M. Ben-bettaieb and F. Abed-meraim, Effect of kinematic hardening on localized necking in substrate supported metal layers, International Journal of Mechanical Sciences, vol.123, pp.177-197, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01541500

J. Besson, G. Cailletaud, J. Chaboche, and S. Forest, Non-linear mechanics of materials, 2010.

J. Besson and R. Foerch, Large scale object-oriented finite element code design. Computer, Methods in Applied Mechanics and Engineering, vol.142, issue.1, pp.165-187, 1997.

J. Besson, D. Steglich, and W. Brocks, Modeling of crack growth in round bars and plane strain specimens, International Journal of Solids and Structures, vol.38, pp.8259-8284, 2001.

D. Bigoni and T. Hueckel, Uniqueness and localization -i -associative and nonassociative elastoplasticity, International Journal of Solids ans Structures, vol.28, pp.197-213, 1991.

D. Bigoni and D. Zaccaria, On strain localization analysis of elastoplastic materials at finite strains, International Journal of Plasticity, vol.9, pp.21-33, 1993.

M. S. Avila, N. Triantafyllidis, W. , and G. , Localization of deformation and loss of macroscopic ellipticity in microstructured solids, Journal of the Mechanics and Physics of Solids, vol.97, pp.275-298, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01360386

R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, vol.6, pp.236-249, 1958.

J. Hutchinson, Plastic buckling. Advances in applied mechanics, vol.14, pp.67-144, 1974.

J. Hutchinson and J. Miles, Bifurcation analysis of the onset of necking in an elastic/-plastic cylinder under uniaxial tension, Journal of the Mechanics and Physics of Solids, vol.22, pp.61-71, 1974.

L. Lee and C. Ades, Plastic torsional buckling strength of cylinders including effects of imperfections, Journal of the Aeronautical Sciences, vol.24, pp.241-248, 1957.

J. Mandel, Plasticité classique et viscoplasticité, CISM Courses and lectures, vol.97, pp.1-187, 1971.

M. Mazière, Éclatement des disques de Turbomachines, 2007.

M. Mazière, J. Besson, S. Forest, B. Tanguy, H. Chalons et al., Overspeed burst of elastoviscoplastic rotating disks -part i: Analytical and numerical stability analyses, European Journal of Mechanics -A/Solids, vol.28, issue.1, pp.36-44, 2009.

S. Mora, C. Maurini, T. Phou, J. Fromental, B. Audoly et al., Solid drops: Large capillary deformations of immersed elastic rods, Physical Review Letters, vol.111, p.114301, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00842852

G. Nefussi and A. Combescure, Coupled buckling and plastic instability for tube hydroforming, International Journal of Mechanical Sciences, vol.44, pp.899-914, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00454897

Q. S. Nguyen, Stability and nonlinear solid mechanics, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00105248

R. Ogden, Elastic and pseudo-elastic instability and bifurcation, 2000.

M. Ortiz, An analytical study of the localized failure modes of concrete, Mechanics of Materials, vol.6, pp.159-174, 1987.

H. Petryk, Material instability and strain-rate discontinuities in incrementally nonlinear continua, Journal of Mechanics and Physics of Solids, vol.40, pp.1227-1250, 1992.

H. Petryk, Theory of bifurcation and instability in time-independent plasticity, Bifurcation and Stability of Dissipative Systems, vol.327, pp.95-152, 1993.

H. Petryk, Material Instabilities in Elastic and Plastic Solids. CISM International Centre for Mechanical Sciences 414, 2000.

P. Pinsky, M. Ortiz, and K. Pister, Numerical integration of rate constitutive equations in finite deformation analysis, Computer Methods in Applied Mechanics an Engineering, vol.40, pp.137-158, 1986.

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

M. Rubin and B. Nadler, An eulerian formulation for large deformations of elastically isotropic elastic-viscoplastic membranes, Journal of Mechanics of Materials and Structures, vol.11, pp.197-216, 2016.

