F. Armero, Large???scale modeling of localized dissipative mechanisms in a local continuum: applications to the numerical simulation of strain localization in rate???dependent inelastic solids, Mechanics of Cohesive???frictional Materials, vol.4, issue.2, pp.101-131, 1999.
DOI : 10.1002/(SICI)1099-1484(199903)4:2<101::AID-CFM78>3.0.CO;2-Y

J. Lubliner, Plasticity Theory, Journal of Applied Mechanics, vol.59, issue.1, p.495, 1990.
DOI : 10.1115/1.2899459

S. S. Moy, Plastic methods for steel and concrete structures, p.271, 1996.

M. P. Nielsen, Limit analysis and concrete plasticity, 1984.

D. Borst, R. Bicanic, N. Mang, H. Meschke, and G. , Computational modelling of concrete structures: Proceedings of EURO-C, p.1022, 1998.

N. Bicanic, R. De-borst, H. Mang, and G. Meschke, Computational modelling of concrete structures: Proceedings of EURO-C 2010, 2010.

M. Dolsek, Development of computing environment for the seismic performance assessment of reinforced concrete frames by using simplified nonlinear models, Bulletin of Earthquake Engineering, vol.39, issue.4, pp.1309-1329, 2010.
DOI : 10.1007/s10518-010-9184-8

P. Fajfar, M. Dolsek, D. Marusic, and A. Stratan, Pre- and post-test mathematical modelling of a plan-asymmetric reinforced concrete frame building, Earthquake Engineering & Structural Dynamics, vol.34, issue.11, pp.1359-1379, 2006.
DOI : 10.1002/eqe.583

M. Markovic, M. Saje, I. Planinc, and S. Bratina, On strain softening in finite element analysis of RC planar frames subjected to fire, Engineering Structures, vol.45, pp.349-361, 2012.
DOI : 10.1016/j.engstruct.2012.06.032

M. Markovic, N. Krauberger, M. Saje, I. Planinc, and S. Bratina, Non-linear analysis of pre-tensioned concrete planar beams, Engineering Structures, vol.46, pp.279-293, 2013.
DOI : 10.1016/j.engstruct.2012.08.004

S. Bratina, M. Saje, and I. Planinc, On materially and geometrically non-linear analysis of reinforced concrete planar frames, International Journal of Solids and Structures, vol.41, issue.24-25, pp.24-25, 2004.
DOI : 10.1016/j.ijsolstr.2004.06.004

J. Mosler, On the modeling of highly localized deformations induced by material failure: The strong discontinuity approach, Archives of Computational Methods in Engineering, vol.41, issue.8, pp.389-446, 2004.
DOI : 10.1007/BF02736230

M. Jirasek, Comparative study on finite elements with embedded discontinuities, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.1-3, pp.1-3, 2000.
DOI : 10.1016/S0045-7825(99)00154-1

C. Linder and F. Armero, Finite elements with embedded strong discontinuities for the modeling of failure in solids, International Journal for Numerical Methods in Engineering, vol.29, issue.12, pp.1391-1433, 2007.
DOI : 10.1002/nme.2042

Z. P. Bazant, Instability ductility and size effect in strain -softening concrete, Journal of the Engineering Mechanics Division, vol.102, issue.2, pp.331-344, 1976.

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

V. Tvergaard, A. Needleman, and K. K. Lo, Flow localization in the plane strain tensile test, Journal of the Mechanics and Physics of Solids, vol.29, issue.2, pp.115-142, 1981.
DOI : 10.1016/0022-5096(81)90019-3

D. Borst and R. , Some recent issues in computational failure mechanics, International Journal for Numerical Methods in Engineering, vol.125, issue.12, pp.1-2, 2001.
DOI : 10.1002/nme.272

G. Pijaudier-cabot and Z. P. Bazant, Nonlocal Damage Theory, Journal of Engineering Mechanics, vol.113, issue.10, pp.1512-1533, 1987.
DOI : 10.1061/(ASCE)0733-9399(1987)113:10(1512)

Z. P. Bazant and B. H. Oh, Crack band theory for fracture of concrete, Materials and Structures, vol.16, issue.3, pp.155-177, 1983.

J. G. Rots, P. Nauta, G. M. Kuster, and J. Blaauwendraad, Smeared Crack Approach and Fracture Localization in Concrete, pp.1-48, 1985.

