N. Aravas, Finite elastoplastic transformations of transversely isotropic metals, International Journal of Solids and Structures, vol.29, issue.17, pp.2137-2157, 1992.
DOI : 10.1016/0020-7683(92)90062-X

N. Aravas, P. Castañeda, and P. , Numerical methods for porous metals with deformation-induced anisotropy, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.36-38, pp.3767-3805, 2004.
DOI : 10.1016/j.cma.2004.02.009

Y. Bao and T. Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space, International Journal of Mechanical Sciences, vol.46, issue.1, pp.81-98, 2004.
DOI : 10.1016/j.ijmecsci.2004.02.006

I. Barsoum and J. Faleskog, Rupture mechanisms in combined tension and shear???Experiments, International Journal of Solids and Structures, vol.44, issue.6, pp.1768-1786, 2007.
DOI : 10.1016/j.ijsolstr.2006.09.031
URL : https://doi.org/10.1016/j.ijsolstr.2006.09.031

A. A. Benzerga, Micromechanics of coalescence in ductile fracture, Journal of the Mechanics and Physics of Solids, vol.50, issue.6, pp.1331-1362, 2002.
DOI : 10.1016/S0022-5096(01)00125-9

A. A. Benzerga, J. Besson, and A. Pineau, Anisotropic ductile fracture, Acta Materialia, vol.52, issue.15, pp.4623-4638, 2004.
DOI : 10.1016/j.actamat.2004.06.020
URL : https://hal.archives-ouvertes.fr/hal-00164227

A. A. Benzerga, J. Besson, and A. Pineau, Anisotropic ductile fracture, Acta Materialia, vol.52, issue.15, pp.4639-4650, 2004.
DOI : 10.1016/j.actamat.2004.06.019
URL : https://hal.archives-ouvertes.fr/hal-00164227

A. A. Benzerga and J. Leblond, Ductile Fracture by Void Growth to Coalescence, Adv. Appl. Mech, vol.44, pp.170-297, 2010.
DOI : 10.1016/S0065-2156(10)44003-X

G. Boisot, L. Laiarinandrasana, J. Besson, C. Fondc, and G. Hochstetterb, Experimental investigations and modeling of volume change induced by void growth in polyamide 11, International Journal of Solids and Structures, vol.48, issue.19, pp.2642-2654, 2011.
DOI : 10.1016/j.ijsolstr.2011.05.016
URL : https://hal.archives-ouvertes.fr/hal-00624022

B. Budiansky, J. W. Hutchinson, and S. Slutsky, Void growth and collapse in viscous solids. Mechanics of Solids, The Rodney Hill 60th aniversary, pp.13-45, 1982.

C. C. Chu and A. Needleman, Void Nucleation Effects in Biaxially Stretched Sheets, Journal of Engineering Materials and Technology, vol.102, issue.3, pp.249-256, 1980.
DOI : 10.1115/1.3224807

Y. Dafalias and F. , The Plastic Spin, Journal of Applied Mechanics, vol.52, issue.4, pp.865-871, 1985.
DOI : 10.1115/1.3169160

K. Danas and . Lms, Homogenization-based constitutive models for viscoplastic porous media with evolving microstructure, 2008.
DOI : 10.1016/j.ijsolstr.2008.02.007
URL : https://doi.org/10.1016/j.ijsolstr.2008.02.007

K. Danas, M. I. Idiart, P. Castañeda, and P. , A homogenization-based constitutive model for two-dimensional viscoplastic porous media, Comptes Rendus M??canique, vol.336, issue.1-2, pp.79-90, 2008.
DOI : 10.1016/j.crme.2007.10.017
URL : https://hal.archives-ouvertes.fr/hal-00491344

K. Danas, M. I. Idiart, P. Castañeda, and P. , A homogenization-based constitutive model for isotropic viscoplastic porous media, International Journal of Solids and Structures, vol.45, issue.11-12, pp.3392-3409, 2008.
DOI : 10.1016/j.ijsolstr.2008.02.007
URL : https://hal.archives-ouvertes.fr/hal-00491345

K. Danas, P. Castañeda, and P. , A finite-strain model for anisotropic viscoplastic porous media: I ??? Theory, European Journal of Mechanics - A/Solids, vol.28, issue.3, pp.387-401, 2009.
DOI : 10.1016/j.euromechsol.2008.11.002
URL : https://hal.archives-ouvertes.fr/hal-00491346

