An approximate yield criterion for anisotropic porous media

Gurson, 1977, Continuum theory of ductile rupture by void nucleation and growth: Part I. Yield criteria and flow rules for porous ductile media, J. Eng. Mat. Tech., 99, 2, 10.1115/1.3443401 G. Perrin, Contribution à l'étude théorique de la rupture ductile des métaux, PhD thesis, École Polytechnique, 1992 Leblond, 2003 Benzerga, 1997, Modèle couplé comportement–endommagement ductile de tôles anisotropes, 673 A.A. Benzerga, Rupture ductile des tôles anisotropes, PhD thesis, École Nationale Supérieure des Mines de Paris, 2000 Benzerga, 2001, Plastic potentials for anisotropic porous solids, Eur. J. Mech., 20, 397, 10.1016/S0997-7538(01)01147-0 Gologanu, 1993, Approximate models for ductile metals containing non-spherical voids – case of axisymmetric prolate ellipsoidal cavities, J. Mech. Phys. Solids, 41, 1723, 10.1016/0022-5096(93)90029-F Gologanu, 1994, Approximate models for ductile metals containing non-spherical voids – case of axisymmetric oblate ellipsoidal cavities, J. Eng. Mat. Tech., 116, 290, 10.1115/1.2904290 Gologanu, 1997, Recent extensions of Gurson's model for porous ductile metals, 61 M. Gologanu, Étude de quelques problèmes de rupture ductile des métaux, PhD thesis, Université Paris 6, 1997 Garajeu, 2000, A micromechanical approach of damage in viscoplastic materials by evolution in size, shape and distribution of voids, Comput. Methods Appl. Mech. Engrg., 183, 223, 10.1016/S0045-7825(99)00220-0 Monchiet, 2006, Approximate yield criteria for anisotropic metals with prolate or oblate voids, C. R. Mecanique, 334, 431, 10.1016/j.crme.2006.06.001 Monchiet, 2008, Macroscopic yield criteria for plastic anisotropic materials containing spheroidal voids, Int. J. Plasticity, 24, 1158, 10.1016/j.ijplas.2007.08.008 Mandel, 1964, Contribution théorique à l'étude de l'écrouissage et des lois de l'écoulement plastique, 502 Hill, 1967, The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids, 15, 79, 10.1016/0022-5096(67)90018-X P. Suquet, Plasticité et homogénéisation, Thèse d'Etat, Université Pierre et Marie Curie, Paris VI, 1982 Hill, 1948, A theory of yielding and plastic flow of anisotropic solids, Proc. Roy. Soc. London A, 193, 281, 10.1098/rspa.1948.0045 Lee, 1992, Axisymmetric deformation of power–law solids containing a dilute concentration of aligned spheroidal voids, J. Mech. Phys. Solids, 40, 1805, 10.1016/0022-5096(92)90052-4 Benzerga, 2004, Anisotropic ductile fracture. Part I: Experiments, Acta Mater., 52, 4623, 10.1016/j.actamat.2004.06.020