G. Abrivard, E. P. Busso, S. Forest, and B. Appolaire, Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part I: theory and numerical implementation, Philos. Mag, vol.92, pp.3618-3642, 2012.
DOI : 10.1080/14786435.2012.717726

URL : https://hal.archives-ouvertes.fr/hal-00750399

G. Abrivard, E. P. Busso, S. Forest, and B. Appolaire, Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part II: application to recrystallisation, Philos. Mag, vol.92, pp.3643-3664, 2012.
DOI : 10.1080/14786435.2012.717726

URL : https://hal.archives-ouvertes.fr/hal-00750399

N. C. Admal, G. Po, and J. Marian, Diffuse-interface polycrystal plasticity: expressing grain boundaries as geometrically necessary dislocations, Mater. Theory, vol.1, issue.1, p.6, 2017.
DOI : 10.1186/s41313-017-0006-0

URL : https://materialstheory.springeropen.com/track/pdf/10.1186/s41313-017-0006-0

N. C. Admal, G. Po, and J. Marian, A unified framework for polycrystal plasticity with grain boundary evolution, Int. J. Plast, 2018.
DOI : 10.1016/j.ijplas.2018.01.014

URL : http://arxiv.org/pdf/1709.10176

K. Ammar, B. Appolaire, G. Cailletaud, F. Feyel, and S. Forest, Finite element formulation of a phase field model based on the concept of generalized stresses, Comput. Mater. Sci, vol.45, pp.800-805, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00379237

M. Ashby, The deformation of plastically non-homogeneous materials, Philos. Mag, vol.21, pp.399-424, 1970.
DOI : 10.1080/14786437008238426

A. Ask, S. Forest, B. Appolaire, K. Ammar, and O. U. Salman, A cosserat crystal plasticity and phase field theory for grain boundary migration, J. Mech. Phys. Solids, vol.115, pp.167-194, 2018.
DOI : 10.1016/j.jmps.2018.03.006

URL : https://hal.archives-ouvertes.fr/hal-01615967

B. Bacroix and R. Brenner, A phenomenological anisotropic description for dislocation storage and recovery processes in fcc crystals, Comput. Mater. Sci, vol.54, pp.97-100, 2012.
DOI : 10.1016/j.commatsci.2011.10.020

A. Bartels and J. Mosler, Efficient variational constitutive updates for Allen-Cahn-type phase field theory coupled to continuum mechanics, Comput. Methods Appl. Mech. Eng, vol.317, pp.55-83, 2017.
DOI : 10.1016/j.cma.2016.11.024

B. Béucia, P. Franciosi, S. Queyreau, D. Chaubet, and B. Bacroix, Sem observations of grain boundary mobility under thermal and plasticity effects, IOP Conference Series: Materials Science and Engineering, vol.89, 2015.

T. Blesgen, Deformation patterning in three-dimensional large-strain Cosserat plasticity, Mech. Res. Commun, vol.62, pp.37-43, 2014.
DOI : 10.1016/j.mechrescom.2014.08.007

T. Blesgen, A variational model for dynamic recrystallization based on Cosserat plasticity, Compos. Part B Eng, vol.115, pp.236-243, 2017.
DOI : 10.1016/j.compositesb.2016.10.005

E. Borukhovich, P. Engels, T. Boehlke, O. Shchyglo, and I. Steinbach, Large strain elasto-plasticity for diffuse interface models, Model. Simul. Mater. Sci. Eng, vol.23, p.34008, 2014.
DOI : 10.1088/0965-0393/22/3/034008

E. Borukhovich, P. S. Engels, J. Mosler, O. Shchyglo, and I. Steinbach, Large deformation framework for phase-field simulations at the mesoscale, Comput. Mater. Sci, vol.108, pp.367-373, 2015.
DOI : 10.1016/j.commatsci.2015.06.021

E. P. Busso and G. Cailletaud, On the selection of active slip systems in crystal plasticity, Int. J. Plast, vol.21, issue.11, pp.2212-2231, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00154559

J. W. Cahn and J. E. Taylor, A unified approach to motion of grain boundaries, relative tangential translation along grain boundaries, and grain rotation, Acta Mater, vol.52, pp.4887-4898, 2004.

G. Cailletaud, O. Diard, F. Feyel, and S. Forest, Computational crystal plasticity: from single crystal to homogenized polycrystals, Tech. Mech, vol.23, pp.130-145, 2003.

J. Clayton and J. Knap, Phase field modeling and simulation of coupled fracture and twinning in single crystals and polycrystals, Comput. Methods Appl. Mech. Eng, vol.312, pp.447-467, 2016.

S. Conti and M. Ortiz, Dislocation microstructures and the effective behavior of single crystals, Arch. Ration. Mech. Anal, vol.176, pp.103-147, 2005.

