P. R. Dawson and A. Kumar, Deformation Process Simulations Using Polycristal, Large plastic deformation of crystalline aggregates, International Center for Mechanical Sciences, Courses and Lectures n° 376, p.247, 1997.

L. Delannay, P. J. Jacques, and S. R. Kalindidi, Finite element modeling of crystal plasticity with grains shaped as truncated octahedrons, International Journal of Plasticity, vol.22, issue.10, pp.22-1879, 2006.
DOI : 10.1016/j.ijplas.2006.01.008

J. D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and relayed problems, Proc. Roy. Soc. London A 241, pp.376-396, 1957.

R. Fortunier, Dual potentials and extremum work principles in single crystal plasticity, Journal of the Mechanics and Physics of Solids, vol.37, issue.6, 1989.
DOI : 10.1016/0022-5096(89)90019-7

A. M. Habraken and L. Duchêne, Anisotropic elasto-plastic finite element analysis using a stress???strain interpolation method based on a polycrystalline model, International Journal of Plasticity, vol.20, issue.8-9, pp.1525-1560, 2004.
DOI : 10.1016/j.ijplas.2003.11.006

A. V. Hershey, The plasticity of an isotropic aggregate of anisotropic facecentered cubic crystals, J. Appl. Mech, vol.21, pp.241-249, 1954.

R. Hill, A theory of the yielding and plastic flow of anisotropic materials, Proc. Roy. Soc. London, A 193, pp.281-297, 1948.

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

R. Hill, Constitutive dual potentials in classical plasticity, Journal of the Mechanics and Physics of Solids, vol.35, issue.1, pp.22-33, 1987.
DOI : 10.1016/0022-5096(87)90025-1

S. Hiwatashi, A. Van-bael, P. Van-houtte, and C. Teodosiu, Modelling of plastic anisotropy based on texture and dislocation structure, Computational Materials Science, vol.9, issue.1-2, p.274, 1997.
DOI : 10.1016/S0927-0256(97)00069-4

H. Honeff and H. Mecking, Analysis of the deformation texture at different rolling conditions, Proceedings of the 6th International Conference on Textures of Materials, pp.347-355, 1981.

W. F. Hosford, A Generalized Isotropic Yield Criterion, Journal of Applied Mechanics, vol.39, issue.2, pp.607-609, 1972.
DOI : 10.1115/1.3422732

J. G. Hu, J. J. Jonas, and T. Ishikawa, FEM simulation of the forming of textured aluminum sheets, Materials Science and Engineering: A, vol.256, issue.1-2, p.51, 1998.
DOI : 10.1016/S0921-5093(98)00813-2

D. Kim, F. Barlat, S. Bouvier, M. Rabahallah, T. Balan et al., Non-quadratic anisotropic potentials based on linear transformation of plastic strain rate, International Journal of Plasticity, vol.23, issue.8, pp.1380-1399, 2007.
DOI : 10.1016/j.ijplas.2007.01.006

URL : https://hal.archives-ouvertes.fr/hal-01193013

U. F. Kocks, C. , and H. , Slip geometry in partially constrained deformation, Acta Metall, p.695, 1982.

S. Li, E. Hoferlin, and A. Van-bael, Application of a Texture-Based Plastic Potential in Earing Prediction of an IF Steel, Advanced Engineering Materials, vol.3, issue.12, pp.990-994, 2001.
DOI : 10.1002/1527-2648(200112)3:12<990::AID-ADEM990>3.0.CO;2-X

R. Masson and A. Zaoui, Self-consistent estimates for the rate-dependentelastoplastic behaviour of polycrystalline materials, Journal of the Mechanics and Physics of Solids, vol.47, issue.7, pp.1543-1568, 1999.
DOI : 10.1016/S0022-5096(98)00106-9

A. Molinari, R. Kouddane, and S. Azhi, On the self-consistent modeling of elastic-plastic behavior of polycrystals, Mechanics of Materials, vol.26, issue.1, pp.43-62, 1997.
DOI : 10.1016/S0167-6636(97)00017-3

K. W. Neale, Use of crystal plasticity in metal forming simulations, International Journal of Mechanical Sciences, vol.35, issue.12, pp.1053-1063, 1993.
DOI : 10.1016/0020-7403(93)90055-Y

M. Rabahallah, T. Balan, S. Bouvier, B. Bacroix, F. Barlat et al., Ability of advanced plastic potentials to predict the anisotropic yielding behaviour, International Journal of Plasticity, 2007.

