K. Alshibli and S. Sture, Shear Band Formation in Plane Strain Experiments of Sand, Journal of Geotechnical and Geoenvironmental Engineering, vol.126, issue.6, pp.495-503, 2000.
DOI : 10.1061/(ASCE)1090-0241(2000)126:6(495)

D. Bigoni, On smooth bifurcations in non-associative elastoplasticity, Journal of the Mechanics and Physics of Solids, vol.44, issue.8, pp.1337-1351, 1996.
DOI : 10.1016/0022-5096(96)00025-7

D. Bigoni, Bifurcation and instability of non-associative elastopastic solids, Material instabilities in elastic and plastic solids, pp.1-52, 2000.

D. Bigoni, Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability, 2012.
DOI : 10.1017/CBO9781139178938

D. Bigoni and T. Hueckel, Uniqueness and localization???I. Associative and non-associative elastoplasticity, International Journal of Solids and Structures, vol.28, issue.2, pp.197-213, 1991.
DOI : 10.1016/0020-7683(91)90205-T

R. Borja, Condition for liquefaction instability in fluid-saturated granular soils, Acta Geotechnica, vol.34, issue.4, pp.211-224, 2006.
DOI : 10.1007/s11440-006-0017-5

R. Brannon and W. Drugan, Influence of non-classical elastic-plastic constitutive features on shock wave existence and spectral solutions, Journal of the Mechanics and Physics of Solids, vol.41, issue.2, pp.297-3300022, 1993.
DOI : 10.1016/0022-5096(93)90010-D

F. Calvetti, G. Combe, and J. Lanier, Experimental micromechanical analysis of a 2D granular material: relation between structure evolution and loading path, Mechanics of Cohesive-Frictional Materials, pp.121-163, 1997.

R. Chambon and D. Caillerie, Existence and uniqueness theorems for boundary value problems involving incrementally non-linear models, Int. J. Solids Structures, pp.5089-5099, 1999.

P. Cundall and O. Strack, A discrete numerical model for granular assemblies, G??otechnique, vol.29, issue.1, pp.47-65, 1979.
DOI : 10.1680/geot.1979.29.1.47

A. Daouadji, F. Darve, H. Gali1, P. Hicher, F. Laouafa et al., Diffuse failure in geomaterials: Experiments, theory and modelling, International Journal for Numerical and Analytical Methods in Geomechanics, vol.33, issue.2, pp.1731-1773, 2011.
DOI : 10.1002/nag.975
URL : https://hal.archives-ouvertes.fr/ineris-00963272

F. Darve, Geomaterials Constitutive Equations and Modelling. Taylor and Francis books. chapter Incrementally nonlinear relationships, pp.213-238, 1990.

F. Darve, G. Servant, F. Laouafa, and H. Khoa, Failure in geomaterials: continuous and discrete analyses, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.27-29, pp.3057-3085, 2004.
DOI : 10.1016/j.cma.2003.11.011
URL : https://hal.archives-ouvertes.fr/ineris-00962876

F. Darve, L. Sibille, A. Daouadji, and F. Nicot, Bifurcations in granular media: macro- and micro-mechanics approaches, Comptes Rendus M??canique, vol.335, issue.9-10, pp.496-515, 2007.
DOI : 10.1016/j.crme.2007.08.005

J. Desrues, Shear band initiation in granular materials : experimentation and theory, in: Darve, Geomaterials Constitutive Equations and Modelling, pp.283-310, 1990.

