E. Aifantis, A proposal for continuum with micristructure, Mechanics Research Communications, vol.5, pp.139-145, 1978.

E. Aifantis, On the microstructural origin of certain inelastic models, Journal of Elasticity, vol.106, pp.326-330, 1984.

R. Asaro, Geometrical effects in the inhomogeneous deformation of ductile single crystals, Acta Metallurgica, vol.27, pp.445-453, 1979.

J. D. Barnichon, Finite Element Modelling in Structural and Petroleum Geology, 1998.

Z. Bazant and T. Belytschiko, Wave propagation in a stran-softening bar : exact solution, Journal of Engineering Mechanics, vol.111, pp.381-389, 1985.

Z. Bazant, T. Belytschiko, and C. T. , Continuum theory for strain-softening, Journal of Engineering Mechanics, vol.110, pp.1666-1692, 1984.

Z. Bazant and B. Lin, Non local yield limit degradation, International Journal for Numerical Methods in Engineering, vol.26, pp.1805-1823, 1988.

Z. Bazant and G. Pijaudier-cabot, Non local continuum damage, localization instability and convergence, Journal of Applied Mechanics, vol.55, pp.287-293, 1988.

J. Beck and K. Woodbury, Inverse problems and parameter estimation : integration of measurements and anlysis, Measurement Science and Technology, vol.9, pp.839-847, 1998.

T. Belytschko, T. Bchang, Y. Hyun, and C. T. , Strain softening materias and finite element solution, Computers et Structures, vol.23, pp.163-180, 1986.

T. Belytschko, J. Fish, and B. Engelmann, A finite element with embedded localization zones, Computer Methods in Applied Mechanics and Engineering, vol.77, pp.59-89, 1988.

J. Bonnans, J. Gilbert, and C. Lemaréchal, Optimisation numerique, Mathématiques et Applications, vol.27, 1997.

M. Bonnet, Problèmes inverese, 2008.

P. Bésuelle, Déformation et rupture dans les roches tendres et les sols indurés : comportement homogènes et localisation, 1999.

P. Bésuelle and R. Chambon, Modeling the post-localization regime with local second gradient models : Non-uniqueness of solutions and non-persistent shear bands, Springer Proceedings in Physics, vol.106, 2006.

P. Bésuelle, R. Chambon, and C. F. , Switching deformation modes in postlocalization solutions with a quasibrittle material, Mechanics of Materials and Structure, vol.1, pp.1115-1134, 2006.

P. Bésuelle and S. Hall, Characterization of the strain localization in a porous rock in plane strain condition using a new true-triaxial apparatus, Springer Series in Geomechanics and Geoengineering, pp.345-350, 2011.

P. Bésuelle and J. Rudnicki, Mechanics of fluid saturated rocks, Shear Bands and Compaction Bands, vol.89, pp.240-273, 2004.

D. Caillerie, R. Chambon, and C. F. , Analytical evidence of shear band bifurcations for softening material, Advances in Bifurcation and Degradation in Gematerials, 2011.

S. Cescotto, General strategy fro nonlinear finite element formulation, Proceedings of the Fifth International Symposium on Numerical Methods in Engineering, pp.155-164, 1989.

R. Chambon, Bifurcation par loclaisation en bandes de cisaillement, une approche avec des lois incrémentalement non linéaires, Journal de Mécanique Théorique et Appliquée, vol.5, pp.277-298, 1986.

R. Chambon, D. Caillerie, E. Hassan, and N. , One-dimensional localisation studied with a second grade model, European Journal of Mechanics-A/Solids, vol.17, pp.637-656, 1998.

R. Chambon, D. Caillerie, and T. Matsuchima, Plastic continuum with microstructure, local second gradient thoeries for geomaterials : localization studies, International Journal of Solids and Structures, vol.38, pp.8503-8527, 2001.

R. Chambon and S. Crochepeyre, Daphnis : a new model for the description of post-localization behaviour : application to sands, Mechanics of CohesiveFrictional Materials, vol.3, pp.127-153, 1998.

