G. Abrivard, A coupled crystal plasticity -phase field formulation to describe microstructural evolution in polycrystalline aggregates during recrystallisation, 2009.
URL : https://hal.archives-ouvertes.fr/pastel-00533060

K. Agbessi, Approches expérimentales et multi-échelles des processus d'amorçage des fissures de fatigue sous chargements complexes, 2013.

E. Agullo, P. Amestoy, A. Buttari, A. Guermouche, G. Joslin et al., Recent advances in sparse direct solvers, 22nd Conference on Structural Mechanics in Reactor Technology, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01060301

A. Ait-yahia, E. Palomo, and D. Barrio, Thermal systems modelling via singular value decomposition: direct and modular approach, Applied Mathematical Modelling, vol.23, issue.6, pp.447-468, 1999.
DOI : 10.1016/S0307-904X(98)10091-4

A. Ait-yahia, E. Palomo, and D. Barrio, Numerical simplification method for statespace models of thermal systems, Numerical Heat Transfer Part B, vol.37, pp.201-225, 2000.

C. Allery, A. Hamdouni, D. Ryckelynck, and N. Verdon, A priori reduction method for solving the two-dimensional Burgers??? equations, Applied Mathematics and Computation, vol.217, issue.15, pp.6671-6679, 2011.
DOI : 10.1016/j.amc.2011.01.065

URL : https://hal.archives-ouvertes.fr/hal-00585095

A. Ammar and F. Chinesta, Circumventing Curse of Dimensionality in the Solution of Highly Multidimensional Models Encountered in Quantum Mechanics Using Meshfree Finite Sums Decomposition, Meshfree Methods for Partial Differential Equations IV, pp.1-17, 2008.
DOI : 10.1007/978-3-540-79994-8_1

URL : https://hal.archives-ouvertes.fr/hal-00289677

A. Ammar, F. Chinesta, and E. Cueto, COUPLING FINITE ELEMENTS AND PROPER GENERALIZED DECOMPOSITIONS, International Journal for Multiscale Computational Engineering, vol.9, issue.1, pp.17-33, 2011.
DOI : 10.1615/IntJMultCompEng.v9.i1.30

URL : https://hal.archives-ouvertes.fr/hal-01500147

A. Ammar, F. Chinesta, E. Cueto, and M. Doblaré, Proper generalized decomposition of time-multiscale models, International Journal for Numerical Methods in Engineering, vol.26, issue.6, pp.569-596, 2012.
DOI : 10.1002/nme.3331

URL : https://hal.archives-ouvertes.fr/hal-01007223

A. Ammar, F. Chinesta, P. Diez, and A. Huerta, An error estimator for separated representations of highly multidimensional models, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.25-28, pp.1872-1880, 2010.
DOI : 10.1016/j.cma.2010.02.012

URL : https://hal.archives-ouvertes.fr/hal-01004991

A. Ammar, F. Chinesta, and A. Falco, On the Convergence of a Greedy Rank-One Update Algorithm for??a??Class of Linear Systems, Archives of Computational Methods in Engineering, vol.21, issue.4, pp.473-486, 2010.
DOI : 10.1007/s11831-010-9048-z

URL : https://hal.archives-ouvertes.fr/hal-01007145

A. Ammar, E. Cueto, and F. Chinesta, Reduction of the chemical master equation for gene regulatory networks using proper generalized decompositions, International Journal for Numerical Methods in Biomedical Engineering, vol.205, issue.5, pp.960-973, 2012.
DOI : 10.1002/cnm.2476

URL : https://hal.archives-ouvertes.fr/hal-01061274

A. Ammar, B. Mokdad, F. Chinesta, and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.139, issue.3, pp.153-176, 2006.
DOI : 10.1016/j.jnnfm.2006.07.007

URL : https://hal.archives-ouvertes.fr/hal-00287087

A. Ammar, B. Mokdad, F. Chinesta, and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.144, issue.2-3, pp.98-121, 2007.
DOI : 10.1016/j.jnnfm.2007.03.009

A. Ammar, M. Normandin, and F. Chinesta, Solving parametric complex fluids models in rheometric flows, Journal of Non-Newtonian Fluid Mechanics, vol.165, issue.23-24, pp.1588-1601, 2010.
DOI : 10.1016/j.jnnfm.2010.08.006

URL : https://hal.archives-ouvertes.fr/hal-01007311

A. Ammar, M. Normandin, F. Daim, D. Gonzalez, E. Cueto et al., Non incremental strategies based on separated representations: applications in computational rheology, Communications in Mathematical Sciences, vol.8, issue.3, p.671, 2010.
DOI : 10.4310/CMS.2010.v8.n3.a4

URL : https://hal.archives-ouvertes.fr/hal-01007108

A. Ammar, D. Ryckelynck, F. Chinesta, and R. Keunings, On the reduction of kinetic theory models related to finitely extensible dumbbells, Journal of Non-Newtonian Fluid Mechanics, vol.134, issue.1-3, pp.136-147, 2006.
DOI : 10.1016/j.jnnfm.2006.01.007

URL : https://hal.archives-ouvertes.fr/hal-00080838

A. Ammar, A. Zghal, F. Morel, and F. Chinesta, On the space-time separated representation of integral linear viscoelastic models, Comptes Rendus M??canique, vol.343, issue.4, pp.247-263, 2015.
DOI : 10.1016/j.crme.2015.02.002

A. Ammar, The proper generalized decomposition: a powerful tool for model reduction, International Journal of Material Forming, vol.33, issue.2, pp.89-102, 2010.
DOI : 10.1007/s12289-009-0647-x

M. Arzt, approche des phénomènes cycliques par la méthode à grand incrément de temps, 1994.

H. Askes and L. J. Sluys, Remeshing strategies for adaptive ALE analysis of strain localisation, European Journal of Mechanics - A/Solids, vol.19, issue.3, pp.447-467, 2000.
DOI : 10.1016/S0997-7538(00)00176-5

J. A. Atwell and B. B. King, Reduced order controllers for spatially distributed systems via proper orthogonal decomposition. rapport technique, 1999.
DOI : 10.1137/s1064827599360091

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.8268

N. Aurby, P. Holmes, J. L. Lumley, and E. Stone, The dynamics of coherent structures in the wall region of a turbulent boundary layer, Journal of Fluid Mechanics, vol.192, pp.115-173, 1988.