K. Danas, P. Castañeda, and P. , A finite-strain model for anisotropic viscoplastic porous media: II ??? Applications, European Journal of Mechanics - A/Solids, vol.28, issue.3, pp.402-416, 2009.
DOI : 10.1016/j.euromechsol.2008.11.003
URL : https://hal.archives-ouvertes.fr/hal-00526643

K. Danas, P. Castañeda, and P. , Influence of the Lode parameter and the stress triaxiality on the failure of elasto-plastic porous materials, International Journal of Solids and Structures, vol.49, issue.11-12
DOI : 10.1016/j.ijsolstr.2012.02.006
URL : https://hal.archives-ouvertes.fr/hal-00755852

M. Dunand and D. Mohr, Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading, Engineering Fracture Mechanics, vol.78, issue.17, 2011.
DOI : 10.1016/j.engfracmech.2011.08.008
URL : https://hal.archives-ouvertes.fr/hal-00826122

M. Dunand and D. Mohr, Hybrid experimental???numerical analysis of basic ductile fracture experiments for sheet metals, International Journal of Solids and Structures, vol.47, issue.9, pp.1130-1143, 2010.
DOI : 10.1016/j.ijsolstr.2009.12.011
URL : https://hal.archives-ouvertes.fr/hal-00620568

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

S. Feld-payet, J. Besson, and F. Feyel, Finite Element Analysis of Damage in Ductile Structures Using a Nonlocal Model Combined with a Three-field Formulation, International Journal of Damage Mechanics, vol.3, issue.1, pp.655-680, 2011.
DOI : 10.1016/0045-7949(84)90231-1
URL : https://hal.archives-ouvertes.fr/hal-00619641

L. Flandi and J. Leblond, A new model for porous nonlinear viscous solids incorporating void shape effects ??? I: Theory, European Journal of Mechanics - A/Solids, vol.24, issue.4, pp.537-551, 2005.
DOI : 10.1016/j.euromechsol.2005.03.003

N. A. Fleck and J. W. Hutchinson, Void Growth in Shear, Proc. R. Soc. Lond. A 407, pp.435-458, 1986.
DOI : 10.1098/rspa.1986.0104

M. G?ar?ajeug?ar?g?ar?ajeu, J. Michel, and P. Suquet, A micromechanical approach of damage in viscoplastic materials by evolution in size, shape and distribution of voids, Comp. Methods Appl. Mech. Engrg, vol.183, pp.223-246, 2000.

G. Jr, W. M. Moody, and N. R. , Ductile fracture, J. Phys. Chem. Solids, vol.48, pp.1035-1074, 1987.

A. Ghahremaninezhad and K. Ravi-chandar, Ductile failure in polycrystalline OFHC copper, International Journal of Solids and Structures, vol.48, issue.24, 2011.
DOI : 10.1016/j.ijsolstr.2011.07.001
URL : https://doi.org/10.1016/j.ijsolstr.2011.07.001

M. Gologanu, J. Leblond, and J. Devaux, Approximate models for ductile metals containing non-spherical voids???Case of axisymmetric prolate ellipsoidal cavities, Journal of the Mechanics and Physics of Solids, vol.41, issue.11, pp.1723-1754, 1993.
DOI : 10.1016/0022-5096(93)90029-F

M. Gologanu, J. Leblond, and J. Devaux, Approximate Models for Ductile Metals Containing Nonspherical Voids???Case of Axisymmetric Oblate Ellipsoidal Cavities, Journal of Engineering Materials and Technology, vol.116, issue.3, pp.290-297, 1994.
DOI : 10.1115/1.2904290

M. Gologanu, J. Leblond, and J. Devaux, Recent Extensions of Gurson???s Model for Porous Ductile Metals, Continuum micromechanics. In: CISM lectures series, pp.61-130, 1997.
DOI : 10.1007/978-3-7091-2662-2_2

A. L. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I???Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, vol.99, issue.1, pp.2-15, 1977.
DOI : 10.1115/1.3443401