N. Bicanic, E. Pramono, S. Sture, and K. J. Willam, On numerical prediction of concrete fracture localizations, Proceedings of NUMETA '85, pp.385-392, 1985.

S. Pietruszczak and Z. Mroz, Finite element analysis of deformation of strain-softening materials, International Journal for Numerical Methods in Engineering, vol.105, issue.3, pp.327-334, 1981.
DOI : 10.1002/nme.1620170303

J. Oliver, A consistent characteristic length for smeared cracking models, International Journal for Numerical Methods in Engineering, vol.52, issue.2, pp.461-474, 1989.
DOI : 10.1002/nme.1620280214

A. C. Eringen, On nonlocal plasticity, International Journal of Engineering Science, vol.19, issue.12, pp.1461-1474, 1981.
DOI : 10.1016/0020-7225(81)90072-0

A. C. Eringen, Theories of nonlocal plasticity, International Journal of Engineering Science, vol.21, issue.7, pp.741-751, 1983.
DOI : 10.1016/0020-7225(83)90058-7

Z. P. Bazant, T. B. Belytschko, and T. P. Chang, Continuum Theory for Strain???Softening, Journal of Engineering Mechanics, vol.110, issue.12, pp.1666-1692, 1984.
DOI : 10.1061/(ASCE)0733-9399(1984)110:12(1666)

E. C. Aifantis, On the Microstructural Origin of Certain Inelastic Models, Journal of Engineering Materials and Technology, vol.106, issue.4, pp.326-330, 1984.
DOI : 10.1115/1.3225725

D. Borst, R. Muhlhaus, and H. B. , Gradient-dependent plasticity: Formulation and algorithmic aspects, International Journal for Numerical Methods in Engineering, vol.137, issue.3, pp.521-539, 1992.
DOI : 10.1002/nme.1620350307

B. D. Coleman and M. L. Hodgdon, On shear bands in ductile materials, Archive for Rational Mechanics and Analysis, vol.90, issue.3, pp.219-247, 1985.

D. Borst, R. Sluys, and L. J. , Localization in a Cosserat continuum under static and dynamic loading conditions, Computer Methods in Applied Mechanics and Engineering, vol.90, pp.1-3, 1991.

D. Borst and R. , SIMULATION OF STRAIN LOCALIZATION: A REAPPRAISAL OF THE COSSERAT CONTINUUM, Engineering Computations, vol.8, issue.4, pp.317-332, 1991.
DOI : 10.1108/eb023842

A. Needleman, Material rate dependence and mesh sensitivity in localization problems, Computer Methods in Applied Mechanics and Engineering, vol.67, issue.1, pp.69-85, 1988.
DOI : 10.1016/0045-7825(88)90069-2

J. M. Ricles, Y. S. Yang, and M. J. Priestley, Modeling Nonductile R/C Columns for Seismic Analysis of Bridges, Journal of Structural Engineering, vol.124, issue.4, pp.415-425, 1998.
DOI : 10.1061/(ASCE)0733-9445(1998)124:4(415)

J. M. Ricles and E. P. Popov, Inelastic link element for EBF seismic analysis, Journal of Structural Engineering, vol.120, issue.2, pp.441-463, 1994.

G. N. Wells and L. J. Sluys, Application of embedded discontinuities for softening solids, Engineering Fracture Mechanics, vol.65, issue.2-3, pp.2-3, 2000.
DOI : 10.1016/S0013-7944(99)00120-4

T. Belytschko, J. Fish, and B. E. Engelmann, A finite element with embedded localization zones, Computer Methods in Applied Mechanics and Engineering, vol.70, issue.1, pp.59-89, 1988.
DOI : 10.1016/0045-7825(88)90180-6

L. Sluys and A. Berends, Discontinuous failure analysis for mode-I and mode-II localization problems, International Journal of Solids and Structures, vol.35, issue.31-32, pp.31-32, 1998.
DOI : 10.1016/S0020-7683(97)00313-2

M. Juki´cjuki´c, Kon?ni elementi za modeliranje lokaliziranih poru?itev v armiranem betonu. Doktorska disertacija, 0197.

J. Simo, J. Oliver, and F. Armero, An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Computational Mechanics, vol.95, issue.5, pp.277-296, 1993.
DOI : 10.1007/BF00372173