Y. Ayed, Approches expérimentales et numériques de l'usinage assisté jet d'eau haute pression : étude des mécanismes d'usure et contribution à la modélisation multiphysiques de la coupe, École Nationale Supérieure d'Arts et Métiers, 2013.

O. Balima, Y. Favennec, and D. Petit, Model Reduction for Heat Conduction with Radiative Boundary Conditions using the Modal Identification Method, Numerical Heat Transfer, Part B: Fundamentals, vol.2, issue.2, pp.107-130, 2007.
DOI : 10.1109/TMAG.2002.804815

URL : https://hal.archives-ouvertes.fr/hal-00162009

K. J. Bathe, Finite Element Procedures in Engineering Analysis, Journal of Pressure Vessel Technology, vol.106, issue.4, 1982.
DOI : 10.1115/1.3264375

V. P. Bennett and D. L. Mcdowell, Crack tip displacements of microstructurally small surface cracks in single phase ductile polycrystals. Engng Fracture Mechanics, pp.185-207, 2003.

V. P. Bennett and D. L. Mcdowell, Polycrystal orientation distribution effects on microslip in high cycle fatigue, International Journal of Fatigue, vol.25, issue.1, pp.1087-1104, 2003.
DOI : 10.1016/S0142-1123(02)00057-9

J. Berthe, Cadre d'approximation espace-temps pour le traitement d'hyper-problèmes. Master's thesis, ENS Cachan, 2010.

D. Bodin, Modèle d'endommagement cyclique : Application à la fatigue des enrobés bitumineux, 2002.

P. Boisse, P. Ladevèze, M. Poss, and P. Rougee, A new large time increment algorithm for anisotropic plasticity, International Journal of Plasticity, vol.7, issue.1-2, pp.65-77, 1991.
DOI : 10.1016/0749-6419(91)90005-J

P. Boisse, P. Ladevèze, and P. Rougée, A large time increment method for elastoplastic problems, Eur.J.Mech, A/solids, vol.4, pp.257-275, 1989.

G. Bolzon and V. Buljak, An effective computational tool for parametric studies and identification problems in materials mechanics, Computational Mechanics, vol.19, issue.6, pp.675-687, 2011.
DOI : 10.1007/s00466-011-0611-8

M. Bonnet, Analyse des structures mécaniques par la méthode des éléments finis, Ecole Polytechnique, département de Mécanique, majeure 2 SeISM, 2005.

M. Bonnet and A. Frangi, Analyse des structures mécaniques par la méthode des éléments finis. Editions de l'Ecole Polytechnique, 2007.

L. Christian and . Borderie, Introduction à la méthode des éléments finis, 2003.

H. Borouchaki, A. Cherouat, P. Laug, and K. Saanouni, Adaptive remeshing for ductile fracture prediction in metal forming, Comptes Rendus M??canique, vol.330, issue.10, pp.709-716, 2002.
DOI : 10.1016/S1631-0721(02)01519-X

G. P. Brooks and J. M. Powers, A Karhunen-Loeve Galerkin Technique with Shock Fitting for Optimization of a Blunt Body Geometry, 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2002.
DOI : 10.2514/6.2002-3861

H. Burlet and G. Cailletaud, Zebulon, a finite element code for nonlinear material behaviour, Proc. Int. Conf. "New advances in structural computations, pp.2-5673, 1991.

W. D. Jr and . Callister, Material Science and Engineering An Introduction, 1999.

C. Jianping, Modélisation numérique des problèmes d'interfaces sable-pieu pour les très grands nombres de cycles : Developpement d'une méthode de sauts de cycles, 2010.

S. Cartel, Méthodes numériques de représentation à variables séparées pour ma résolution des problèmes paramétriques en mécanique non-linéaire des structures, 2011.

L. Champaney, P. Boucard, and S. Guinard, Adaptive multi-analysis strategy for contact problems with friction, Computational Mechanics, vol.16, issue.1, pp.305-315, 2008.
DOI : 10.1007/s00466-007-0213-7

L. Champaney, P. Ladevèze, and P. Talbot, A non-incremental computational strategy for plastic or viscoplastic structures with unilateral contact, Computational Mechanics New Trends and, 1998.

H. Chen and A. R. Ponter, A direct method on the evolution of ratchet limit, Journal of Pressure Vessel Technology, vol.132, 2010.

