis of the Bauschinger effect in microcrystals, Acta Materialia, vol.56, pp.5477-5491, 2008.

E. O. Hall, The deformation and ageing of mild steels, Proc. Phys. Soc. London B, vol.64, pp.747-753, 1951.

C. S. Han, H. Gao, Y. Huang, and W. D. Nix, Mechanism-based strain gradient crystal plasticity-i. theory, Journal of the Mechanics and Physics of Solids, vol.53, pp.1188-1203, 2005.

N. Hansen, Polycrystalline strengthening. Metallurgical Transactions A 16A, p.2167, 1985.

N. Hansen, Hall-Petch relation and boundary strengthening, Scripta Materialia, vol.51, pp.801-806, 2004.

S. Haouala, S. Lucarini, J. Llorca, and J. 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.

R. Hill, Continuum micromechanics of elastoplastic polycrystals, Journal of the Mechanics and Physics of Solids, vol.13, pp.89-101, 1965.

J. P. Hirth, The influence of grain boundaries on mechanical properties, Metallurgical Transactions, vol.3, pp.3047-3067, 1972.

J. Jiang, T. B. Britton, and A. J. Wilkinson, Evolution of intragranular stresses and dislocation densities during cyclic deformation of polycrystalline copper, Acta Materialia, vol.94, pp.193-204, 2015.

M. Jiang, B. Devincre, and G. Monnet, Effects of the grain size and shape on the flow stress: A dislocation dynamics study, International Journal of Plasticity, vol.113, pp.111-124, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01931425

M. Kabel, S. Fliegener, and M. Schneider, Mixed boundary conditions for FFTbased homogenization at finite strains, Comp. Mech, vol.57, issue.2, pp.193-210, 2016.

D. Kiener, C. Motz, W. Grosinger, D. Weygand, and R. Pippan, Cyclic response of copper single crystal micro-beams, Scripta Materialia, vol.63, pp.500-503, 2010.

P. J. Konijnenberg, S. Zaefferer, and D. Raabe, Assessment of geometrically necessary dislocation levels derived by 3D EBSD, Acta Materialia, vol.99, pp.402-414, 2015.

E. Kröner, Kontinuumstheorie der Versetzungen und Eigenspannungen, Ergebnisse der Angewewandte Mathematik, vol.5, 1958.

E. Kröner, Zur plastischen Verformung des Vielkristalls, Acta Metallurgica, vol.9, pp.155-161, 1961.

E. Kröner, Continuum theory of defects, Physics of defects Les Houches Session 35 North Holland, pp.215-315, 1981.

L. P. Kubin, G. Canova, M. Condat, B. Devincre, V. Pontikis et al., Dislocation microstructure and plastic flow : a 3-d simulation. Solid state Phenomena 23-24, pp.455-472, 1992.

F. Lavergne, R. Brenner, and K. Sab, Effects of grain size distribution on the stress heterogeneity on yield stress of polycrystals, Computational Materials Science, vol.77, pp.387-398, 2013.

R. Lebensohn, N-site modeling of a 3D viscoplatic polycrystal using Fast Fourier Transform, Acta Materialia, vol.49, pp.2723-2737, 2001.

R. Lebensohn, R. Brenner, O. Castelnau, and A. Rollett, Orientation imagebased micromechanical modelling of subgrain texture evolution in polycrystalline copper, Acta Mater, vol.56, pp.3914-3926, 2008.

R. Lebensohn, J. Escobedo, E. Cerreta, D. Dennis-koller, C. Bronkhorst et al., Modeling void growth in polycrystalline materials, Acta Mater, vol.61, pp.6918-6932, 2013.

R. Lebensohn, M. Montagnat, P. Mansuy, P. Duval, J. Meysonnier et al., Modeling viscoplastic behavior and heterogeneous intracrystalline deformation of columnar ice polycrystals, Acta Mater, vol.57, pp.1405-1415, 2009.
URL : https://hal.archives-ouvertes.fr/insu-00420863

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.46, pp.3018-3026, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00300102

R. A. Lebensohn, M. I. Idiart, . Ponte-castañeda, and P. G. Vincent, Dilatational viscoplasticity of polycrystalline solids with intergranular cavities, Philosophical Magazine, vol.91, pp.3038-3067, 2011.

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, pp.59-69, 2012.

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.