C. Truesdell and R. Toupin, The classical field theory of mechanics, 1960.

R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, vol.6, pp.236-249, 1958.

R. Hill and J. Hutchinson, Bifurcation phenomena in the plane tension test, Journal of the Mechanics and Physics of Solids, vol.23, pp.239-264, 1975.

J. Hutchinson and J. Miles, Bifurcation analysis of the onset of necking in an elastic/-plastic cylinder under uniaxial tension, Journal of the Mechanics and Physics of Solids, vol.22, pp.61-71, 1974.

L. Lee and C. Ades, Plastic torsional buckling strength of cylinders including effects of imperfections, Journal of the Aeronautical Sciences, vol.24, pp.241-248, 1957.

M. Mazière, Éclatement des disques de Turbomachines, 2007.

G. Nefussi and A. Combescure, Coupled buckling and plastic instability for tube hydroforming, International Journal of Mechanical Sciences, vol.44, pp.899-914, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00454897

Q. S. Nguyen, Stability and nonlinear solid mechanics, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00105248

S. Okazawa, Structural bifurcation for ductile necking localization, International Journal of Non-Linear Mechanics, vol.45, pp.35-41, 2010.

H. Petryk, Material Instabilities in Elastic and Plastic Solids. CISM International Centre for Mechanical Sciences 414, 2000.

M. Rubin and B. Nadler, An eulerian formulation for large deformations of elastically isotropic elastic-viscoplastic membranes, Journal of Mechanics of Materials and Structures, vol.11, pp.197-216, 2016.

S. Stören and J. Rice, Localized necking in thin sheets, Journal of the Mechanics and Physics of Solids, vol.23, issue.6, pp.421-441, 1975.

K. Thermann, Post-critical plastic deformation pattern in incrementally nonlinear materials at finite strain. CISM International Centre for Mechanical Sciences 414, 2000.

F. Abed-meraim, Contributionsà la prédiction d'instabilités de type structure et matériau : modélisation de critères et formulation d'éléments finis adaptésà la simulation des structures minces. Mémoire HDR dissertation, Arts et Métiers ParisTech, 2009.

A. R. Aguiar, L. P. Prado, and E. , Analytical and numerical investigation of failure of ellipticity for a class of hyperelastic laminates, European Journal of Mechanics A/Solids, vol.61, pp.110-121, 2017.

M. Ben-bettaieb and F. Abed-meraim, Effect of kinematic hardening on localized necking in substrate supported metal layers, International Journal of Mechanical Sciences, vol.123, pp.177-197, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01541500

A. Benallal and C. Comi, Localization analysis via a geometrical method, International Journal of Solids and Structures, vol.33, pp.99-119, 1996.
URL : https://hal.archives-ouvertes.fr/hal-01718320

J. Besson, G. Cailletaud, J. Chaboche, and S. Forest, Non-linear mechanics of materials, 2010.

J. Besson and R. Foerch, Large scale object-oriented finite element code design. Computer, Methods in Applied Mechanics and Engineering, vol.142, issue.1, pp.165-187, 1997.

J. Besson, D. Steglich, and W. Brocks, Modeling of crack growth in round bars and plane strain specimens, International Journal of Solids and Structures, vol.38, pp.8259-8284, 2001.

D. Bigoni, Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability, 2012.

D. Bigoni and T. Hueckel, Uniqueness and localization -i -associative and nonassociative elastoplasticity, International Journal of Solids ans Structures, vol.28, pp.197-213, 1991.

D. Bigoni and D. Zaccaria, Loss of strong ellipticity in non-associative elastoplasticity, Journal of the Mechanics and Physics of Solids, vol.40, pp.1313-1331, 1992.

D. Bigoni and D. Zaccaria, On strain localization analysis of elastoplastic materials at finite strains, International Journal of Plasticity, vol.9, pp.21-33, 1993.

R. De-borst, G. Wells, and L. Sluys, Some observations on embedded discontinuity models. Engineering Computations, vol.18, pp.241-254, 2001.