R. Chambon, S. Crochepeyre, and C. R. , An algorithm and a method to search bifurcation points in non-linear problems, International Journal for Numerical Methods in Engineering, vol.51, pp.315-332, 2001.

R. Chambon and J. Moullet, Uniqueness studies in boundary value problems involving some second gradient models, Computer Methods in Applied Mechanics and Engineering, vol.193, pp.2771-2796, 2004.

R. Charlier, Approche unifiée de quelques problèmes non linéaires de mécanique des milieux continus par la méthode des éléments finis, 1987.

J. Christoffersen and J. Hutchinson, A class of phenomenological corner theories of plasticity, Journal of the Mechanics and Physics of Solids, vol.27, pp.465-487, 1979.

E. Cosserat and F. Cosserat, Théorie des corps déformables, 1909.

M. Crisfield, Non-linear Finite Element Analysis of Solids and Structures, volume1, 1991.

D. Borst and R. , Simulation of strain localization : a reappraisal of the cosserat continuum, vol.4, pp.317-332, 1991.

D. Borst, R. Mühlhaus, and H. , Gradient -dependent plasticity : formulation and algorithmic aspects, International Journal for Numerical Methods in Engineering, vol.35, pp.521-539, 1992.

D. Borst, R. Sluys, L. Mühlhaus, and H. , Continuum models for discontinuous media, Fracture process in Concrete, Rock and Ceramics, pp.601-618, 1991.

J. Desrues, La localisation de la déformation dans les matériaux granulaires, 1984.

J. Desrues, Limitation du choix de l'angle de frottement pour le critére de plasticité drucker-prager. Revue Française de Génie Civil, vol.6, pp.853-862, 2002.

J. Desrues, R. Chambon, M. Mokni, and F. Mazerolle, Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography, Géotech-nique, vol.46, pp.529-546, 1996.

J. Desrues and G. Viggiani, Strain localisation in sand : an overview of the experimental results obtained in grenoble using stereophotogrammetry, International Journal for Numerical and Analytical Methods in Geomechanics, vol.28, pp.279-321, 2004.

N. El-hassan, Modelisation theorique et numerique de la localisation de la deformation dans les geomateriaux, 1997.

K. El-moustapha, P. Bésuelle, and Y. Sieffert, Identification d'une loi de comportement enrichie pour les géomatériaux en prsence d'une localisation de la défor-mation, Congrés Français de Mécanique, 2013.

K. El-moustapha, P. Bésuelle, and Y. Sieffert, Identification of enriched constitutive models for geomaterials in the presence of strain localization, ALERT Geomaterials, 2013.

K. El-moustapha, P. Bésuelle, and Y. Sieffert, Identification of enriched constitutive models for geomaterials in the presence of strain localization, LAGASHOP, 2013.

R. Fernandes, C. Chavant, and C. R. , A simplified second gradient model for dilatant materials : Theory and numerical implementation, International Journal of Solids and Structures, vol.45, pp.5289-5307, 2008.

P. Germain, La méthode des puissances virtuelles en mécanique des milieux continus, premiére partie : théorie du second gradient, Journal de Mécanique, vol.12, pp.235-274, 1973.

P. Gill, W. Muray, and W. M. , Practical optimization, 1982.

D. Goldberg, Genetic algorithms in search, optimization and machine learning, 1989.

J. Hadamard, Leçon sur la propagation des ondes et les équations de l'hydrodynamique, 1903.

B. Haimson and C. Chang, A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability ofwesterly granite, International Journal of Rock Mechanics, vol.35, pp.285-296, 2000.

S. Hall, D. Muir-wood, E. Ibraim, and G. Viggiani, Localised deformation patterning in 2d granular materials revealed by digital image correlation, 2000.

R. Hill, Acceleration waves in solids, Journal of the Mechanics and Physics of Solids, vol.10, pp.1-16, 1962.

R. Hill and J. Hutchinson, Bifurcation phenomena in the plane tension test, Journal of the Mechanics and Physics of Solids, vol.33, pp.239-264, 1975.