R. A. Lebensohn and C. N. Tomé, A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals, Acta Metallurgica and Materialia, vol.41, pp.2611-2624, 1993.

S. B. Lee, R. A. Lebensohn, and A. D. Rollett, Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms, International Journal of Plasticity, vol.27, pp.707-727, 2011.

S. Lefebvre, B. Devincre, and T. Hoc, Yield stress strengthening in ultrafinegrained metals: A two-dimensional simulation of dislocation dynamics, Journal of the Mechanics and Physics of Solids, vol.55, pp.788-802, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00276782

J. Li, X. 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, pp.135-146, 2012.

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

C. Mareau and S. Berbenni, An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method, International Journal of Plasticity, vol.64, pp.134-150, 2015.

C. Mareau and M. R. Daymond, Micromechanical modelling of twinning in polycrystalline materials: Application to magnesium, International Journal of Plasticity, vol.85, pp.156-171, 2016.

R. Masson, M. Bornert, P. Suquet, and A. Zaoui, An affine formulation for the prediction of the effective properties of non linear composites and poly-crystals, Journal of the Mechanics and Physics of Solids, vol.48, issue.6-7, pp.1203-1227, 2000.

H. Mecking, Low-temperature deformation of polycrystals, Deformation of polycrystals, pp.73-86, 1981.

H. Mecking and U. F. Kocks, Kinetics of flow and strain-hardening, Acta Metallurgica, vol.29, pp.1865-1875, 1981.

S. Mercier and A. Molinari, Homogenization of elasticviscoplastic heterogeneous materials: self-consistent and Mori-Tanaka schemes, International Journal of Plasticity, vol.25, pp.1024-1048, 2009.

M. A. Meyers and K. K. Chawla, Grain size strengthening (chapter 14, Mechanical Metallurgy: Principles and Applications, pp.494-514, 1984.

J. C. Michel, H. Moulinec, and P. Suquet, A computational scheme for linear and non-linear composites with arbitrary phase contrast, International Journal of Numerical Methods Engineering, vol.52, pp.139-160, 2001.

D. P. Mika and P. R. Dawson, Effects of grain interaction on deformation in polycrystals, Mater Sci Eng A, vol.257, pp.62-76, 1998.

A. Molinari, G. R. Canova, and S. Ahzi, A self-consistent approach of the large deformation polycrystal viscoplasticity, Acta Metallurgica and Materialia, vol.35, pp.2983-2994, 1987.

H. Moulinec and P. Suquet, A fast numerical method for computing the linear and non linear properties of composites. Comptes Rendus de l'Académie des, Sciences de 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, Comput. Meth, 1998.
URL : https://hal.archives-ouvertes.fr/hal-01282728

, Appl. Mech. Eng, vol.157, pp.69-94

W. Müller, Mathematical vs. experimental stress analysis of inhomogeneities in solids, Journal of Physics IV, vol.6, issue.C1, pp.139-148, 1996.

W. Müller, Fourier transforms and their application to the formation of texture and changes of morphology in solids, 1998.

L. Nicola, Y. Xiang, J. Vlassak, E. Vandergiessen, and A. Needleman, Plastic deformation of freestanding thin films: experiments and modeling, Journal of the Mechanics and Physics of Solids, vol.54, pp.2089-2110, 2006.

C. Niordson and J. W. Hutchinson, Non-uniform plastic deformation of micron scale objects, International Journal for Numerical Methods in Engineering, vol.56, pp.961-975, 2003.

C. F. Niordson and J. W. Kysar, Computational strain gradient crystal plasticity, Journal of the Mechanics and Physics of Solids, vol.62, pp.31-47, 2014.

C. F. Niordson and B. N. Legarth, Strain gradient effects on cyclic plasticity, Journal of the Mechanics and Physics of Solids, vol.58, pp.542-557, 2010.

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

N. Ohno and D. Okumura, Higher-order stress and grain size effects due to selfenergy of geometrically dislocations, Journal of the Mechanics and Physics of Solids, vol.55, pp.1879-1898, 2007.

N. Ohno, D. Okumura, and T. Shibata, Grain size dependent yield behavior under loading, unloading and reverse loading, International Journal of Modern Physics B, vol.22, pp.5937-5942, 2008.

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

W. Pantleon, Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction, Scripta Materialia, vol.58, issue.11, pp.994-997, 2008.