C. Defaisse, Étude de la rupture ductile d'un acierà très haute résistance pour des applications aéronautiques, 2018.

C. Defaisse, M. Mazière, L. Marcin, and J. Besson, Ductile fracture of an ultra-high strength steel under low to moderate stress triaxiality, Engineering Fracture Mechanics, vol.194, pp.301-318, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01780585

I. Doghri and R. Billardon, Investigation of localization due to damage in elasto-plastic materials, Mechanics of Materials, vol.19, issue.2, pp.129-149, 1995.

P. Gourgiotis and D. Bigoni, Stress channelling in extreme couple-stress materialspart i: Strong ellipticity, wave propagation, ellipticity, and discontinuity relations, Journal of the Mechanics and Physics of Solids, vol.88, pp.150-168, 2016.

G. Gruben, D. Morin, M. Langseth, and O. Hopperstad, Strain localization and ductile fracture in advanced high-strength steel sheets, European Journal of Mechanics A/Solids, vol.61, pp.315-329, 2017.

R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, vol.6, pp.236-249, 1958.

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

M. Jirásek, Mathematical analysis of strain localization. Revue Europeenne de Genie Civil, vol.11, pp.977-991, 2007.

P. Liu, Extended finite element method for strong discontinuity analysis of strain localization of non-associative plasticity materials, International Journal of Solids and Structures, vol.72, pp.174-189, 2015.

J. Mandel, Propagation des surfaces de discontinuité dans un milieuélastoplastique, Stress waves in anelastic solids, pp.331-340, 1964.

J. Mandel, Conditions de stabilité et postulat de drucker, Rheology and Soil Mechanics, pp.58-68, 1966.

J. Marsden and T. Hughes, Mathematical Foundations of Elasticity, 1983.

M. Mear and J. Hutchinson, Influence of yield surface curvature on flow localization in dilatant plasticity, Mechanics of Materials, vol.4, pp.395-407, 1985.

J. Mosler, Numerical analyses of discontinuous material bifurcation: strong and weak discontinuities, Computer Methods in applied Mechanics and Engineering, vol.194, pp.979-1000, 2005.

A. Mota, Q. Chen, J. Foulk, J. Ostien, L. et al., A cartesian parametrization for the numerical analysis of material instability, International Journal for Numerical Methods in Engineering, vol.108, issue.2, pp.156-180, 2016.

Z. Néda, R. Brechet, and Y. , Reconsideration of continuum percolation of isotropically oriented sticks in three dimensions, Physical Review E, vol.59, pp.3717-3719, 1999.

M. Neilsen and H. Schreyer, Bifurcations in elastic-plastic materials, International Journal of Solids and Structures, vol.40, pp.521-544, 1993.

Q. S. Nguyen, Stability and nonlinear solid mechanics, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00105248

J. Oliver, A. Huespe, J. Cante, and G. Diaz, On the numerical resolution of the discontinuous material bifurcation problem, International Journal for Numerical Methods in Engineering, vol.6, pp.786-804, 2010.

M. Ortiz, An analytical study of the localized failure modes of concrete, Mechanics of Materials, vol.6, pp.159-174, 1987.

H. Petryk, Material instability and strain-rate discontinuities in incrementally nonlinear continua, Journal of Mechanics and Physics of Solids, vol.40, pp.1227-1250, 1992.

H. Petryk, Theory of bifurcation and instability in time-independent plasticity, Bifurcation and Stability of Dissipative Systems, vol.327, pp.95-152, 1993.

H. Petryk, Plastic instability : Criteria and computational approaches, Archives of Computational Methods in Engineering, vol.4, pp.111-151, 1997.

H. Petryk, Material Instabilities in Elastic and Plastic Solids. CISM International Centre for Mechanical Sciences 414, 2000.

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

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

S. Sanborn and J. Prévost, Frictional slip plane growth by localization detection and the extended finite element method (xfem), International Journal for Numerical and Analytical Methods in Geomechanics, vol.35, pp.1278-1298, 2011.