J. Holland, Adaptation in Natural and Artificial Systems, 1992.

M. Jirásek, Nonlocal models for damage and fracture : Comparison of approaches, International Journal of Sol, vol.35, pp.4133-4145, 1998.

M. Jirásek, Computational resolution of strong discontinuities, Fifth World Congress on Comutational Mechanics, 2002.

M. Jirásek, Numerical modeling of strong discontinuities, Numerical Modelling in Geomechanics, vol.6, pp.1133-1146, 2002.

C. Johnson and R. Scott, A finite element method for problems in perfect plsaticity using discontinuous trial functions. Non linear finite elment analysis in stuctural mechanics, pp.307-324, 1981.

P. Kotronis and F. Collin, Implementation of path following techniques into the finite element code lagamine, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00100402

P. Kotronis, F. Collin, P. Bésuelle, R. Chambon, and M. J. , Local second gradient models and damage mechanics : 1d post-localization studies in concrete specimens. Bifurcation, Instabilities, Degradation in Geomechanics, pp.127-142, 2007.

P. Lanatà, Caractérisation de la localisation de la déformation dans des roches poreuses en conditions triaxiales vraies

B. Lecampion, Identification de lois de comportement des roches argileuses, 2002.
URL : https://hal.archives-ouvertes.fr/pastel-00002114

B. Lecampion, A. Contantinescu, N. Minh, and D. , Parameter identification for lined tunnels in viscoplastic medium, International Journal for Numerical and Analytical Methods in Geomechanics, vol.26, pp.1191-1211, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00111357

Y. Leroy and M. Ortiz, Finite element analysis of strain localization in frictional materials, International Journal for Numerical and Analytical Methods in Geomechanics, vol.13, pp.53-74, 1989.

S. Levasseur, . Malécot-y, B. Boulon, and F. E. , Soil parameter identification using a genetic algorithm, International Journal for Numerical and Analytical Methods in Geomechanics, vol.32, pp.189-213, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01998321

G. Maier and G. Gioda, Optimization method for parametric identification of geotechnical systems, Numerical Methods in Geomechanics, vol.92, pp.273-304, 1982.

J. Mandel, Rhéologie et mécanque des sols, chapter conditions de stabilité et postulat de drucker, pp.58-68, 1966.

T. Matsuchima, R. Chambon, and D. C. , Large strain finite element analysis of a local second gradient model : application to localization, International Journal for Numerical Methods in Engineering, vol.54, pp.499-521, 2002.

J. Mazars, A description of micro and macroscale da of concrete structures, Engineering Fracture Mechanics, pp.729-737, 1986.

H. Mühlhaus, Shear band analysis in granular media by cosserat thoery, IngenieurArchiv, vol.56, pp.389-399, 1986.

H. Mühlhaus, Application of cosserat thoery in numerical solutions of limited load problems, Ingenieur-Archiv, vol.59, pp.124-137, 1989.

H. Mühlhaus and E. Aifantis, A variational principle for gradient plasticity, International Journal of Solids and Structures, vol.28, pp.845-857, 1991.

H. Mühlhaus and I. Vardoulakis, The thickness of shear bands in granural materials, vol.37, pp.271-283, 1987.

R. Mindlin, Influence of couple-stress on stress concentration, Experimental Maechanics, vol.3, pp.1-7, 1963.

R. Mindlin, Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis, vol.16, pp.51-78, 1964.

R. Mindlin, One first stran-gradient thoeries in linear elasticity, International Journal of Solids and Structures, vol.4, pp.109-124, 1968.

K. Morsegaard and A. Tarantola, Monte carlo sampling of solutions to inverse problems in, Journal of Geophysiscal Research, vol.100, pp.12431-12447, 1995.

A. Needleman, A material rate dependence and mesh sensitivity localization problems, Computer Methods in Applied Mechanics and Engineering, vol.67, pp.69-86, 1988.