E. Cosserat and F. Cosserat, Théorie des corps déformables, 1909.

A. Ask,

P. Dluzewski, Finite deformation of polar media in angular coordinates, Arch. Mech, vol.43, pp.783-793, 1991.

A. C. Eringen, Polar and nonlocal field theories, Continuum Physics, vol.4, 1976.

A. C. Eringen, Nonlocal Continuum Field Theories, 2002.

A. C. Eringen and C. B. Kafadar, Part I. Polar field theories, Continuum Physics, pp.1-73, 1976.

U. Essmann and H. Mughrabi, Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities, Philos. Mag. A, vol.40, issue.6, pp.731-756, 1979.

D. Fan and L. Q. Chen, Computer simulation of grain growth using a continuum field model, Acta Mater, vol.45, issue.2, pp.611-622, 1997.

S. Forest, F. Barbe, and G. Cailletaud, Cosserat modelling of size effects in the mechanical behaviour of polycrystals and multiphase materials, Int. J. Solids Struct, vol.37, pp.7105-7126, 2000.

S. Forest, G. Cailletaud, and R. Sievert, A Cosserat theory for elastoviscoplastic single crystals at finite deformation, Arch. Mech, vol.49, issue.4, pp.705-736, 1997.

S. Forest and N. Guéninchault, Inspection of free energy functions in gradient crystal plasticity, Acta Mech. Sin, vol.29, pp.763-772, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00942896

S. Forest and M. Rubin, A rate-independent crystal plasticity model with a smooth elastic-plastic transition and no slip indeterminacy, Eur. J. Mech. A Solids, vol.55, pp.278-288, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01251477

C. Gérard, B. Bacroix, M. Bornert, G. Cailletaud, J. Crépin et al., Hardening description for fcc materials under complex loading paths, Proceedings of the 17th International Workshop on Computational Mechanics of Materials, vol.45, pp.751-755, 2009.

P. Germain, P. Suquet, and Q. S. Nguyen, Continuum thermodynamics. ASME Trans. Ser. E J. Appl. Mech, vol.50, pp.1010-1020, 1983.

G. Gottstein and L. Shvindlerman, Grain Boundary Migration in Metals, 2010.

M. E. Gurtin, Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance, Physica D Nonlinear Phenom, vol.92, issue.3, pp.178-192, 1996.

M. E. Gurtin and M. T. Lusk, Sharp-interface and phase-field theories of recrystallization in the plane, Physica D Nonlinear Phenom, vol.130, issue.1-2, pp.133-154, 1999.

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

F. Humphreys and M. Hatherly, Recrystallization and Related Annealing Phenomena, 2004.

M. Jafari, M. Jamshidian, S. Ziaei-rad, D. Raabe, and F. Roters, Constitutive modeling of strain induced grain boundary migration via coupling crystal plasticity and phase-field methods, Int. J. Plast, vol.99, pp.19-42, 2017.

C. Kafadar and A. Eringen, Micropolar media-I the classical theory, Int. J. Eng. Sci, vol.9, issue.3, pp.271-305, 1971.

S. Kessel, Lineare Elastizitätstheorie des anisotropen Cosserat-Kontinuums, Abhandlungen der Braunschweig. Wiss. Ges, vol.16, pp.1-22, 1964.

R. Kobayashi and Y. Giga, Equations with singular diffusivity, J. Stat. Phys, vol.95, issue.5-6, pp.1189-1220, 1999.

R. Kobayashi, J. A. Warren, and W. C. Carter, A continuum model of grain boundaries, Physica D, vol.140, issue.1-2, pp.141-150, 2000.

U. F. Kocks and H. Mecking, Physics and phenomenology of strain hardening: the FCC case, Prog. Mater. Sci, vol.48, pp.171-273, 2003.

E. Kröner, On the physical reality of torque stresses in continuum mechanics, Int. J. Eng. Sci, vol.1, pp.261-278, 1963.

E. Kröner, Benefits and shortcomings of the continuous theory of dislocations, Int. J. Solids Struct, vol.38, pp.1115-1134, 2001.

R. Lakes, A pathological situation in micropolar elasticity, J. Appl. Mech, vol.52, pp.234-235, 1985.

C. Ling, S. Forest, J. Besson, B. Tanguy, and F. Latourte, A reduced micromorphic single crystal plasticity model at finite deformations. Application to strain localization and void growth in ductile metals, Int. J. Solids Struct, vol.134, pp.43-69, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01722948

A. E. Lobkovsky and J. A. Warren, Sharp interface limit of a phase-field model of crystal grains, Phys. Rev. E, vol.63, issue.5, p.51605, 2001.

J. Mandel, Plasticité classique et viscoplasticité: course held at the Department of Mechanics of Solids, 1971.

J. Mayeur and D. Mcdowell, An evaluation of higher-order single crystal strength models for constrained thin films subjected to simple shear, J. Mech. Phys. Solids, vol.61, pp.1935-1954, 2013.