Z. Hashin, The elastic moduli of heterogeneous materials, J. Appl. Mech, pp.143-150, 1962.

R. Hill, Aspects of invariance in solids mechanics Advances in Applied Mechanics 18, pp.1-75, 1978.

M. I. Idiart, H. Moulinec, P. P. Castañeda, and P. Suquet, Macroscopic behavior and field fluctuations in viscoplastic composites: Second-order estimates versus full-field simulations, Journal of the Mechanics and Physics of Solids, vol.54, issue.5, pp.1029-1063, 2006.
DOI : 10.1016/j.jmps.2005.11.004
URL : https://hal.archives-ouvertes.fr/hal-00111463

M. I. Idiart, Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates, Journal of the Mechanics and Physics of Solids, vol.56, issue.8, pp.2599-2617, 2008.
DOI : 10.1016/j.jmps.2008.03.004

M. I. Idiart, The macroscopic behavior of power-law and ideally plastic materials with elliptical distribution of porosity, Mechanics Research Communications, vol.35, issue.8, pp.583-588, 2008.
DOI : 10.1016/j.mechrescom.2008.06.002

G. R. Johnson and W. H. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Engineering Fracture Mechanics, vol.21, issue.1, pp.31-48, 1985.
DOI : 10.1016/0013-7944(85)90052-9

M. Kailasam, N. Aravas, P. Castañeda, and P. , Porous metals with developing anisotropy: Constitutive models, computational issues and applications to deformation processing, Computer Modeling in Engineering and Sciences, vol.1, pp.105-118, 2000.

M. Kailasam, P. Castañeda, and P. , The Evolution of Anisotropy in Porous Materials and its Implications for Shear Localization, IUTAM Symposium on Mechanics of Granular and Porous Materials, pp.365-376, 1997.
DOI : 10.1007/978-94-011-5520-5_33

M. Kailasam, P. Castañeda, and P. , A general constitutive theory for linear and nonlinear particulate media with microstructure evolution, Journal of the Mechanics and Physics of Solids, vol.46, issue.3, pp.427-465, 1998.
DOI : 10.1016/S0022-5096(97)00095-1

M. Kailasam, P. Castañeda, P. , W. , and J. R. , The effect of particle size, shape, distribution and their evolution on the constitutive response of nonlinearly viscous composites. I. Theory, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.355, issue.1730, pp.1835-1852, 1997.
DOI : 10.1098/rsta.1997.0092

M. Kailasam, P. Castañeda, P. , W. , and J. R. , The effect of particle size, shape, distribution and their evolution on the constitutive response of nonlinearly viscous composites. II. Examples, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.355, issue.1730, pp.1853-1872, 1997.
DOI : 10.1098/rsta.1997.0093

J. Leblond and M. Gologanu, External estimate of the yield surface of an arbitrary ellipsoid containing a confocal void, Comptes Rendus M??canique, vol.336, issue.11-12, pp.813-819, 2008.
DOI : 10.1016/j.crme.2008.10.006

J. Leblond, G. Perrin, and P. Suquet, Exact results and approximate models for porous viscoplastic solids, International Journal of Plasticity, vol.10, issue.3, pp.213-235, 1994.
DOI : 10.1016/0749-6419(94)90001-9

J. Michel and P. Suquet, The constitutive law of nonlinear viscous and porous materials, Journal of the Mechanics and Physics of Solids, vol.40, issue.4, pp.783-812, 1992.
DOI : 10.1016/0022-5096(92)90004-L

D. Mohr and F. Ebnoether, Plasticity and fracture of martensitic boron steel under plane stress conditions, International Journal of Solids and Structures, vol.46, issue.20, pp.3535-3547, 2009.
DOI : 10.1016/j.ijsolstr.2009.05.011
URL : https://hal.archives-ouvertes.fr/hal-00826129

D. Mohr and S. Henn, Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental???Numerical Method, Experimental Mechanics, vol.32, issue.1, pp.805-820, 2007.
DOI : 10.1115/1.3443401

V. Monchiet, E. Charkaluk, and D. Kondo, An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields, Comptes Rendus M??canique, vol.335, issue.1, pp.32-41, 2007.
DOI : 10.1016/j.crme.2006.12.002
URL : https://hal.archives-ouvertes.fr/hal-00136688

K. Nahshon and J. W. Hutchinson, Modification of the Gurson Model for shear failure, European Journal of Mechanics - A/Solids, vol.27, issue.1, pp.1-17, 2008.
DOI : 10.1016/j.euromechsol.2007.08.002

A. Needleman and J. R. Rice, Limits to ductility set by plastic flow localization Mechanics of Sheet Metal Forming, pp.237-267, 1978.