J. Chenot, C. Béraudo, M. Bernacki, and L. Fourment, Finite Element Simulation of Multi Material Metal Forming, Procedia Engineering, vol.81, pp.2427-2432, 2014.
DOI : 10.1016/j.proeng.2014.10.345

URL : https://hal.archives-ouvertes.fr/hal-01110930

F. Chinesta, A. Ammar, and E. Cueto, On the use of proper generalized decompositions for solving the multidimensional chemical master equation, Revue europ??enne de m??canique num??rique, vol.19, issue.1-3, pp.53-64, 2010.
DOI : 10.3166/ejcm.19.53-64

URL : https://hal.archives-ouvertes.fr/hal-01007161

F. Chinesta, A. Ammar, and E. Cueto, Proper generalized decomposition of multiscale models, International Journal for Numerical Methods in Engineering, vol.197, issue.5, pp.1114-1132, 2010.
DOI : 10.1002/nme.2794

URL : https://hal.archives-ouvertes.fr/hal-01007222

F. Chinesta, A. Ammar, and E. Cueto, Proper generalized decomposition of multiscale models, International Journal for Numerical Methods in Engineering, vol.197, issue.5, pp.8-91114, 2010.
DOI : 10.1002/nme.2794

URL : https://hal.archives-ouvertes.fr/hal-01007222

F. Chinesta, A. Ammar, and E. Cueto, Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensionnal models, Archives of Computationnal Methods in Engineering, pp.1-24, 2010.

F. Chinesta, A. Ammar, A. Falco, and M. Laso, On the reduction of stochastic kinetic theory models of complex fluids, Modelling and Simulation in Materials Science and Engineering, vol.15, issue.6, pp.639-652, 2007.
DOI : 10.1088/0965-0393/15/6/004

URL : https://hal.archives-ouvertes.fr/hal-01476037

F. Chinesta, A. Ammar, and P. Joyot, Proper generalized decomposition of multiscale models. The nanometric and micrometric scales of the structure and mechanics of materials revisited : An introduction to he challenges of fully deterministic numerical descriptions, pp.191-213, 2008.
DOI : 10.1002/nme.2794

URL : https://hal.archives-ouvertes.fr/hal-01007222

F. Chinesta, A. Ammar, F. Lemarchand, P. Beauchene, and F. Boust, Alleviating mesh constraints: Model reduction, parallel time integration and high resolution homogenization, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.5, pp.400-413, 2008.
DOI : 10.1016/j.cma.2007.07.022

URL : https://hal.archives-ouvertes.fr/hal-01004980

F. Chinesta, E. Cueto, D. Ryckelynck, and A. Ammar, Alpha-nem and model reduction : two new and powerful numerical strategies for describe flows involving short fiber suspensions
URL : https://hal.archives-ouvertes.fr/hal-00020781

J. Y. Cognard, P. Ladeveze, and P. Talbot, A large time increment approach for thermo-mechanical problems Advances in Engineering Software, pp.583-593, 1999.

J. Y. Cognard and P. Ladevèze, A large time increment approach for cyclic viscoplasticity, International Journal of Plasticity, vol.9, issue.2, pp.141-157, 1993.
DOI : 10.1016/0749-6419(93)90026-M

F. Comte, M. H. Maitournam, P. Burry, and T. Mac-lan-nguyen, A direct method for the solution of evolution problems, Comptes Rendus M??canique, vol.334, issue.5, pp.317-322, 2006.
DOI : 10.1016/j.crme.2006.02.007

URL : https://hal.archives-ouvertes.fr/hal-00111464

L. Cordier and M. Bergmann, Réduction de dynamique par décomposition orthogonale aux valeurs propres (pod), Optimisation et Contrôle des Ecoulements et des Transferts, pp.12-17, 2006.

J. Corgnard and P. Ladevèze, A large time increment approach for cyclic viscoplasticity, International Journal of Plasticity, vol.9, issue.2, pp.141-157, 1993.
DOI : 10.1016/0749-6419(93)90026-M

V. Courtier, Réduction de modèle et simplification de l'intégration de loi de comportement pour la prévision de la durée de vie, 2013.

R. D. Cramer and I. M. Navon, Efficiency of a pod-based reduced second-order adjoint model in 4d-var data assimililation, International Journal for Numerical Methods in Fluids, vol.53, issue.6, pp.985-1004, 2007.

M. Cremonesi, D. Néron, P. Guidault, and P. Ladevèze, A PGD-based homogenization technique for the resolution of nonlinear multiscale problems, Computer Methods in Applied Mechanics and Engineering, vol.267, pp.275-292, 2013.
DOI : 10.1016/j.cma.2013.08.009

URL : https://hal.archives-ouvertes.fr/hal-01403834

Y. Debard, Méthode des éléments finis : élasticité plane, Master modélisation numérique et réalité virtuelle, 2011.

J. Delmas, Fonctions de forme et points d'intégration des éléments finis. EDF recherche et développement, GNU FDL, 2013.

F. Deprettere, Svd and signal processing : algorithms, analysis and applications, 1988.

O. Diard, S. Leclercq, G. Rousselier, and G. Cailletaud, Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity, International Journal of Plasticity, vol.21, issue.4, pp.691-722, 2005.
DOI : 10.1016/j.ijplas.2004.05.017

URL : https://hal.archives-ouvertes.fr/hal-00165134

Z. Z. Du, J. Wang, and W. Fan, Direcy cyclic method for solder joint relibaility analysis, IMECE2006, 2006.
DOI : 10.1115/imece2006-13016

A. Dumon, C. Allery, and A. Ammar, Proper general decomposition (PGD) for the resolution of Navier???Stokes equations, Journal of Computational Physics, vol.230, issue.4, pp.1387-1407, 2011.
DOI : 10.1016/j.jcp.2010.11.010

URL : https://hal.archives-ouvertes.fr/hal-01061383

A. Dumon, C. Allery, and A. Ammar, Proper Generalized Decomposition method for incompressible Navier???Stokes equations with a spectral discretization, Applied Mathematics and Computation, vol.219, issue.15, pp.8145-8162, 2013.
DOI : 10.1016/j.amc.2013.02.022