J. Mayeur, D. Mcdowell, and D. Bammann, Dislocation-based micropolar single crystal plasticity: comparison of multi-and single criterion theories, J. Mech. Phys. Solids, vol.59, pp.398-422, 2011.

Y. Mellbin, H. Hallberg, and M. Ristinmaa, An extended vertex and crystal plasticity framework for efficient multiscale modeling of polycrystalline materials, Int. J. Solids Struct, vol.125, pp.150-160, 2017.

S. D. Mesarovic, S. Forest, and J. P. Jaric, Size-dependent energy in crystal plasticity and continuum dislocation models, Proc. R. Soc. A Math. Phys. Eng. Sci, vol.471, p.20140868, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01131017

P. Neff, The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric, ZAMM J. Appl. Math. Mech. Zeitschrift für Angewandte Mathematik und Mechanik, vol.86, pp.892-912, 2006.

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

N. Ohno and D. Okumura, Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations, J. Mech. Phys. Solids, vol.55, pp.1879-1898, 2007.

L. Priester, Grain Boundaries: From Theory to Engineering, Springer Series in Materials Science, vol.172, 2013.

, A Cosserat-phase-field theory of crystal plasticity

T. Pusztai, G. Bortel, and L. Gránásy, Phase field theory of polycrystalline solidification in three dimensions, Eur. Lett.), vol.71, issue.1, pp.131-137, 2005.

V. D. Rancourt, B. Appolaire, S. Forest, and K. Ammar, Homogenization of viscoplastic constitutive laws within a phase field approach, J. Mech. Phys. Solids, vol.88, pp.35-48, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01271808

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

C. Sansour, A unified concept of elastic-viscoplastic Cosserat and micromorphic continua, Journal de Physique IV, vol.8, pp.8-341, 1998.

D. Schneider, F. Schwab, E. Schoof, A. Reiter, C. Herrmann et al., On the stress calculation within phase-field approaches: a model for finite deformations, Comput. Mech, vol.60, pp.203-217, 2017.

P. Shanthraj, B. Svendsen, L. Sharma, F. Roters, and D. Raabe, Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture, J. Mech. Phys. Solids, vol.99, pp.19-34, 2017.

R. Sievert, Zur Zerlegung der Verformungsmaße des Cosserat-Kontinuums bei großen inelastischen Deformationen, Z. Angew. Math. Mech, vol.75, pp.205-206, 1995.

I. Steinbach and F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D Nonlinear Phenom, vol.134, issue.4, pp.385-393, 1999.

I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler et al., A phase field concept for multiphase systems, Physica D Nonlinear Phenom, vol.94, issue.3, pp.135-147, 1996.

A. Sutton and R. Ballufi, Interfaces in Crystalline Solids, 2007.

B. Svendsen, Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations, J. Mech. Phys. Solids, vol.50, pp.124-131, 2002.

C. Teodosiu and F. Sidoroff, A theory of finite elastoviscoplasticity of single crystals, Int. J. Eng. Sci, vol.14, pp.165-176, 1976.

Z. T. Trautt and Y. Mishin, Grain boundary migration and grain rotation studied by molecular dynamics, Acta Mater, vol.60, pp.2407-2424, 2012.

M. A. Tschopp, S. P. Coleman, and D. L. Mcdowell, Symmetric and asymmetric tilt grain boundary structure and energy in cu and al (and transferability to other fcc metals), Integr. Mater. Manuf. Innov, vol.4, issue.1, p.11, 2015.

M. Upmanyu, D. J. Srolovitz, A. E. Lobkovsky, J. A. Warren, and W. C. Carter, Simultaneous grain boundary migration and grain rotation, Acta Mater, vol.54, pp.1707-1719, 2006.

A. Vondrous, P. Bienger, S. Schreijäg, M. Selzer, D. Schneider et al., Combined crystal plasticity and phase-field method for recrystallization in a process chain of sheet metal production, Comput. Mech, vol.55, issue.2, pp.439-452, 2015.

J. A. Warren, R. Kobayashi, A. E. Lobkovsky, and W. C. Carter, Extending phase field models of solidification to polycrystalline materials, Acta Mater, vol.51, issue.20, pp.6035-6058, 2003.
DOI : 10.1016/s1359-6454(03)00388-4

S. Wulfinghoff, S. Forest, and T. Böhlke, Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures, J. Mech. Phys. Solids, vol.79, pp.1-20, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01149855

Z. Package, Non-linear Material and Structure Analysis Suite, 2013.

L. Zhao, P. Chakraborty, M. Tonks, and I. Szlufarska, On the plastic driving force of grain boundary migration: a fully coupled phase field and crystal plasticity model, Comput. Mater. Sci, vol.128, pp.320-330, 2017.