M. Scales, N. Tardif, and S. Kyriakides, Ductile failure of aluminum alloy tubes under combined torsion and tension, International Journal of Solids and Structures, pp.116-128, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01802248

L. Szabó, Comments on loss of strong ellipticity in elastoplasticity, International Journal of Solids and Structures, vol.37, pp.3775-3806, 2000.

L. Van-hove, Sur l'extension de la condition de Legendre du calcul des variations aux intégrales multiplesà plusieurs fonctions inconnues, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, vol.50, pp.18-23, 1947.

N. Asmolovskiy, A. Tkachuk, and M. Bischoff, Numerical approaches to stability analysis of cylindrical composite shells based on load imperfections, Engineering Computations, vol.32, issue.2, pp.498-518, 2015.

J. Besson, G. Cailletaud, J. Chaboche, and S. Forest, Non-linear mechanics of materials, 2010.

D. Bigoni, Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability, 2012.

C. Defaisse, M. Mazière, L. Marcin, and J. Besson, Ductile fracture of an ultra-high strength steel under low to moderate stress triaxiality, Engineering Fracture Mechanics, vol.194, pp.301-318, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01780585

L. Daehli, D. Morin, T. Børvik, and O. Hopperstad, Influence of yield surface curvature on the macroscopic yielding and ductile failure of isotropic porous plastic materials, Journal of the Mechanics and Physics of Solids, vol.107, pp.253-283, 2017.

M. Di-pasqua, R. Khakimova, S. Castro, M. Arbelo, A. Riccio et al., Investigation on the geometric imperfections driven local buckling onset in composite conical shells, Applied Composite Materials, vol.23, issue.4, pp.879-897, 2016.

J. Eftang and A. Patera, A port-reduced static condensation reduced basis element method for large component-synthesized structures: approximation and a posteriori error estimation, Advanced Modeling and Simulation in Engineering Sciences, vol.1, issue.1, p.49, 2014.

L. Gardner, Elastic local buckling stresses for full structural steel cross-sections (oral presentation), European Solid Mechanics Conference, 2018.

P. Gosselet and C. Rey, Non-overlapping domain decomposition methods in structural mechanics, Archives of Computational Methods in Engineering, vol.13, pp.515-572, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00277626

B. Harrison, L. Yuan, and S. Kyriakides, Measurement of lined pipe liner imperfections and the effect on wrinkling and collapse under bending. International Conference on Offshore Mechanics and Arctic Engineering, p.5, 2016.

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.23, pp.239-264, 1975.

J. Hutchinson and V. Tvergaard, Shear band formation in plane strain, International Journal of Solids and Structures, vol.17, issue.5, pp.451-470, 1981.

A. Ibrahimbegovic, Geometric and material instabilities, 2009.

B. Kriegsmann, M. Hilburger, and R. Rolfes, The effects of geometric and loading imperfections on the response and lower-bound buckling load of a compression-loaded cylindrical shell, 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, vol.1, 2012.

L. Lee and C. Ades, Plastic torsional buckling strength of cylinders including effects of imperfections, Journal of the Aeronautical Sciences, vol.24, pp.241-248, 1957.

J. Mandel, Propagation des surfaces de discontinuité dans un milieuélastoplastique, Stress waves in anelastic solids, pp.331-340, 1964.

J. Mandel, Conditions de stabilité et postulat de drucker, Rheology and Soil Mechanics, pp.58-68, 1966.

M. Mear and J. Hutchinson, Influence of yield surface curvature on flow localization in dilatant plasticity, Mechanics of Materials, vol.4, pp.395-407, 1985.

Q. S. Nguyen, Stability and nonlinear solid mechanics, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00105248

R. Perez, X. Wang, and M. Mignolet, Nonintrusive structural dynamic reduced order modeling for large deformations: Enhancements for complex structures, Journal of Computational and Nonlinear Dynamics, vol.9, 2014.

H. Petryk, Plastic instability : Criteria and computational approaches, Archives of Computational Methods in Engineering, vol.4, pp.111-151, 1997.