URL : https://hal.archives-ouvertes.fr/hal-01062396

A. Dumon, Réduction dimensionnelle de type PGF pour la résolution des écouement incompressibles, 2011.

D. Dureisseix, P. Ladevèze, and B. A. Schrefler, A LATIN computational strategy for multiphysics problems: application to poroelasticity, International Journal for Numerical Methods in Engineering, vol.2, issue.10, pp.1489-1510, 2003.
DOI : 10.1002/nme.622

URL : https://hal.archives-ouvertes.fr/hal-00321790

C. Déprés, M. C. Fivel, and L. Tabourot, A dislocation-based model for low-amplitude fatigue behaviour of face-centred cubic single crystals, Scripta Materialia, vol.58, issue.12, pp.1086-1089, 2008.
DOI : 10.1016/j.scriptamat.2008.02.027

B. S. Everitt and G. Dunn, Applied multivariate data analysis, 2001.
DOI : 10.1002/9781118887486

M. Fahl, Trust-Region methods for flow control based on Reduced Order Modeling, 2001.

N. Petrinic and F. Dunne, Introduction to computational plasticity, 2006.

F. Galland, A. Gravouil, E. Malvesin, and M. Rochette, A global model reduction approach for 3D fatigue crack growth with confined plasticity, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.5-8, pp.5-8699, 2011.
DOI : 10.1016/j.cma.2010.08.018

URL : https://hal.archives-ouvertes.fr/hal-00938580

S. Ganapathysubramanian and N. Zabaras, Design across length scales: a reduced-order model of polycrystal plasticity for the control of microstructure-sensitive material properties, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.45-47, pp.5017-5034, 2004.
DOI : 10.1016/j.cma.2004.04.004

S. Ghosh, Y. Bhandari, and M. Groeber, CAD-based reconstruction of 3D polycrystalline alloy microstructures from FIB generated serial sections, Computer-Aided Design, vol.40, issue.3, pp.293-310, 2008.
DOI : 10.1016/j.cad.2007.11.003

A. Godin, Estimation sur des bases orthogonales des propriétés thermiques de matériaux hétérogènes a propriétés constantes par morceaux, 2013.

D. Gonzalez, A. Ammar, F. Chinesta, and E. Cueto, Recent advances on the use of separated representations, International Journal for Numerical Methods in Engineering, vol.30, issue.1, pp.637-659, 2010.
DOI : 10.1002/nme.2710

D. Gonzalez, E. Cueto, F. Chinesta, P. Diez, and A. Huerta, Streamline upwind/Petrov-Galerkin-based stabilization of proper generalized decompositions for high-dimensional advection-diffusion equations, International Journal for Numerical Methods in Engineering, vol.59, issue.9, pp.1216-1232, 2013.
DOI : 10.1002/nme.4493

URL : https://hal.archives-ouvertes.fr/hal-01007352

R. Guerchais, F. Morel, and N. Saintier, The role of the microstructure and defects on crack initiation in 316l stainless steel under multiaxial high cycle fatigue, 11th International Fatigue Congress, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01082940

R. Guerchais, C. Robert, F. Morel, and N. Saintier, Micromechanical study of the loading path effect in high cycle fatigue, International Journal of Fatigue, vol.59, pp.64-75, 2014.
DOI : 10.1016/j.ijfatigue.2013.09.014

URL : https://hal.archives-ouvertes.fr/hal-01084146

R. Guerchais, N. Saintier, F. Morel, and C. Robert, Micromechanical investigation of the influence of defects in high cycle fatigue, International Journal of Fatigue, vol.67, pp.159-172, 2014.
DOI : 10.1016/j.ijfatigue.2014.01.005

URL : https://hal.archives-ouvertes.fr/hal-01084156

R. Guerchais, N. Saintier, F. Morel, and C. Robert, Influence of the microstructure and voids on the high-cycle fatigue strength of 316l stainless steel under multiaxial loading. Fatigue and Fracture of Engineering Materials and structures, pp.1087-1104, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01309594

G. Raphaël, Influence d'accidents géométriques et du mode de chargement sur le comportement en fatigue à grand nombre de cycles d'un acier inoxydable austénitique 316L, École Nationale Supérieure d'Arts et Métiers, 2014.

F. Guilhem, Étude numérique des champs mécaniques locaux dans les agrégats polycristallins d'acier 316L sous chargement de fatigue, 2011.

Y. Guilhem, S. Basseville, F. Curtit, J. Stéphan, and G. Cailletaud, Champs locaux, effets de joints de grains et de surface dans les agrégats polycristallins 3d, CSMA 11ème Colloque national en calcul des structures, pp.13-17, 2013.

Y. Guilhem, S. Basseville, F. Curtit, J. Stéphan, and G. Cailletaud, Investigation of the effect of grain clusters on fatigue crack initiation in polycrystals, International Journal of Fatigue, vol.32, issue.11, pp.1748-1763, 2010.
DOI : 10.1016/j.ijfatigue.2010.04.003

URL : https://hal.archives-ouvertes.fr/hal-00509802

Y. Guilhem, S. Basseville, F. Curtit, J. Stéphan, and G. Cailletaud, Numerical investigations of the free surface effect in three-dimensional polycrystalline aggregates, Computational Materials Science, vol.70, pp.150-162, 2013.
DOI : 10.1016/j.commatsci.2012.11.052

URL : https://hal.archives-ouvertes.fr/hal-01017647

C. Gérard, Mesures de champs et identification de modèles de plasticité cristalline, 2008.

B. Halphen, Problèmes quasi-statiques en viscoplasticité, 1978.

M. Hammoud, M. Beringhier, and J. Grandidier, A reduced simulation applied to the viscoelastic fatigue of polymers, Comptes Rendus M??canique, vol.342, issue.12, pp.671-691, 2014.
DOI : 10.1016/j.crme.2014.07.008

W. Buffière and . Ludwig, 3-d growth of a short fatigue crack within a polycrystalline microstructure studied using combined diffraction and phasecontrast x-ray tomography, Acta Materialia, vol.52, issue.2, pp.590-601, 2011.