G. Sachs, Zur Ableitung einer Flie??bedingung, Z. Ver. Deu. Ing, vol.72, pp.734-736, 1928.
DOI : 10.1007/978-3-642-92045-5_12

G. I. Taylor, Plastic strain in metals, J. Inst. Metals, vol.62, pp.307-324, 1938.

L. S. Toth and P. Van-houtte, Discretization technique for orientation distribution functions, textures and microstructure, pp.229-244, 1992.

A. Van-bael, Anisotropic Yield Loci Derived from Crystallographic Data and their Application in Finite-element Simulations of Plastic Forming Processes, 1994.

P. Van-houtte, On the equivalence of the relaxed Taylor theory and the Bishop-Hill theory for partially constrained plastic deformation of crystals, Materials Science and Engineering, vol.55, issue.1, pp.69-77, 1982.
DOI : 10.1016/0025-5416(82)90085-4

P. Van-houtte, A Comprehensive Mathematical Formulation of an Extended Taylor???Bishop???Hill Model Featuring Relaxed Constraints, the Renouard???Wintenberger Theory and a Strain Rate Sensitivity Model, Textures and Microstructures, vol.8, pp.8-9, 1988.
DOI : 10.1155/TSM.8-9.313

P. Van-houtte, K. Mols, A. Van-bael, and E. Aernoudt, Application of Yield Loci Calculated From Texture Data, Textures and Microstructures, vol.11, issue.1, pp.23-39, 1989.
DOI : 10.1155/TSM.11.23

P. Van-houtte, A. Van-bael, J. Winters, E. Aernoudt, F. Hall et al., Modelling of complex forming processes, Modelling of Plastic Deformation and Its Engineering Applications (Proc. of the 13th Risø Inter. Symp. on Mat. Sci.), pp.161-172, 1992.

A. Van-bael and P. Van-houtte, Convex fourth and sixth-order plastic potentials derived form crystallographic texture, Non Linear Mechanics of Anisotropic Materials. Proceedings of the Sixth European Mechanics of Materials Conference (EMMC6), 2002.

P. Van-houtte, Application of plastic potentials to strain rate sensitive and insensitive anisotropic materials, International Journal of Plasticity, vol.10, issue.7, pp.719-748, 1994.
DOI : 10.1016/0749-6419(94)90043-4

M. Arminjon and B. Bacroix, On plastic potentials for anisotropic metals and their derivation from the texture function, Acta Mechanica, vol.11, issue.3-4, pp.219-243, 1991.
DOI : 10.1007/BF01177098

M. Arminjon, B. Bacroix, D. Imbault, and J. L. Raphanel, A forth-order plastic potentiel for anisotropic metals and its analytical calculation from texture data, Acta Mech, pp.33-51, 1994.

B. Bacroix and P. Gilormini, Finite-element simulations of earing in polycristalline materials using a texture-adjusted strain-rate potential, Modelling Simul, Mater. Sci. Eng, vol.3, pp.1-21, 1995.

F. Barlat, Strain rate potential for metals and its application to minimum plastic work path calculations, International Journal of Plasticity, vol.9, issue.1, pp.51-63, 1993.
DOI : 10.1016/0749-6419(93)90013-G

H. L. Cao, Modélisation mécanique et simulation numérique de l'emboutissage, Thèse de doctorat, 1990.

M. Dutko, D. Peric, and D. R. Owen, Universal anisotropic yield criterion based on superquadric functional representation: Part 1. Algorithmic issues and accuracy analysis, Computer Methods in Applied Mechanics and Engineering, vol.109, issue.1-2, pp.73-93, 1993.
DOI : 10.1016/0045-7825(93)90225-M

A. Eterovic, L. Bathe, and K. J. , A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kenematic hardening using the logarithmic stress and strain measures, Int. J. Num. Meth. Eng, pp.30-1099, 1990.