K. Garikipati and T. J. Hughes, A study of strain localization in a multiple scale framework???The one-dimensional problem, Computer Methods in Applied Mechanics and Engineering, vol.159, issue.3-4, pp.193-222, 1998.
DOI : 10.1016/S0045-7825(97)00271-5

N. Moes, J. Dolbow, and T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131-150, 1999.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A

URL : https://hal.archives-ouvertes.fr/hal-01004829

E. N. Dvorkin, A. M. Cuitino, and G. Gioia, Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions, International Journal for Numerical Methods in Engineering, vol.2, issue.3, pp.541-564, 1990.
DOI : 10.1002/nme.1620300311

M. Klisinski, K. Runesson, and S. Sture, Finite Element with Inner Softening Band, Journal of Engineering Mechanics, vol.117, issue.3, pp.575-587, 1991.
DOI : 10.1061/(ASCE)0733-9399(1991)117:3(575)

R. Larsson and K. Runesson, Element-Embedded Localization Band Based on Regularized Displacement Discontinuity, Journal of Engineering Mechanics, vol.122, issue.5, pp.402-411, 1996.
DOI : 10.1061/(ASCE)0733-9399(1996)122:5(402)

J. Oliver, D. Linero, A. Huespe, and O. Manzoli, Two-dimensional modeling of material failure in reinforced concrete by means of a continuum strong discontinuity approach, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.5, pp.332-348, 2008.
DOI : 10.1016/j.cma.2007.05.017

J. Dujc, B. Brank, A. Ibrahimbegovic, and D. Brancherie, An embedded crack model for failure analysis of concrete solids, Computers & concrete, vol.7, issue.4, pp.331-346, 2010.
DOI : 10.12989/cac.2010.7.4.331

D. Brancherie and A. Ibrahimbegovic, Novel anisotropic continuum???discrete damage model capable of representing localized failure of massive structures, Engineering Computations, vol.26, issue.1/2, pp.1-2, 2009.
DOI : 10.1108/02644400910924825

A. Ibrahimbegovic and D. Brancherie, Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure, Computational Mechanics, vol.31, issue.1-2, pp.1-2, 2003.
DOI : 10.1007/s00466-002-0396-x

F. Armero and D. Ehrlich, Numerical modeling of softening hinges in thin Euler???Bernoulli beams, Computers & Structures, vol.84, issue.10-11, pp.10-11, 2006.
DOI : 10.1016/j.compstruc.2005.11.010

D. Ehrlich and F. Armero, Finite element methods for the analysis of softening plastic hinges in beams and frames, Computational Mechanics, vol.35, issue.4, pp.237-264, 2005.
DOI : 10.1007/s00466-004-0575-z

B. H. Pham, Stress-resultant models for optimal design of reinforced-concrete frames. Doctoral thesis, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00538958

B. H. Pham, L. Davenne, D. Brancherie, and A. Ibrahimbegovic, Stress resultant model for ultimate load design of reinforced-concrete frames: combined axial force and bending moment, Computers and Concrete 7, pp.303-315, 2010.
DOI : 10.12989/cac.2010.7.4.303

J. Wackerfuss, Efficient finite element formulation for the analysis of localized failure in beam structures, International Journal for Numerical Methods in Engineering, vol.1, issue.3, pp.1217-1250, 2008.
DOI : 10.1002/nme.2116

J. Dujc, B. Brank, and A. Ibrahimbegovic, Multi-scale computational model for failure analysis of metal frames that includes softening and local buckling, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.21-22, 2010.
DOI : 10.1016/j.cma.2009.09.003

G. Jelenic, P. Sculac, and L. Skec, Plain-and reinforced-concrete planar beam finite elements with embedded transversal cracking, Proceedings of ECCOMAS 2012, 2012.

L. Skec and G. Jelenic, Analysis of a geometrically exact multi-layer beam with a rigid interlayer connection . Acta Mechanica. DOI: 10, pp.707-720, 1007.