T. Herbland, Une méthode de correction élastoplastique pour le calcul en fatigue des zones de concentration de contraintes sous chargement cyclique multiaxial non proportionnel, 2009.

C. Heyberger, PGD espace-temps adaptée pour le traitement de problèmes paramétrés, 2014.

P. Holmes, J. Lumley, and G. Berkooz, Turbulence, coherent structures, dynamical systems and symmetry, 1996.
DOI : 10.1017/cbo9780511622700

P. Holmes, J. Lumley, G. Berkooz, J. , and R. Wittenberg, Low-dimensional models of coherent structures in turbulence, Physics Reports, vol.287, issue.4, pp.337-384, 1997.
DOI : 10.1016/S0370-1573(97)00017-3

A. Hor, N. Saintier, C. Robert, T. Palin-luc, and F. Morel, Statistical assessment of multiaxial HCF criteria at the grain scale, International Journal of Fatigue, vol.67, pp.151-158, 2014.
DOI : 10.1016/j.ijfatigue.2014.01.024

URL : https://hal.archives-ouvertes.fr/hal-01057879

H. Hotelling, Analysis of complex statistical variables in principal components, J. Exp. Psy, vol.24, p.417, 1953.

E. Héripré, M. Dexet, J. Crépin, L. Gélébart, A. Roos et al., Coupling between experimental measurements and polycrystal finite element calculations for micromechanical study of metallic materials, International Journal of Plasticity, vol.23, issue.9, pp.1512-1539, 2007.
DOI : 10.1016/j.ijplas.2007.01.009

J. Chaboche, J. Besson, G. Cailletaud, and S. Forest, Mécanique non-linéaire des matériaux, Hermes, 2001.

M. Jabbado and M. H. Maitournam, A high-cycle fatigue life model for variable amplitude multiaxial loading, Fatigue & Fracture of Engineering Materials & Structures, vol.25, issue.1, pp.67-75, 2008.
DOI : 10.1111/j.1460-2695.2007.01201.x

URL : https://hal.archives-ouvertes.fr/hal-00418562

T. J. Hughes and J. C. Simo, Computational Inelasticity, 1997.

G. Hatt and J. L. Batoz, Modélisation des Structures par Éléments Finis, I?III, 1991.

T. Kanit, Determination of representative volume element for random microstructures, 2002.

T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach, International Journal of Solids and Structures, vol.40, issue.13-14, pp.3647-3679, 2003.
DOI : 10.1016/S0020-7683(03)00143-4

H. Karaouni, Nouveaux outils pour la conception fiable des structures, 2001.

K. Karhunen, Uber lineare methoden füer wahrscheiniogkeitsrechnung Annales of Academic Science Fennicae, Series A1, Mathematical Physics, pp.3-79, 1946.

K. Karhunen, Zur spektraltheorie stochastischer prozesse, Ann. Acad. Sci. Fennicae, p.37, 1946.

P. Kerfriden, P. Gosselet, S. Adhikari, and S. Bordas, Bridging proper orthogonal decomposition methods and augmented Newton???Krylov algorithms: An adaptive model order reduction for highly nonlinear mechanical problems, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.5-8, pp.5-8850, 2011.
DOI : 10.1016/j.cma.2010.10.009

URL : https://hal.archives-ouvertes.fr/hal-00537900

L. Khalij, Détermination directe des états limites et des champs de contraintes résiduelles pour les structures chargées cycliquement application de la méthode d'analyse simplifiée, 2002.

D. A. Knoll and P. R. Mchugh, Newton-Krylov methods applied to a system of convection-diffusion-reaction equations, Computer Physics Communications, vol.88, issue.2-3, pp.141-160, 1995.
DOI : 10.1016/0010-4655(95)00062-K

K. Krabbenhoft, Basic Computational Plasticity, 2002.

R. D. Krieg and D. B. Krieg, Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model, Journal of Pressure Vessel Technology, vol.99, issue.4, pp.510-515, 1977.
DOI : 10.1115/1.3454568

S. Kruch, An efficient cycles jump technique for viscoplastic structures calculations involving large number of cycles, pp.1733-1744, 1992.

K. Kunisch and S. Volkwein, Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition, Journal of Optimization Theory and Applications, vol.6, issue.2, pp.345-371, 1999.
DOI : 10.1023/A:1021732508059

P. Ladeveze, J. Y. Cognard, and P. Talbot, A Non-incremental and Adaptive Computational Approach in Thermo-viscoplasticity, IUTAM Symposium on Micro-and Macrostructural Aspects of the Thermoplasticity, pp.281-291, 1999.
DOI : 10.1007/0-306-46936-7_27

P. Ladevèze, Sur une famille d'algorithmes en mécanique des structures, Comptes Rendus Acad. Sc. Paris, t. 300 série II, pp.41-44, 1985.

P. Ladevèze, La méthode à grand increment pour l'analyse de structures à comportement non linéaire décrit par variables internes, Série II, issue.11, 1989.

P. Ladevèze, The large time increment method for the analysis of structures with non-linear behavior described by internal variables, Comptes Rendus De L'Academie Des Sciences Serie Ii, pp.1095-1099, 1989.