P. Genevois, Etude expérimentale et modélisation du comportement plastique anisotrope de tles d'acier en grandes transformations, Thèse de doctorat, 1992.

R. Hill, Constitutive dual potentials in classical plasticity, Journal of the Mechanics and Physics of Solids, vol.35, issue.1, pp.23-33, 1987.
DOI : 10.1016/0022-5096(87)90025-1

S. Hiwatashi, A texture and microstructure-based constitutive model for plastic anisotropy and its application to forming limit prediction under strain path changes, 1998.

E. Hoferlin, Incorporation of an accurate model of texture and strain-path induced anisotropy in simulations of sheet metal forming, Thèse de doctorat, 2001.

T. J. Hughes, Numerical implementation of constitutive models: Rate independent deviatoric plasticity: S. Nemat-Masser et al. (editeurs), Theoretical foundation for large-scale computations for nonlinear material behavior, pp.29-57, 1984.

T. Ladreyt, Modélisation bidimensionnelle et simulation numérique des processus de mise en forme des tles dans l'industrie automobile, Thèse de doctorat, 1992.

E. H. Lee, Elastic-plastic deformations at finite strains, J. Appl; Mech, vol.36, 1969.

S. Li, E. Hoferlin, A. Van-bael, P. Van-houtte, and C. Teodosiu, Finite element modeling of plastic anisotropy induced by texture and strain-path change, International Journal of Plasticity, vol.19, issue.5, pp.647-674, 2003.
DOI : 10.1016/S0749-6419(01)00079-1

J. Mandel, Définition d'un repère privilégié pour l'étude des transformations anélastiques du polycristal, J. Méc. Appl, vol.1, p.7, 1982.

. Makinouchi, Elastic-plastic stress analysis of binding and forming of sheet metal; computer modelling of sheet metal forming process, p.161, 1985.

A. Makinouchi, Finite element modelling of draw-bending process of sheet metal; numerical methods in industrial forming processes, Proc. NUMIFORM'86 Conf, p.327, 1986.

M. Ortiz and J. C. Simo, An analysis of a new class of integration algorithms for elastoplastic constitutive relations, International Journal for Numerical Methods in Engineering, vol.51, issue.3, pp.353-366, 1986.
DOI : 10.1007/978-1-4615-9988-3

M. D. Ortiz, E. Owen, E. Hinton, and . Onate, Some computational aspects of finite deformation plasticity, Proc. 2.end Int. Conf. on computational plasticity, p.1717, 1987.

M. S. Park and B. C. Lee, GEOMETRICALLY NON-LINEAR AND ELASTOPLASTIC THREE-DIMENSIONAL SHEAR FLEXIBLE BEAM ELEMENT OF VON-MISES-TYPE HARDENING MATERIAL, International Journal for Numerical Methods in Engineering, vol.56, issue.3, pp.383-408, 1996.
DOI : 10.1002/sapm197352287

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes: The art of scientific computing, 1992.

K. Schweizerhof and J. O. Hallquist, Explicit integration schemes and contact formulations for thin sheet metal forming, FE-simulation of 3-D sheet metal forming processes in automotive industry, VDI Berichte Nr, vol.894, p.405, 1991.

F. Sidoroff, Formulation Elasto-plastique en grandes déformations, 1981.

L. Szabó and J. J. Jonas, Consistent tangent operator for plasticity models based on the plastic strain rate potential, Computer Methods in Applied Mechanics and Engineering, vol.128, issue.3-4, pp.315-323, 1995.
DOI : 10.1016/0045-7825(95)00884-5

V. Tabacaru, H. Haddadi, C. Maier, S. Bouvier, and C. Teodosiu, Essais de traction/cisaillement et identification de trois modèles élasto-plastiques pour les acier DP600, pp.500-506, 2003.