C. Paramatmuni and A. K. Kanjarla, A crystal plasticity FFT based study of deformation twinning, anisotropy and micromechanics in HCP materials: Application to AZ31 alloy, International Journal of Plasticity, vol.113, pp.269-290, 2019.

M. Peach and J. Koehler, The forces exerted on dislocations and the stress fields produced by them, Physical Review, vol.80, issue.3, pp.436-439, 1950.

C. Perrin, S. Berbenni, H. Vehoff, and M. Berveiller, Role of discrete intragranular slip on lattice rotations in polycrystalline Ni: Experimental and micromechanical studies, Acta Materialia, vol.58, pp.4639-4649, 2010.

N. J. Petch, The cleavage strength of polycryystals, J. Iron Steel Inst, vol.174, pp.25-28, 1953.

J. M. Pipard, N. Nicaise, S. Berbenni, O. Bouaziz, and M. Berveiller, A new mean field micromechanical approach to capture grain size effects, Computational Materials Science, vol.45, pp.604-610, 2009.

S. Puri, A. Das, and A. Acharya, Mechanical response of multicrystalline thin films in mesoscale field dislocation mechanics, Journal of the Mechanics and Physics of Solids, vol.59, pp.2400-2417, 2011.

S. Puri and A. Roy, Plastic deformation of multicrystalline thin films: Grain size distribution vs. grain orientation, Computational Materials Science, vol.52, pp.20-24, 2012.

S. Puri, A. Roy, A. Acharya, and D. Dimiduk, Modeling dislocation sources and size effects at initial yield in continuum plasticity, Journal of Mechanics of Materials and Structures, vol.4, issue.9, pp.1603-1618, 2009.

V. Randle, N. Hansen, and D. J. Jensen, The deformation behaviour of grain boundary regions in polycrystalline aluminium, Philosophical Magazine A, vol.73, issue.2, pp.265-282, 1996.

A. W. Richards, R. A. Lebensohn, and K. Bhattacharya, Interplay of martensitic phase transformation and plastic slip in polycrystals, Acta Materialia, vol.61, pp.4384-4397, 2013.

T. Richeton, S. Berbenni, and M. Berveiller, Grain-size dependent accommodation due to intragranular distribution of dislocation loops, Acta Materialia, vol.57, pp.1347-1356, 2009.

T. Richeton, L. T. Le, T. Chauve, M. Bernacki, S. Berbenni et al., Modelling the transport of geometrically necessary dislocations on slip systems: application to single and multi-crystals of ice, Modelling and Simulation in Materials Science and Engineering, vol.25, issue.27pp, p.25010, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01479768

T. Richeton, G. F. Wang, and C. Fressengeas, Continuity constraints at the interfaces and their consequences on the work hardening of metal-matrix composites, Journal of the Mechanics and Physics of Solids, vol.59, pp.2023-2043, 2011.

A. D. Rollett, R. A. Lebensohn, M. Groeber, Y. Choi, L. Rohrer et al., Stress hot spots in viscoplastic deformation of polycrystals, Modell. Simul. Mater. Sci. Eng, vol.18, p.74005, 2010.

A. Rovinelli, Y. Guilhem, H. Proudhon, R. A. Lebensohn, W. Ludwig et al., Assessing reliability of fatigue indicator parameters for small crack growth via a probabilistic framework, Modell. Simul. Mater. Sci. Eng, vol.25, 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 3-D fatigue crack growth rate of short cracks using multimodal data via Bayesian network: in-situ experiments and crystal plasticity simulations, Journal of the Mechanics and Physics of Solids, vol.115, pp.208-229, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01729179

A. Roy and A. Acharya, Finite element approximation of field dislocation mechanics, J. Mech. Phys. Solids, vol.53, pp.143-170, 2005.

A. Roy and A. Acharya, Size effects and idealized dislocation microstructure at small scales : Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics : Part II, Journal of the Mechanics and Physics of Solids, vol.54, pp.1711-1743, 2006.

A. Roy, S. Puri, and A. Acharya, Phenomenological mesoscopic field dislocation mechanics, lower-order gradient plasticity, and transport of mean excess dislocation density, Model. Simul. Mater. Sci. Eng, vol.15, pp.167-180, 2007.

H. Sabar, M. Berveiller, V. Favier, and S. Berbenni, A new class of micro-macro models for elastic-viscoplastic heterogeneous materials, International Journal of Solids and Structures, vol.39, pp.3257-3276, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00128381

S. Scheriau and R. Pippan, Influence of grain size on orientation changes during plastic deformation, Materials Science and Engineering A, vol.493, pp.48-52, 2008.

