L. Sibille, F. Nicot, F. Donze, and F. Darve, Material instability in granular assemblies from fundamentally different models, International Journal for Numerical and Analytical Methods in Geomechanics, vol.26, issue.3, pp.457-481, 2007.
DOI : 10.1007/978-3-7091-2768-1

L. Sibille, F. Donzé, F. Nicot, B. Chareyre, and F. Darve, Bifurcation detection and catastrophic failure, Acta Geotecnica, vol.3, issue.1, pp.14-24, 2007.

F. Nicot and F. Darve, A micro-mechanical investigation of bifurcation in granular materials, International Journal of Solids and Structures, vol.44, issue.20, pp.6630-6652, 2007.
DOI : 10.1016/j.ijsolstr.2007.03.002
URL : https://doi.org/10.1016/j.ijsolstr.2007.03.002

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 : 10.1007/978-3-7091-2562-5_5

F. Nicot, L. Sibille, and F. Darve, Bifurcation in granular materials: An attempt for a unified framework, International Journal of Solids and Structures, vol.46, issue.22-23, pp.3938-3947, 2009.
DOI : 10.1016/j.ijsolstr.2009.07.008
URL : https://hal.archives-ouvertes.fr/hal-01005291

I. Vardoulakis, M. Goldscheider, and G. Gudehus, Formation of shear bands in sand bodies as a bifurcation problem, International Journal for Numerical and Analytical Methods in Geomechanics, vol.1, issue.2, pp.99-128, 1978.
DOI : 10.1097/00010694-197806000-00014

I. Vardoulakis and J. Sulem, Bifurcation Analysis in Geomechanics, 1995.

H. Petryk, Theory of Bifurcation and Instability in Time-Independent Plasticity, CISM Courses and Lecturers, pp.95-152, 1993.
DOI : 10.1007/978-3-7091-2712-4_3

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

D. Bigoni, Bifurcation and Instability of Non-Associative Elastoplastic Solids, Material Instabilities in Elastic and Plastic Solids, Petryk H (ed.). CISM Courses and Lecturers, pp.1-52, 2000.
DOI : 10.1007/978-3-7091-2562-5_1

R. Chambon and D. Caillerie, Existence and uniqueness theorems for boundaryvalue problems involving incrementally non linear models, International Journal of Solids and Structures, vol.36, issue.33, pp.5089-5099, 1999.
DOI : 10.1016/S0020-7683(98)00212-1

R. Nova, Controllability of the incremental response of soil specimens subjected to arbitrary loading programs, Journal of Mechanical behavior of Materials, vol.5, issue.2, pp.193-201, 1994.

K. Runesson and Z. Mroz, A note on nonassociated plastic flow rules, International Journal of Plasticity, vol.5, issue.6, pp.639-658, 1989.
DOI : 10.1016/0749-6419(89)90005-3

M. Klisinski, Z. Mroz, and K. Runesson, Structure of constitutive equations in plasticity for different choices of state and control variables, International Journal of Plasticity, vol.8, issue.3, pp.221-243, 1992.
DOI : 10.1016/0749-6419(92)90049-I

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-00969865

M. Iordache and K. Willam, Localized failure analysis in elastoplastic Cosserat continua, Computer Methods in Applied Mechanics and Engineering, vol.151, issue.3-4, pp.3-4559, 1998.
DOI : 10.1016/S0045-7825(97)00166-7

Y. Leroy and A. Molinari, Stability of steady states in shear zones, Journal of the Mechanics and Physics of Solids, vol.40, issue.1, pp.181-212, 1992.
DOI : 10.1016/0022-5096(92)90310-X

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.236-249, 1958.
DOI : 10.1016/0022-5096(58)90029-2

H. Petryk, Theory of Material Instability in Incrementally Nonlinear Plasticity, CISM Material Instabilities in Elastic and Plastic Solids, Petrik H, pp.261-331, 1999.
DOI : 10.1007/978-3-7091-2562-5_5

M. Ishaq, Sur les spectres des matrices Séminaire Dubreuil, Algèbre et Théorie des Nombres, vol.9, pp.1-14, 1955.

F. Darve and S. Labanieh, Incremental constitutive law for sands and clays: Simulations of monotonic and cyclic tests, International Journal for Numerical and Analytical Methods in Geomechanics, vol.2, issue.2, pp.243-275, 1982.
DOI : 10.1002/nag.1610060209

F. Darve, The expression of rheological laws in incremental form and the main classes of constitutive equations, Geomaterials Constitutive Equations and Modelling, Darve F, pp.123-148, 1990.

F. Darve, E. Flavigny, and M. Meghachou, Constitutive modelling and instabilities of soil behaviour, Computers and Geotechnics, vol.17, issue.2, pp.203-224, 1995.
DOI : 10.1016/0266-352X(95)93869-K

F. Prunier, F. Nicot, F. Darve, F. Laouafa, and S. Lignon, 3D multiscale bifurcation analysis of granular media, Journal of Engineering Mechanics (ASCE), vol.135, issue.6, pp.1-17, 2009.
DOI : 10.1061/(asce)em.1943-7889.0000003

N. Challamel, F. Nicot, J. Lerbet, and F. Darve, On the stability of non-conservative elastic systems under mixed perturbations, European Journal of Environmental and Civil Engineering, vol.8, issue.5, pp.347-367, 2008.
DOI : 10.1002/nag.1610020107

N. Challamel, F. Nicot, J. Lerbet, and F. Darve, A theoretical link between second-order work and stability under kinematics constraints, Engineering Structures, 2010.