P. M. Anderson, N. A. Fleck, and K. L. Johnson, Localization of plastic deformation in shear due to microcracks, Journal of the Mechanics and Physics of Solids, vol.38, issue.5, 1990.
DOI : 10.1016/0022-5096(90)90028-3

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, p.723, 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 shearExperiments, Int. J. Solids Struct, vol.44, pp.727-1768, 2007.
DOI : 10.1016/j.ijsolstr.2006.09.031
URL : https://doi.org/10.1016/j.ijsolstr.2006.09.031

I. Barsoum and J. Faleskog, Rupture mechanisms in combined tension and shearMicromechanics, Int. J. Solids Struct, vol.729, pp.44-5481, 2007.
DOI : 10.1016/j.ijsolstr.2007.01.010
URL : https://doi.org/10.1016/j.ijsolstr.2007.01.010

I. Barsoum and J. Faleskog, Micromechanical analysis on the influence of the Lode parameter on void growth and coalescence, International Journal of Solids and Structures, vol.48, issue.6, 2011.
DOI : 10.1016/j.ijsolstr.2010.11.028

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, Coalescence-Controlled Anisotropic Ductile Fracture, Journal of Engineering Materials and Technology, vol.17, issue.1, pp.121-221, 1999.
DOI : 10.1115/1.3601204

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

B. Budiansky, J. W. Hutchinson, and S. Slutsky, Void growth and collapse in viscous solids. Mechanics of Solids The 737, 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 and N. Aravas, Numerical modeling of elasto-plastic porous materials with void shape effects at finite deformations, Composites Part B: Engineering, vol.43, issue.6
DOI : 10.1016/j.compositesb.2011.12.011
URL : https://hal.archives-ouvertes.fr/hal-00755844

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, 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. Eur. 751 J. Mech, pp.402-416, 2009.
DOI : 10.1016/j.euromechsol.2008.11.003
URL : https://hal.archives-ouvertes.fr/hal-00526643

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, 2010.
DOI : 10.1016/j.ijsolstr.2009.12.011
URL : https://hal.archives-ouvertes.fr/hal-00620568

J. M. Duva and J. W. Hutchinson, Constitutive potentials for dilutely voided nonlinear materials, Mechanics of Materials, vol.3, issue.1, pp.41-54, 1984.
DOI : 10.1016/0167-6636(84)90013-9

J. D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R. Soc. Lond. 756 A 241, pp.376-396, 1957.

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, p.758, 2005.
DOI : 10.1016/j.euromechsol.2005.03.003

L. Flandi and J. Leblond, A new model for porous nonlinear viscous solids incorporating void shape effects ??? II: Numerical validation, European Journal of Mechanics - A/Solids, vol.24, issue.4, pp.552-571, 2005.
DOI : 10.1016/j.euromechsol.2005.03.004

M. G?ar?ajeug?ar?g?ar?ajeu, J. Michel, and P. Suquet, A micromechanical approach of damage in viscoplastic materials by evolution in 762 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.

G. Geymonat, S. Müller, and N. Triantafyllidis, Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity, Archive for Rational Mechanics and Analysis, vol.52, issue.3, pp.231-290, 1993.
DOI : 10.1017/S0308210500015080

M. Gologanu, J. Leblond, and J. Devaux, Approximate models for ductile metals containing non-spherical voids, p.767, 1993.
DOI : 10.1016/0022-5096(93)90029-f

M. Gologanu, J. Leblond, and J. Devaux, Approximate models for ductile metals containing non-spherical voids, p.769, 1994.
DOI : 10.1016/0022-5096(93)90029-f

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

J. W. Hancock and A. C. Mackenzie, On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress-states, Journal of the Mechanics and Physics of Solids, vol.24, issue.2-3, pp.147-160, 1976.
DOI : 10.1016/0022-5096(76)90024-7

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, compu- 778 tational 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 780 localization, IUTAM Symposium on Mechanics of Granular and Porous Materials, p.781, 1997.

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

S. M. Keralavarma and A. A. Benzerga, A constitutive model for plastically anisotropic solids with non-spherical voids, Journal of the Mechanics and Physics of Solids, vol.58, issue.6, 2010.
DOI : 10.1016/j.jmps.2010.03.007

R. A. Lebensohn, M. I. Idiart, P. Castañeda, P. Vincent, and P. , Dilatational viscoplasticity of polycrystalline solids 791 with intergranular cavities, 2011.

B. J. Lee and M. E. Mear, Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids, Journal of the Mechanics and Physics of Solids, vol.40, issue.8, pp.1805-1836, 1992.
DOI : 10.1016/0022-5096(92)90052-4

L. Roy, G. Embury, J. D. Edwards, G. Ashby, and M. F. , A model of ductile fracture based on the nucleation and growth of voids, Acta Metallurgica, vol.29, issue.8, pp.1509-1522, 1981.
DOI : 10.1016/0001-6160(81)90185-1

L. Pamies, O. , P. Castañeda, and P. , Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I???Analysis, Journal of the Mechanics and Physics of Solids, vol.55, issue.8, pp.1677-1701, 2007.
DOI : 10.1016/j.jmps.2007.01.007
URL : https://hal.archives-ouvertes.fr/hal-00311891

L. Pamies, O. , P. Castañeda, and P. , Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: II???Results, Journal of the Mechanics and Physics of Solids, vol.55, issue.8, pp.1702-1728, 2007.
DOI : 10.1016/j.jmps.2007.01.008
URL : https://hal.archives-ouvertes.fr/hal-00311892

Y. Liu, P. Castañeda, and P. , Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals, Journal of the Mechanics and Physics of Solids, vol.52, issue.2, pp.467-495, 2004.
DOI : 10.1016/S0022-5096(03)00078-4

F. A. Mcclintock, A Criterion for Ductile Fracture by the Growth of Holes, Journal of Applied Mechanics, vol.35, issue.2, pp.363-371, 1968.
DOI : 10.1115/1.3601204

F. A. Mcclintock, PLASTICITY ASPECTS OF FRACTURE, Fracture, pp.47-225, 1971.
DOI : 10.1016/B978-0-12-449703-0.50007-2

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.806-812, 1992.
DOI : 10.1016/0022-5096(92)90004-L

J. Michel, O. Lopez-pamies, P. Castañeda, P. Triantafyllidis, and N. , Microscopic and macroscopic instabilities in finitely strained porous elastomers, Journal of the Mechanics and Physics of Solids, vol.55, issue.5, pp.900-938, 2007.
DOI : 10.1016/j.jmps.2006.11.006
URL : https://hal.archives-ouvertes.fr/hal-00106306

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, 2009.
DOI : 10.1016/j.ijsolstr.2009.05.011
URL : https://hal.archives-ouvertes.fr/hal-00826129

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 816 of Sheet Metal Forming, pp.237-267, 1978.

K. L. Nielsen and V. Tvergaard, Ductile shear failure or plug failure of spot welds modelled by modified Gurson model, Engineering Fracture Mechanics, vol.77, issue.7, 2010.
DOI : 10.1016/j.engfracmech.2010.02.031

T. Pardoen and J. W. Hutchinson, An extended model for void growth and coalescence, Journal of the Mechanics and Physics of Solids, vol.48, issue.12, pp.2467-2512, 2000.
DOI : 10.1016/S0022-5096(00)00019-3

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. , 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, 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 832, 1976.

D. Teirlinck, F. Zok, J. D. Embury, and M. F. Ashby, Fracture mechanism maps in stress space, Acta Metallurgica, vol.36, issue.5, pp.1213-1228, 1988.
DOI : 10.1016/0001-6160(88)90274-X

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