C. Teodosiu and F. Sidoroff, A theory of the finite elastoplasticity of single crystal, Int. J, 1976.

C. Teodosiu and P. Genevois, Modelling large deformation anisotropic plastic behaviour of mild steel, Proc. Int. Symp. MECAMAT on inelastic behaviour of solids: Models and utilisation, p.211, 1988.

C. Teodosiu and H. L. Cao, Residual stress after axisymetric deep drawing, Proc. 15st Biennial congress I.D.D.R.G. on controlling sheet metal forming processes North American Deep Drawing Research Group: ASM International, p.309319, 1988.

C. Teodosiu, The plastic spin: Microstructural origin and computationnal significance, 1989.

A. Van-bael, Anisotropic yield loci derived from crystallographic data and their application in finit-element simulations of plastic forming processes, 1994.

A. Van-bael and P. Van-houtte, Convex fourth and sixth-order plastic potentials derived form crystallographic texture, Non Linear Mechanics of Anisotropic Materials. Proceedings of the Sixth European Mechanics of Materials Conference (EMMC6), 2002.

J. W. Yoon, D. Y. Yang, and K. Chung, Elasto-plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials, Computer Methods in Applied Mechanics and Engineering, vol.174, issue.1-2, 1999.
DOI : 10.1016/S0045-7825(98)00275-8

H. Ziegler, An introduction to thermomechanics, North-Holland, 1977.

Y. Zhou, J. J. Jonas, L. Szabo, A. Makinde, M. Jain et al., Incorporation of an anisotropic (texture-based) strain-rate potential into three-dimensional finite element simulations, International Journal of Plasticity, vol.13, issue.1-2, pp.165-181, 1997.
DOI : 10.1016/S0749-6419(97)00006-5

J. Alves, Simulaçao numerica do processo de estampagem de chapas matalicas modelacao mecanica e metodos numericos, 2003.

M. Arminjon and B. Bacroix, On plastic potentials for anisotropic metals and their derivation from the texture function, Acta Mechanica, vol.11, issue.3-4, pp.219-243, 1991.
DOI : 10.1007/BF01177098

M. Arminjon, B. Bacroix, D. Imbault, and J. L. Raphanel, A fourth-order plastic potential for anisotropic metals and its analytical calculation from the texture function, Acta Mechanica, vol.34, issue.1-4, pp.33-51, 1994.
DOI : 10.1007/BF01201818

B. Bacroix and P. Gilormini, Finite-element simulations of earing in polycrystalline materials using a texture-adjusted strain-rate potential, Modelling and Simulation in Materials Science and Engineering, vol.3, issue.1, pp.1-21, 1995.
DOI : 10.1088/0965-0393/3/1/001

F. Barlat and O. Richmond, Prediction of tricomponent plane stress yield surfaces and associated flow behaviour of strongly textured FCC polycrystalline sheet, Materials Sciences and Engineering, issue.3, pp.1-21, 1987.

F. Barlat, D. J. Lege, and J. C. Brem, A six-component yield function for anisotropic materials, International Journal of Plasticity, vol.7, issue.7, p.693, 1991.
DOI : 10.1016/0749-6419(91)90052-Z

F. Barlat, K. Chung, and O. Richmond, Strain rate potential for metals and its application to minimum plastic work path calculations, International Journal of Plasticity, vol.9, issue.1, pp.51-63, 1993.
DOI : 10.1016/0749-6419(93)90013-G

F. Barlat, H. Aretz, J. W. Yoon, M. E. Karabin, J. C. Brem et al., Linear transformation based anisotropic yield function, Int. J. Plasticity, vol.21, 1009.
DOI : 10.1016/j.ijplas.2004.06.004

F. Barlat and K. Chung, Anisotropic strain rate potential for aluminum alloy plasticity, Proc. 8th ESAFORM Conference on Material Forming, 2005.