P. Ladevèze, M??canique non lin??aire des structures, Revue Fran??aise de G??nie Civil, vol.1, issue.2, 1996.
DOI : 10.1080/12795119.1997.9692126

P. Ladevèze, Nonlinear Computational Structural Mechanics-New approaches and nonincremental methods of calculation, 1999.

P. Ladevèze and A. Nouy, On a multiscale computational strategy with time and space homogenization for structural mechanics, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, p.192, 2003.
DOI : 10.1016/S0045-7825(03)00341-4

P. Ladevèze and D. Néron, Une strat??gie de calcul multi??chelle avec homog??n??isation en espace et en temps, Comptes Rendus M??canique, vol.330, issue.10, pp.683-689, 2002.
DOI : 10.1016/S1631-0721(02)01514-0

P. Ladevèze, D. Néron, and J. Passieux, The LATIN multiscale computational method and the Proper Generalized Decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.1287-1296, 2009.
DOI : 10.1016/j.cma.2009.06.023

P. Ladevèze, J. Passieux, and D. Néron, The LATIN multiscale computational method and the Proper Generalized Decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.1287-1296, 2010.
DOI : 10.1016/j.cma.2009.06.023

P. Ladevèze and U. Perego, Duality preserving discretization of the large time increment methods, Computer Methods in Applied Mechanics and Engineering, vol.189, issue.1, pp.205-232, 2000.
DOI : 10.1016/S0045-7825(99)00310-2

L. D. Lathauwer, B. A. Moor, and J. Vandewalle, A Multilinear Singular Value Decomposition, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.4, pp.1253-1278, 2000.
DOI : 10.1137/S0895479896305696

A. J. Laub and V. C. Klema, The singular value decomposition : its computation and some applications, IEEE Transactions on Automatic Control, vol.25, pp.164-176, 1980.

R. A. Lebensohn, N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform, Acta Materialia, vol.49, issue.14, pp.2723-2737, 2001.
DOI : 10.1016/S1359-6454(01)00172-0

R. A. Lebensohn, A. K. Kanjarla, and P. Eisenlohr, An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials, International Journal of Plasticity, vol.32, issue.33, pp.32-3359, 2012.
DOI : 10.1016/j.ijplas.2011.12.005

R. A. Lebensohn and C. N. Tomé, A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys, Acta Metallurgica et Materialia, vol.41, issue.9, pp.2611-2624, 1993.
DOI : 10.1016/0956-7151(93)90130-K

P. A. Legresley and J. J. Alonso, Airfoil design optimization using reduced order models based on proper orthogonal decomposition, Fluids 2000 Conference and Exhibit, 2000.
DOI : 10.2514/6.2000-2545

J. Lemaitre and I. Doghri, Damage 90: a post processor for crack initiation, Computer Methods in Applied Mechanics and Engineering, vol.115, issue.3-4, pp.197-232, 1994.
DOI : 10.1016/0045-7825(94)90060-4

P. M. Lesne and S. Savalle, Numerical analysis of an engine turbine disk loaded with a large number of thermomecanical cycles, Proceedings of 2nd International Conference on Computational Plasticity, pp.591-602, 1989.

A. Leygue, F. Chinesta, and M. Beringhier, Towards a framework for non-linear thermal models in shell domains, International Journal of Numerical Methods for Heat and Fluid Flow, vol.23, issue.1, pp.55-73, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01007391

L. Yan, Amorçage de fissures en fatigue dans un acier 304L : influence la microstructure et d'un chargement d'amplitude variable, 2012.

Y. C. Liang, H. P. Lee, S. P. Lim, W. Z. Lin, and K. H. Lee, PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS???PART I: THEORY, Journal of Sound and Vibration, vol.252, issue.3, pp.527-544, 2002.
DOI : 10.1006/jsvi.2001.4041

R. Lillbacka, E. Johnson, and M. Ekh, A model for short crack propagation in polycrystalline materials. Engng Fracture Mechanics, pp.223-232, 2006.

T. H. Lin, K. K. Wong, N. J. Teng, and S. R. Lin, Micromechanic analysis of fatigue band crossing grain boundary, Materials Science and Engineering: A, vol.246, issue.1-2, pp.169-179, 1998.
DOI : 10.1016/S0921-5093(97)00692-8

M. M. Loève, Probability theory, Pricenton : Van Nostrand, 1955.

M. M. Loève, Probability theory. The University Series in Higher Mathematics, 1963.

J. L. Lumley, The structure of inhomogeneous turbulent flows, Atmospheric Turbulence and Radio Wave Propagation, pp.221-227, 1967.

J. L. Lumley, Atmospheric turbulence and wave propagation. the structure of inhomogeneous turbulence, 1967.

J. L. Lumley, The structure of inhomogeneous turbulent flows Atmospheric Turbulence and Radio Wave Propagation, pp.166-178, 1967.