A. Needleman and V. Tvergaard, Finite element analysis of localization in plasticity, Finite Elements -Special Problems in Solid Mechanics, vol.5, pp.94-157, 1982.

J. Nougier, Méthodes de calcul numérique, Hermes Sciences, 2001.

J. Oliver and J. Simo, Modelling strong discontinuities by means of strain softening constituve equations. Computer Modelling of Concrete Structres, pp.363-372, 1994.

L. Parker, Understanding inverse thoery, Annual Review of Earth and Planetary Sciences, vol.5, pp.35-64, 1977.

M. Pastor, C. Rubio, P. Mura, J. Peraire, J. Vilote et al., Numerical analysis of locaization, Numerical Models in Geomechanics, pp.339-348, 1992.

G. Pijaudier-cabot and Z. Bazant, Non local damge theory, Journal of Engineering Mechanics, vol.113, pp.1512-1533, 1986.

G. Pijaudier-cabot, Strain localization and bifurcation in a non local continuum, Internationl Journal of Solids and Structures, vol.13, pp.1761-1775, 1993.

J. Rice and R. Rudnicki, A note on some features of the theory of localization of deformation, Internationl Journal of Solids and Structures, vol.16, pp.597-605, 1980.

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

E. Riks, An incremental approach to the solution of snapping and buckling problems, International Journal of Solids and Structures, vol.15, pp.529-551, 1979.

S. Roweis, Levenberg-Marquardt optimization, 1996.

J. Rudnicki and J. Rice, Conditions for the localization of deformation in pressuresensitive dilatant materials, Journal of the Mechanics and Physics of Solids, vol.23, pp.371-394, 1975.

M. Sambridge and K. Mosegaard, Monte carlo methods in geophysiscal inverse problems, Reviews of Geophysics, vol.40, 2002.

J. Santamarina and D. Fratta, Introduction to descrete signal and inverse problems in civil engineering, 1998.

Y. Sieffert, A. Holo, S. Chambon, and R. , Loss of uniqueness of numerical solutions of the borehole problem modelled with enhanced media, International Journal of Solids and Structures, vol.46, pp.3173-3197, 2009.
URL : https://hal.archives-ouvertes.fr/hal-02004127

L. Sluys, Wave propagation, localisation and disperation in softening solids, 1992.

J. Sulem and I. Vardoulakis, Bifurcation analysis of the triaxial test on rocks specimens, Acta Mechanica, vol.83, pp.195-212, 1990.

T. Takemura, M. Oda, and M. Takahashi, Microstructure observation in deformed geomaterials using microfocus x-ray computed tomography, 2004.

A. Tarantola, Inverse Problem Theory, 1987.

D. Taylor, Fundamentals of Soil Mechanics, 1948.

N. Triantafyllidis, Bifurcation phenomena in pure bending, Journal of the Mechanics and Physics of Solids, vol.28, pp.221-245, 1980.

E. Tudisco, Development and application of time-lapse ultrasonic tomography for laboratory char-acterisation of localized deformation inhard soils / soft rocks, 2013.

I. Vardoulakis and E. Aifantis, A grdient flow theory of plasticity for granular materials, Acta Mechanica, vol.87, pp.197-217, 1991.

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.2, pp.99-128, 1978.

I. Vardoulakis and J. Sulem, Application fo bifurcation thoery to rock mechanics problems. Comprehensive Rock Mechanics, 1993.

X. Wang, Modélisation numérique des problémes avec localisation de la déforma-tion en bandes de cisaillement, 1993.

G. Wepmner, Discrete approximations related to nonlinear theories of solids, International Journal of Solids and Structures, vol.7, pp.1581-1599, 1971.

A. Zervos, P. Papanastasiou, and I. Vardoulakis, A finite element displacement formulation for gradient elstoplasticity, International Journal for Numerical Methods in Engineering, vol.50, pp.1369-1388, 2001.