D. Banabic, The Publishing House of the Romanian Academy, pp.415-418

J. F. Bishop and R. Hill, XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses., The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol.72, issue.327, pp.414-427, 1951.
DOI : 10.1098/rspa.1923.0023

L. Bourne and R. Et-hill, On the correlation of the directional properties of rolled sheets in tension and cupping tests, Philosophical Magazine, vol.41, pp.671-681, 1950.

K. Chung and K. Shah, Finite element simulation of sheet metal forming for planar anisotropic metals, International Journal of Plasticity, vol.8, issue.4, pp.453-476, 1992.
DOI : 10.1016/0749-6419(92)90059-L

P. Flores, L. Duchêne, T. Lelotte, C. Bouffioux, F. Houdaigui et al., Model Identification and FE Simulations: Effect of Different Yield Loci and Hardening Laws in Sheet Forming, pp.371-381, 2005.

R. Hill, A Theory of the Yielding and Plastic Flow of Anisotropic Metals, Proc. R. Soc. Lond., A193, p.281, 1948.
DOI : 10.1098/rspa.1948.0045

R. Hill, The mathematical theory of plasticity, pp.317-332, 1990.

E. Hoferlin, Incorporation of an accurate model of texture and strain-path induced anisotropy in simulations of sheet metal forming, 2001.

E. Hoferlin, S. Li, A. Van-bael, and P. Van-houtte, Texture-and microstructure-induced anisotropy:micro-macro modelling, implementation, Simulation of Materials Processing: Theory,Methods and Applications, Proc. of Inter. Conf. Numiform 2001. Swets & Zeitlinger, pp.209-214, 2001.

J. G. Hu, J. J. Jonas, and T. Ishikawa, FEM simulation of the forming of textured aluminum sheets, Materials Science and Engineering: A, vol.256, issue.1-2, p.51, 1998.
DOI : 10.1016/S0921-5093(98)00813-2

S. Li, E. Hoferlin, and A. Van-bael, Application of a Texture-Based Plastic Potential in Earing Prediction of an IF Steel, Advanced Engineering Materials, vol.3, issue.12, pp.990-994, 2001.
DOI : 10.1002/1527-2648(200112)3:12<990::AID-ADEM990>3.0.CO;2-X

L. P. Moreira and G. Ferron, Influence of the plasticity model in sheet metal forming simulations, Journal of Materials Processing Technology, vol.155, issue.156, pp.155-156, 2004.
DOI : 10.1016/j.jmatprotec.2004.04.269

L. P. Moreira, Étude numérique de l'influence du modèle de plasticité sur le comportement des tôles lors de l'emboutissage, Thèse de Doctorat, 2002.

M. Rabahallah, T. Balan, S. Bouvier, B. Bacroix, C. Teodosiu et al., Finite element simulation of sheet metal forming using anisotropic strain-rate potentials Impact of the parameter identification of plastic potentials on the finite element simulation of sheet metal forming, Proc. Conf Proc. Conf, 2007.

W. Schaller, Sheet Metal Industries, pp.621-624, 1972.

L. Szabó and J. J. Jonas, Consistent tangent operator for plasticity models based on the plastic strain rate potential, Computer Methods in Applied Mechanics and Engineering, vol.128, issue.3-4, pp.315-323, 1995.
DOI : 10.1016/0045-7825(95)00884-5

D. V. Wilson and R. D. Bulter, The role of cup-drawing tests in measuring drawability, Journal of the Institute of Metals, vol.90, pp.473-483, 1962.

J. W. Yoon, F. Barlat, R. E. Dick, and M. E. Karabin, Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function, International Journal of Plasticity, vol.22, issue.1, pp.174-193, 2006.
DOI : 10.1016/j.ijplas.2005.03.013

Y. Zhou, J. J. Jonas, J. Savoie, A. Makinde, and S. R. Macewen, Effect of texture on earing in FCC metals: Finite element simulations, International Journal of Plasticity, vol.14, issue.1-3, pp.14-117, 1998.
DOI : 10.1016/S0749-6419(97)00044-2