J. Desrues and G. Viggiani, Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry, International Journal for Numerical and Analytical Methods in Geomechanics, vol.28, issue.4, pp.279-321, 2004.
DOI : 10.1002/nag.338

N. Hadda, F. Nicot, F. Bourrier, L. Sibille, F. Radjai et al., Micromechanical analysis of second order work in granular media, Granular Matter, vol.13, issue.5, pp.221-235, 2013.
DOI : 10.1007/s10035-013-0402-3
URL : https://hal.archives-ouvertes.fr/hal-00843264

C. Han and I. Vardoulakis, Plane-strain compression experiments on water-saturated fine-grained sand, G??otechnique, vol.41, issue.1, pp.49-78, 1991.
DOI : 10.1680/geot.1991.41.1.49

R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, vol.6, issue.3, pp.239-249, 1958.
DOI : 10.1016/0022-5096(58)90029-2

S. Imposimato and R. Nova, An investigation on the uniqueness of the incremental response of elastoplastic models for virgin sand, Mechanics of Cohesive-frictional Materials, vol.118, issue.1, pp.65-87, 1998.
DOI : 10.1002/(SICI)1099-1484(199801)3:1<65::AID-CFM42>3.0.CO;2-9

M. Klisinski, Z. , M. Runesson, and K. , Structure of constitutive equations in plasticity for different choices of state and control variables, International Journal of Plasticity, vol.8, issue.3, pp.221-2430749, 1992.
DOI : 10.1016/0749-6419(92)90049-I

F. Laouafa and F. Darve, Modelling of slope failure by a material instability mechanism, Computers and Geotechnics, vol.29, issue.4, pp.301-325, 2002.
DOI : 10.1016/S0266-352X(01)00030-1

J. Lerbet, M. Aldowaji, N. Challamel, F. Nicot, F. Prunier et al., P-positive definite matrices and stability of nonconservative systems, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.20, issue.2, pp.409-422, 2012.
DOI : 10.1002/zamm.201100055
URL : https://hal.archives-ouvertes.fr/hal-00745248

J. Lerbet, O. Kirillov, M. Aldowaji, N. Challamel, F. Nicot et al., Additional constraints may soften a non-conservative structural system: Buckling and vibration analysis, International Journal of Solids and Structures, vol.50, issue.2, pp.363-370, 2013.
DOI : 10.1016/j.ijsolstr.2012.09.014
URL : https://hal.archives-ouvertes.fr/hal-00756558

S. Lignon, F. Laouafa, F. Prunier, H. Khoa, F. et al., Hydro-mechanical modelling of landslides with a material instability criterion, G??otechnique, vol.59, issue.6, pp.513-524, 2009.
DOI : 10.1680/geot.7.00121
URL : https://hal.archives-ouvertes.fr/ineris-00963152

A. Love, A treatise on the mathematical theory of elasticity, 1927.
URL : https://hal.archives-ouvertes.fr/hal-01307751

D. Mohr, M. Dunand, and K. H. Kim, Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading, International Journal of Plasticity, vol.26, issue.7, pp.939-956, 2010.
DOI : 10.1016/j.ijplas.2009.11.006
URL : https://hal.archives-ouvertes.fr/hal-00620567

F. Nicot and F. Darve, Diffuse and localized failure modes: Two competing mechanisms, International Journal for Numerical and Analytical Methods in Geomechanics, vol.57, issue.4, pp.586-601, 2011.
DOI : 10.1002/nag.912

F. Nicot, F. Darve, and H. Khoa, Bifurcation and second-order work in geomaterials, International Journal for Numerical and Analytical Methods in Geomechanics, vol.43, issue.8, pp.1007-1032, 2007.
DOI : 10.1002/nag.573

F. Nicot, N. Hadda, F. Bourrier, L. Sibille, R. Wan et al., Inertia effects as a possible missing link between micro and macro second-order work in granular media, International Journal of Solids and Structures, vol.49, issue.10, pp.1252-1258, 2012.
DOI : 10.1016/j.ijsolstr.2012.02.005
URL : https://hal.archives-ouvertes.fr/hal-01006982

F. Nicot, L. Sibille, and F. Darve, Failure in rate-independent granular materials as a bifurcation toward a dynamic regime, International Journal of Plasticity, vol.29, pp.136-154, 2012.
DOI : 10.1016/j.ijplas.2011.08.002

R. Nova, CONTROLLABILITY OF THE INCREMENTAL RESPONSE OF SOIL SPECIMENS SUBJECTED TO ARBITRARY LOADING PROGRAMMES, Journal of the Mechanical Behavior of Materials, vol.5, issue.2, pp.193-201, 1994.
DOI : 10.1515/JMBM.1994.5.2.193

V. Osinov and W. Wu, Instability and ill-posedness in the deformation of plastic solids: some correlations through simple examples, Trends in Applications of Mathematics to Mechanics, pp.361-370, 2005.