M. H. Maitournam, C. Krebs, and A. Galtier, A multiscale fatigue life model for complex cyclic multiaxial loading, International Journal of Fatigue, vol.33, issue.2, pp.232-240, 2011.
DOI : 10.1016/j.ijfatigue.2010.08.017

URL : https://hal.archives-ouvertes.fr/hal-00525572

J. Mandel, J. Zarka, and B. Halphen, Adaptation d'une structure elastoplastique a ecrouissage cinematique, Mechanics Research Communications, vol.4, issue.5, pp.309-314, 1977.
DOI : 10.1016/0093-6413(77)90007-6

N. Maouche, M. H. Maitournam, K. Dang, and . Van, On a new method of evaluation of the inelastic state due to moving contacts, Wear, vol.203, issue.204, pp.203-204139, 1997.
DOI : 10.1016/S0043-1648(96)07428-5

N. Maouche, Modélisation des phénomènes d'endommagement dus aux contacts à faible amplitude de débatement, 1997.

C. Mareau and S. Berbenni, An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method, International Journal of Plasticity, vol.64, pp.134-150, 2015.
DOI : 10.1016/j.ijplas.2014.08.011

C. Mareau, D. Cuillerier, and F. Morel, Experimental and numerical study of the evolution of stored and dissipated energies in a medium carbon steel under cyclic loading, Mechanics of Materials, vol.60, pp.93-106, 2013.
DOI : 10.1016/j.mechmat.2013.01.011

URL : https://hal.archives-ouvertes.fr/hal-00821795

M. Marinelli, A. E. Bartali, J. W. Signorelli, P. Evrard, V. Aubin et al., Activated slip systems and microcrack path in LCF of a duplex stainless steel, Materials Science and Engineering: A, vol.509, issue.1-2, pp.81-88, 2009.
DOI : 10.1016/j.msea.2009.01.012

URL : https://hal.archives-ouvertes.fr/hal-00761283

R. Markovinovic and J. Jansen, Accelerating iterative solution methods using reduced-order models as solution predictors, International Journal for Numerical Methods in Engineering, vol.4, issue.5, pp.525-541, 2006.
DOI : 10.1002/nme.1721

R. Masson and A. Zaoui, Self-consistent estimates for the rate-dependentelastoplastic behaviour of polycrystalline materials, Journal of the Mechanics and Physics of Solids, vol.47, issue.7, pp.1543-1568, 1999.
DOI : 10.1016/S0022-5096(98)00106-9

G. Maîtrejean, Contribution à la modélistaion numérique de la théorie cinétique des suspensions, 2011.

F. Morel and N. Huyen, A new criterion of fatigue strengh for out-of-phase bending and torsion of hard metals, International Journal of Fatigue, vol.16, pp.377-384, 1994.

F. Morel and N. Huyen, Plasticity and damage heterogeneity in fatigue, Theoretical and Applied Fracture Mechanics, pp.98-127, 2008.
DOI : 10.1016/j.tafmec.2007.10.006

H. Moulinec and P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2, pp.69-94, 1998.
DOI : 10.1016/S0045-7825(97)00218-1

URL : https://hal.archives-ouvertes.fr/hal-01282728

L. Méric and G. Cailletaud, Single Crystal Modeling for Structural Calculations: Part 2???Finite Element Implementation, Journal of Engineering Materials and Technology, vol.113, issue.1, pp.171-182, 1991.
DOI : 10.1115/1.2903375

D. Neron and P. Ladeveze, Proper Generalized Decomposition for Multiscale and??Multiphysics Problems, Archives of Computational Methods in Engineering, vol.193, issue.1???4, pp.351-372, 2010.
DOI : 10.1007/s11831-010-9053-2

H. Neuber, Theory of Stress Concentration for Shear-Strained Prismatical Bodies With Arbitrary Nonlinear Stress-Strain Law, Journal of Applied Mechanics, vol.28, issue.4, pp.544-551, 1961.
DOI : 10.1115/1.3641780

Q. S. Nguyen, On the elastic plastic initial-boundary value problem and its numerical integration, Int. J. for Numerical Methods in Engng, vol.11, pp.817-832, 1977.
URL : https://hal.archives-ouvertes.fr/hal-00105639

A. Nouy, A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.45-48, pp.4251-4537, 2007.
DOI : 10.1016/j.cma.2007.05.016

URL : https://hal.archives-ouvertes.fr/hal-00366619

A. Nouy, Generalized spectral decomposition method for solving stochastic finite element equations: Invariant subspace problem and dedicated algorithms, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.51-52, pp.4718-4736, 2008.
DOI : 10.1016/j.cma.2008.06.012

URL : https://hal.archives-ouvertes.fr/hal-00366613

A. Nouy and P. Ladevèze, Multiscale Computational Strategy With Time and Space Homogenization: A Radial-Type Approximation Technique for Solving Microproblems, International Journal for Multiscale Computational Engineering, vol.2, issue.4, p.170, 2004.
DOI : 10.1615/IntJMultCompEng.v2.i4.40

URL : https://hal.archives-ouvertes.fr/hal-00368058

A. Nouy and O. P. Le-maitre, Generalized spectral decomposition for stochastic nonlinear problems, Journal of Computational Physics, vol.228, issue.1, pp.202-235, 2009.
DOI : 10.1016/j.jcp.2008.09.010

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.594.6239

J. Z. Zhu, O. C. Zienkiewicz, and R. L. Taylor, The Finite Element Method : Its Basis and Fundamentals, 2005.

R. L. Taylor and O. C. Zienkiewicz, The Finite Element Method vol I-II, 2000.

H. Oudin, Méthode des éléments finis, Ecole centrale de Nantes, 2008.

J. Pacull, B. Mochel, R. Masson, and O. Débordes, Modèle numérique micromécanique d'agrégat polycrystallin pour le comportement des combustibles oxydes, 19ème Congès Français de Mécanique, pp.24-28, 2009.

A. Paquin, H. Sabar, and M. Berveiller, Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials, Archive of Applied Mechanics (Ingenieur Archiv), vol.69, issue.1, pp.14-35, 1999.
DOI : 10.1007/s004190050201

H. Park and W. Lee, An efficient method of solving the navier-stokes equations for flow controls, Phys. Rep, vol.287, pp.337-384, 1997.