T. E. Regulation, Eurocode 3: Design of steel structures -Part 1-1: General rules and rules for buildings. The European Union, 2005.

J. Remmers and R. De-borst, Delamination buckling of fibre-metal laminates, Science and Technology, vol.61, issue.15, pp.2207-2213, 2001.

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

D. Ryckelynck, A priori hyperreduction method: an adaptive approach, Journal of Computational Physics, vol.202, issue.1, pp.346-366, 2005.

E. Ryzhak, On stability of homogeneous elastic bodies under boundary conditions weaker than displacement conditions, The Quarterly Journal of Mechanics and Applied Mathematics, vol.47, issue.4, pp.663-672, 1994.

J. Simo, J. Oliver, A. , and F. , An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Computational Mechanics, vol.12, pp.277-296, 1993.

L. Van-hove, Sur l'extension de la condition de Legendre du calcul des variations aux intégrales multiplesà plusieurs fonctions inconnues, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, vol.50, pp.18-23, 1947.

F. Walport, L. Gardner, E. Real, I. Arrayago, and D. Nethercot, Effects of material nonlinearity on the global analysis and stability of stainless steel frames, Journal of Constructional Steel Research, 2018.

H. Wang, X. Yao, L. Li, Z. Sang, and B. Krakauer, Imperfection sensitivity of externally-pressurized, thin-walled, torispherical-head buckling, Thin-Walled Structures, vol.113, pp.104-110, 2017.

C. Combescure and R. S. Elliott, Hierarchical honeycomb material design and optimization: Beyond linearized behavior, International Journal of Solids and Structures, pp.161-169, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01648159

C. Combescure, P. Henry, and R. S. Elliott, Post-bifurcation and stability of a finitely strained hexagonal honeycomb subjected to equi-biaxial in-plane loading, International Journal of Solids and Structures, pp.296-318, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01647871

C. Defaisse, Étude de la rupture ductile d'un acierà très haute résistance pour des applications aéronautiques, 2018.

C. Defaisse, M. Mazière, L. Marcin, and J. Besson, Ductile fracture of an ultra-high strength steel under low to moderate stress triaxiality, Engineering Fracture Mechanics, vol.194, pp.301-318, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01780585

D. Gerbig, A. Bower, V. Savic, H. , and L. , Coupling digital image correlation and finite element analysis to determine constitutive parameters in necking tensile specimens, International Journal of Solids and Structures, pp.496-509, 2016.

M. Kamaya and M. Kawakubo, A procedure for determining the true stress-strain curve over a large range of strains using digital image correlation and finite element analysis, Mechanics of Materials, vol.43, issue.5, pp.243-253, 2011.

L. Lacourt, B. Figliuzzi, S. Forest, D. Ryckelynck, F. Willot et al., étude de la nocivité des défauts dans les soudures et les pièces obtenues par fabrication additive, ColloqueMECAMAT Fatigue des Structures et des Matériaux, 2017.

L. Lee and C. Ades, Plastic torsional buckling strength of cylinders including effects of imperfections, Journal of the Aeronautical Sciences, vol.24, pp.241-248, 1957.

J. Li, G. Yang, T. Siebert, M. F. Shi, Y. et al., A method of the direct measurement of the true stress-strain curve over a large strain range using multi-camera digital image correlation, Optics and Lasers in Engineering, vol.107, pp.194-201, 2018.

J. Mandel, Propagation des surfaces de discontinuité dans un milieuélastoplastique, Stress waves in anelastic solids, pp.331-340, 1964.

C. Olivier, Décompositions tensorielles et factorisations de calculs intensifs appliquées a l'identification de modèles de comportement non linéaire, 2017.

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

D. Ryckelynck, A priori hyperreduction method: an adaptive approach, Journal of Computational Physics, vol.202, issue.1, pp.346-366, 2005.

E. Ryzhak, On stability of homogeneous elastic bodies under boundary conditions weaker than displacement conditions, The Quarterly Journal of Mechanics and Applied Mathematics, vol.47, issue.4, pp.663-672, 1994.