K. W. Schwarz, Simulation of dislocations on the mesoscopic scale I. Methods and examples, Journal of Applied Physics, vol.85, issue.1, pp.108-119, 1999.

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

L. Sharma, R. H. Peerlings, P. Shanthraj, F. Roters, and M. G. Geers, FFT-based interface decohesion modelling by a nonlocal interphase, Adv. Model. Simul. Eng. Sci, vol.5, p.7, 2012.

V. P. Smyshlyaev and N. A. Fleck, The role of strain gradients in the grain size effect for polycrystals, Journal of the Mechanics and Physics of Solids, vol.44, pp.465-495, 1996.

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, Procedia IUTAM, vol.3, pp.76-90, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00644773

V. Taupin, S. Berbenni, and C. Fressengeas, Size effects on the hardening of channel-type microstructures: a field dislocation mechanics-based approach, Acta Materialia, vol.60, pp.664-673, 2012.

V. Taupin, S. Berbenni, C. Fressengeas, and O. Bouaziz, On particle size effects: An internal length mean field approach using field dislocation mechanics, Acta Materialia, vol.58, pp.5532-5544, 2010.

V. Taupin, S. Varadhan, J. Chevy, C. Fressengeas, A. J. Beaudoin et al., Effects of size on the dynamics of dislocations in ice single crystals, Physical Review Letters, vol.99, p.155507, 2007.
URL : https://hal.archives-ouvertes.fr/insu-00377504

A. Thompson, M. I. Baskes, and W. F. Flanagan, The dependence of polycrystal work hardening on grain size, Acta Metallurgica, vol.21, pp.1017-1028, 1973.

M. V. Upadhyay, L. Capolungo, V. Taupin, C. Fressengeas, and R. A. 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.

E. Van-der-giessen and A. Needleman, Discrete dislocation plasticity: A simple planar approach, Modelling and Simulation in Materials Science and Engineering, vol.3, pp.689-735, 1995.

S. Varadhan, A. J. Baudoin, A. Acharya, and C. Fressengeas, Dislocation transport using Galerkin/least squares formulation. Modelling and Simulation in Materials, Science and Engineering, vol.14, pp.1245-1270, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00119274

S. Varadhan, A. J. Beaudoin, and C. Fressengeas, Lattice incompatibility and strain-aging in single crystals, Journal of the Mechanics and Physics of Solids, vol.57, pp.1733-1748, 2009.

M. Verdier, M. Fivel, and I. Groma, Mesoscopic scale simulation of dislocation dynamics in FCC metals: Principles and applications. Modelling and Simulation, Materials Science Engineering, vol.6, pp.755-770, 1998.

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.

S. Waheed, R. Hao, A. Bhowmik, D. S. Balint, and F. Giuliani, A unifying scaling for the Bauschinger effect in highly confined thin films: a discrete dislocation plasticity study. Modelling and Simulation in, Materials Science and Engineering, vol.25, issue.5, p.54003, 2017.

D. Wallis, L. N. Hansen, T. B. Britton, and A. J. Wilkinson, Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction, Ultramicroscopy, vol.168, pp.34-45, 2016.

H. Wang, P. D. Wu, C. N. Tomé, and Y. Huang, A finite strain elasticviscoplastic self-consistent model for polycrystalline materials, Journal of the Mechanics and Physics of Solids, vol.58, pp.594-612, 2010.

G. J. Weng, A micromechanical theory of grain size dependence in metal plasticity, Journal of the Mechanics and Physics of Solids, vol.31, pp.193-203, 1983.

F. Willot, Fourier-based schemes for computing the mechanical response of composites with accurate local fields, Comptes Rendus Mecanique, vol.343, pp.232-245, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01096757

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

S. Wulfinghoff, S. Forest, and T. Böhlke, Strain gradient plasticity modeling of cyclic behavior of laminate structures, Journal of the Mechanics and Physics of Solids, vol.79, pp.1-20, 2015.

A. Zeghadi, S. Forest, A. F. Gourgues, and O. Bouaziz, Cosserat continuum modelling of grain size effects in metal polycrystals, Proceedings in Applied Mathematics and Mechanics (PAMM), vol.5, pp.79-82, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00145075