M. Juki´cjuki´c, Finite elements for modeling of localized failure in reinforced concrete, 2013.

J. Oliver, MODELLING STRONG DISCONTINUITIES IN SOLID MECHANICS VIA STRAIN SOFTENING CONSTITUTIVE EQUATIONS. PART 1: FUNDAMENTALS, International Journal for Numerical Methods in Engineering, vol.7, issue.21, pp.3575-3600, 1996.
DOI : 10.1002/(SICI)1097-0207(19961115)39:21<3575::AID-NME65>3.0.CO;2-E

J. Oliver, MODELLING STRONG DISCONTINUITIES IN SOLID MECHANICS VIA STRAIN SOFTENING CONSTITUTIVE EQUATIONS. PART 2: NUMERICAL SIMULATION, International Journal for Numerical Methods in Engineering, vol.19, issue.21, pp.3601-3623, 1996.
DOI : 10.1002/(SICI)1097-0207(19961115)39:21<3601::AID-NME64>3.0.CO;2-4

F. Armero and K. Garikipati, An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids, International Journal of Solids and Structures, vol.33, issue.20-22, pp.20-22, 1996.
DOI : 10.1016/0020-7683(95)00257-X

T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering, vol.55, issue.5, pp.601-620, 1999.
DOI : 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S

G. N. Wells and L. J. Sluys, A new method for modelling cohesive cracks using finite elements, International Journal for Numerical Methods in Engineering, vol.3, issue.12, pp.2667-2682, 2001.
DOI : 10.1002/nme.143

A. Hansbo and P. Hansbo, A finite element method for the simulation of strong and weak discontinuities in solid mechanics, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.33-35, pp.33-35, 2004.
DOI : 10.1016/j.cma.2003.12.041

S. Mariani and U. Perego, Extended finite element method for quasi-brittle fracture, International Journal for Numerical Methods in Engineering, vol.68, issue.1, pp.103-126, 2003.
DOI : 10.1002/nme.761

J. Oliver, A. E. Huespe, and P. J. Sanchez, A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.37-40, pp.37-40, 2006.
DOI : 10.1016/j.cma.2005.09.020

J. Dujc, Finite element analysis of limit load and localized failure of structures, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00505153

J. Dujc, B. Brank, and A. Ibrahimbegovic, Quadrilateral finite element with embedded strong discontinuity for failure analysis of solids, Computer Modeling in Engineering and Sciences, vol.69, issue.3, pp.223-259, 2010.

J. Dujc, B. Brank, and A. Ibrahimbegovic, Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids, International Journal for Numerical Methods in Engineering, vol.76, issue.4, pp.1075-1098, 2013.
DOI : 10.1002/nme.4475

G. E. Lane, Behavior of reinforced concrete beams under combined axial and lateral loading. Air force weapons laboratory. Kirtland air force base, 1972.

F. J. Vecchio and M. B. Emara, Shear deformations in reinforced concrete frames, ACI Structural Journal, vol.89, issue.1, pp.46-56, 1992.

A. Ibrahimbegovic, Nonlinear solid mechanics: Theoretical formulations and finite element solution methods, p.574, 2009.
DOI : 10.1007/978-90-481-2331-5

M. Jukic, B. Brank, and A. Ibrahimbegovic, Embedded discontinuity finite element formulation for failure analysis of planar reinforced concrete beams and frames, Engineering Structures, vol.50, pp.115-125, 2013.
DOI : 10.1016/j.engstruct.2012.07.028

W. B. Cranston, Tests on reinforced concrete frames, 1: Pinned portal frames, 1965.

M. Saje, I. Planinc, and S. Bratina, Large displacements and instability of beam-like structural systems In: Engineering structures under extreme conditions: Multi-physics and multi-scale computer models in nonlinear analysis and optimal design, pp.329-350, 2005.

M. Juki´cjuki´c, Kon?ni elementi za modeliranje lokaliziranih poru?itev v armiranem betonu. Doktorska disertacija, p.199, 2013.

J. Oliver and A. E. Huespe, Theoretical and computational issues in modelling material failure in strong discontinuity scenarios, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.27-29, pp.27-29, 2004.
DOI : 10.1016/j.cma.2003.08.007

L. Li, D. Brancherie, J. Favergeon, and J. M. Roelandt, Numerical approach for the description of different fracture modes for Zr/ZrO2 system ??? Deterministic and probabilistic aspects, Surface and Coatings Technology, vol.205, issue.5, pp.1475-1480, 2010.
DOI : 10.1016/j.surfcoat.2010.07.099