L. Van-hove, Sur l'extension de la condition de Legendre du calcul des variations aux intégrales multiplesà plusieurs fonctions inconnues, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, vol.50, pp.18-23, 1947.

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, High Yield material: Comparison between global instability (Fixed/Fixed case) results (full lines) and reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation. White filling: global instability modes, Figure, vol.8

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, High Yield material: Comparison global instability (Circular/Fixed case) results (full lines) with reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation. White filling: global instability modes, vol.30

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, High Yield material: Comparison global instability (Flat/Fixed case) results (full lines) with reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation, Figure, vol.8

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, Low Yield material: Comparison global instability (Fixed/Fixed case) results (full lines) with reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation. White filling: global instability modes, vol.32

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, Low Yield material: Comparison between the global instability analysis (Circular/Fixed case) results (full lines) and the reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation. White filling: global instability modes, vol.33

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, Low Yield material: Comparison between global instability (Flat/Fixed case) results (full lines) and reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation. White filling: global instability modes, vol.34

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, High Ductility material: Comparison between global instability (Fixed/Fixed case) results (full lines) and reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation. White filling: global instability modes, Figure, vol.8

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, High Ductility material: Comparison between global instability (Circular/Fixed case) results (full lines) with reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation, Figure, vol.8

. L/d=1,

. L/d=2,

. L/d=3,

. L/d=5,

. L/d=7,

. L/d=10,

. L/d=12,

, High Ductility material: Comparison global instability (Flat/Fixed case) results (full lines) with reference design curves (dashed lines) for tubes loaded in torsion. Black filling: maximum equivalent shear stress obtained during simulation. White filling: global instability modes, Figure, vol.8

, Weakened boundary conditions: Flat/Fixed. Design curves obtained with the global and local instability analysis in a full finite deformation for the three materials considered for tubes loaded in torsion, vol.38

J. Besson, G. Cailletaud, J. Chaboche, and S. Forest, Non-linear mechanics of materials, 2010.

D. Bigoni and T. Hueckel, Uniqueness and localization -i -associative and nonassociative elastoplasticity, International Journal of Solids ans Structures, vol.28, pp.197-213, 1991.

D. Bigoni and D. Zaccaria, On strain localization analysis of elastoplastic materials at finite strains, International Journal of Plasticity, vol.9, pp.21-33, 1993.

M. S. Avila, N. Triantafyllidis, W. , and G. , Localization of deformation and loss of macroscopic ellipticity in microstructured solids, Journal of the Mechanics and Physics of Solids, vol.97, pp.275-298, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01360386

D. Drucker, A more fundamental approach to stress-strain relations, First US National Congress of Applied Mechanics, pp.487-491, 1951.

J. Hadamard, Leçons sur la propagation des ondes et leséquations de l'hydrodynamique, 1903.

B. Halphen, Sur le champ des vitesses en thermoplasticité finie, International Journal of Solid Structures, pp.947-960, 1975.

R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, vol.6, pp.236-249, 1958.

R. Hill, On constitutive inequalities for simple materials-ii, Journal of the Mechanics Physics Solids, pp.315-322, 1968.

J. Lemaitre, J. L. Chaboche, A. Benallal, and R. Desmorat, Mécanique des matériaux solides -3èmeédition, 2009.

J. Mandel, Propagation des surfaces de discontinuité dans un milieuélastoplastique, Stress waves in anelastic solids, pp.331-340, 1964.

J. Mandel, Conditions de stabilité et postulat de drucker, Rheology and Soil Mechanics, pp.58-68, 1966.

J. Mandel, Plasticité classique et viscoplasticité, CISM Courses and lectures, vol.97, pp.1-187, 1971.

M. Mear and J. Hutchinson, Influence of yield surface curvature on flow localization in dilatant plasticity, Mechanics of Materials, vol.4, pp.395-407, 1985.

Q. S. Nguyen, Stability and nonlinear solid mechanics, p.277, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00105248

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

C. Truesdell and R. Toupin, The classical field theory of mechanics, 1960.