H. Petryk, Material instability and strain-rate discontinuities in incrementally nonlinear continua, Journal of the Mechanics and Physics of Solids, vol.40, issue.6, pp.1227-12500022, 1992.
DOI : 10.1016/0022-5096(92)90014-S

C. Di-prisco and R. Nova, Stability problems related to static liquefaction of loose sand. Localisation and Bifurcation Theory for Soils and Rocks Chambon, Balkema, pp.59-70, 1994.

B. Raniecki and O. Bruhns, Bounds to bifurcation stresses in solids with non-associated plastic flow law at finite strain, Journal of the Mechanics and Physics of Solids, vol.29, issue.2, 1981.
DOI : 10.1016/0022-5096(81)90021-1

J. Rice, The localization of plastic deformation, Theoretical and Applied Mechanics, pp.207-220, 1976.

J. Rice and J. Rudnicki, A note on some features of the theory of localization of deformation, International Journal of Solids and Structures, vol.16, issue.7, pp.597-605, 1980.
DOI : 10.1016/0020-7683(80)90019-0

K. Runesson and Z. Mroz, A note on nonassociated plastic flow rules, International Journal of Plasticity, vol.5, issue.6, pp.639-6580749, 1989.
DOI : 10.1016/0749-6419(89)90005-3

L. Sibille and F. Froiio, A numerical photogrammetry technique for measuring microscale kinematics and fabric in Schneebeli materials, Granular Matter, vol.435, issue.4, pp.183-193, 2007.
DOI : 10.1007/s10035-006-0032-0

L. Sibille, F. Nicot, F. Donzé, and F. Darve, Analysis of failure occurrence from direct simulations, European Journal of Environmental and Civil Engineering, vol.3, issue.2, pp.187-201, 2009.
DOI : 10.1002/nag.591
URL : https://hal.archives-ouvertes.fr/hal-01005248

J. Sladen, R. Hollander, and J. Krahn, The liquefaction of sands, a collapse surface approach, Canadian Geotechnical Journal, vol.22, issue.4, pp.564-578, 1985.
DOI : 10.1139/t85-076

T. Stoughton and J. Yoon, Anisotropic hardening and non-associated flow in proportional loading of sheet metals, International Journal of Plasticity, vol.25, issue.9, pp.1777-1817, 2009.
DOI : 10.1016/j.ijplas.2009.02.003

A. Taherizadeh, D. Green, and J. Yoon, Evaluation of advanced anisotropic models with mixed hardening for general associated and non-associated flow metal plasticity, International Journal of Plasticity, vol.27, issue.11, pp.1781-1802, 2011.
DOI : 10.1016/j.ijplas.2011.05.001

A. Tordesillas, S. Pucilowski, L. Sibille, F. Nicot, and F. Darve, Multiscale characterisation of diffuse granular failure, Philosophical Magazine, vol.3, issue.36, pp.4547-4587, 2012.
DOI : 10.1080/14786435.2012.715766
URL : https://hal.archives-ouvertes.fr/hal-01008511

K. Valanis, On the Uniqueness of Solution of the Initial Value Problem in Softening Materials, Journal of Applied Mechanics, vol.52, issue.3, pp.649-653, 1985.
DOI : 10.1115/1.3169115

J. Weber, Recherches concernant les contraintes intergranulaires dans les milieux pulvérulents, Bulletin de Liaison des Ponts-et-Chaussées, vol.20, pp.1-20, 1966.