P. Castañeda and P. , The effective mechanical properties of nonlinear isotropic composites, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.45-71, 1991.
DOI : 10.1016/0022-5096(91)90030-R

P. Castañeda and P. , Effective Properties in Power-Law Creep, Mechanics of Creep Brittle Materials, pp.218-229, 1991.
DOI : 10.1007/978-94-011-3688-4_19

P. Castañeda and P. , Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I???theory, Journal of the Mechanics and Physics of Solids, vol.50, issue.4, pp.737-757, 2002.
DOI : 10.1016/S0022-5096(01)00099-0

P. Castañeda and P. , Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: II???applications, Journal of the Mechanics and Physics of Solids, vol.50, issue.4, pp.759-782, 2002.
DOI : 10.1016/S0022-5096(01)00098-9

P. Castañeda, P. Willis, and J. R. , The effect of spatial distribution on the effective behavior of composite materials and cracked media, Journal of the Mechanics and Physics of Solids, vol.43, issue.12, pp.1919-1951, 1995.
DOI : 10.1016/0022-5096(95)00058-Q

P. Castañeda, P. Zaidman, and M. , Constitutive models for porous materials with evolving microstructure, Journal of the Mechanics and Physics of Solids, vol.42, issue.9, pp.1459-1497, 1994.
DOI : 10.1016/0022-5096(94)90005-1

J. R. Rice and D. M. Tracey, On the ductile enlargement of voids in triaxial stress fields???, Journal of the Mechanics and Physics of Solids, vol.17, issue.3, pp.201-217, 1969.
DOI : 10.1016/0022-5096(69)90033-7

J. R. Rice, The localization of plastic deformation, Proceedings of the14 th International Congress of Theoretical and Applied Mechanics, pp.207-220, 1976.

F. Scheyvaerts, P. R. Onck, C. Tekogolu, and T. Pardoen, The growth and coalescence of ellipsoidal voids in plane strain under combined shear and tension, Journal of the Mechanics and Physics of Solids, vol.59, issue.2, pp.373-397, 2011.
DOI : 10.1016/j.jmps.2010.10.003

P. Suquet, Overall potentials and extremal surfaces of power law or ideally plastic composites, Journal of the Mechanics and Physics of Solids, vol.41, issue.6, pp.981-1002, 1993.
DOI : 10.1016/0022-5096(93)90051-G

P. Suquet, Overall Properties of Nonlinear Composites, C. R. Acad. Sci. Paris II, vol.320, pp.563-571, 1995.
DOI : 10.1007/978-94-009-1756-9_19

V. Tvergaard, Influence of voids on shear band instabilities under plane strain conditions, International Journal of Fracture, vol.6, issue.4, pp.389-407, 1981.
DOI : 10.1080/14786445108561065

V. Tvergaard, Material Failure by Void Growth to Coalescence, Adv. Appl. Mech, vol.27, pp.83-151, 1990.
DOI : 10.1016/S0065-2156(08)70195-9

V. Tvergaard, Behaviour of voids in a shear field, International Journal of Fracture, vol.50, issue.11, pp.41-49, 2009.
DOI : 10.1115/1.3443401

P. Vincent and Y. Monerie, Yield criterion for a rigid-ideally plastic material with randomly oriented cracks C. R. Mecanique, pp.297-303, 2008.
DOI : 10.1016/j.crme.2007.11.020

J. R. Willis, Variational principles and bounds for the overall properties of composites, Continuum Models and Discrete Systems 2, pp.185-212, 1978.

J. R. Willis, Variational and Related Methods for the Overall Properties of Composites, Adv. Appl. Mech, vol.21, pp.1-78, 1981.
DOI : 10.1016/S0065-2156(08)70330-2

J. R. Willis, On methods for bounding the overall properties of nonlinear composites, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.73-86, 1991.
DOI : 10.1016/0022-5096(91)90031-I