H. Park and L. Sirovich, Turbulent thermal convection in a finite domain: Part II. Numerical results, Physics of Fluids A: Fluid Dynamics, vol.100, issue.3, pp.1659-1668, 1990.
DOI : 10.1098/rspa.1954.0197

H. Park and L. Sirovich, accelerated disturbance damping of an unknown distributed system by nonlinear feedback, AIChE Journal, vol.38, issue.9, pp.1461-1476, 1992.

H. M. Park and D. H. Cho, The use of the Karhunen-Lo??ve decomposition for the modeling of distributed parameter systems, Chemical Engineering Science, vol.51, issue.1, pp.81-98, 1996.
DOI : 10.1016/0009-2509(95)00230-8

H. M. Park and M. W. Lee, An efficient method of solving the Navier-Stokes equations for flow control, International Journal for Numerical Methods in Engineering, vol.46, issue.6, pp.1133-1155, 1998.
DOI : 10.1002/(SICI)1097-0207(19980330)41:6<1133::AID-NME329>3.0.CO;2-Y

H. M. Park and M. W. Lee, Boundary control of the Navier???Stokes equation by empirical reduction of modes, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.1-3, pp.165-186, 2000.
DOI : 10.1016/S0045-7825(99)00146-2

H. M. Park and M. W. Lee, Control of Navier-Stokes equations by means of mode reduction, International Journal for Numerical Methods in Fluids, vol.7, issue.4, pp.535-557, 2000.
DOI : 10.1002/1097-0363(20000630)33:4<535::AID-FLD20>3.0.CO;2-H

H. M. Park and T. Y. Yoon, Solution of inverse radiation problems using the Karhunen???Lo??ve Galerkin procedure, Journal of Quantitative Spectroscopy and Radiative Transfer, vol.68, issue.5, pp.489-506, 2001.
DOI : 10.1016/S0022-4073(00)00038-8

J. C. Passieux, P. Ladevèze, and D. Néron, A scalable time???space multiscale domain decomposition method: adaptive time scale separation, Computational Mechanics, vol.39, issue.32???33, pp.621-633, 2010.
DOI : 10.1007/s00466-010-0504-2

K. Pearson, On lines and planes of closest to points in space, Philosophical Magazine, vol.40, issue.4, pp.1446-1474, 1901.

R. H. Peerlings, W. A. Brekelmans, R. De-borst, and M. G. Geers, Gradient-enhanced damage modelling of high-cycle fatigue, International Journal for Numerical Methods in Engineering, vol.2, issue.12, pp.1547-1569, 2000.
DOI : 10.1002/1097-0207(20001230)49:12<1547::AID-NME16>3.0.CO;2-D

M. Peigney and C. Strolz, Approche par contr??le optimal des structures ??lastoviscoplastiques sous chargement cyclique, Comptes Rendus Acad. Sc. Paris Série II b, t 329, 2001.
DOI : 10.1016/S1620-7742(01)01381-2

D. Peirce, R. J. Asaro, and A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, vol.31, issue.12, pp.1951-1976, 1983.
DOI : 10.1016/0001-6160(83)90014-7

B. Pommier, M. H. Maitournam, and G. , Détermination de cycle limite par une méthode cyclique directe, actes du 5ème colloque national de calcul des structures, 2001.

B. Pommier, Détermination de la réponse asymptotique d'une structure anélastique soumise à un chargement thermomécanique cyclique, 2003.

W. Prager, The theory of plasticity: a survey of recent achievements, Proc. Inst. Mech. Engrs, pp.41-57, 1955.
DOI : 10.1243/PIME_PROC_1955_169_015_02

E. Pruliere, F. Chinesta, and A. Ammar, On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition, Mathematics and Computers in Simulation, vol.81, issue.4, pp.791-810, 2010.
DOI : 10.1016/j.matcom.2010.07.015

URL : https://hal.archives-ouvertes.fr/hal-00704427

C. P. Przybyla and D. L. Mcdowell, Simulated microstructure-sensitive extreme value probabilities for high cycle fatigue of duplex Ti???6Al???4V, International Journal of Plasticity, vol.27, issue.12, pp.1871-1895, 2011.
DOI : 10.1016/j.ijplas.2011.01.006

A. L. Pécheur, M. Clavel, F. Curtit, J. M. Stephan, C. Rey et al., Polycrystal modelling of fatigue: Pre-hardening and surface roughness effects on damage initiation for 304L stainless steel, International Journal of Fatigue, vol.45, pp.48-60, 2012.
DOI : 10.1016/j.ijfatigue.2012.06.014

S. Quilici, S. Forest, and G. Cailletaud, On size effects in torsion of multi-and polycrystalline specimens, Journal de Physique IV, vol.8, pp.39-48, 1998.

A. Radermacher and S. Reese, Proper orthogonal decomposition-based model reduction for non-linear biomechanical analysis, International Journal of Materials Engineering Innovation, vol.4, issue.2, pp.149-165, 2013.
DOI : 10.1504/IJMATEI.2013.054393

A. Radermacher and S. Reese, Model reduction in elastoplasticity: proper orthogonal decomposition combined with adaptive sub-structuring, Computational Mechanics, vol.2, issue.2, pp.677-687, 2014.
DOI : 10.1007/s00466-014-1020-6

B. Ravindra, COMMENTS ON ???ON THE PHYSICAL INTERPRETATION OF PROPER ORTHOGONAL MODES IN VIBRATIONS???, Journal of Sound and Vibration, vol.219, issue.1, pp.189-192, 1999.
DOI : 10.1006/jsvi.1998.1895

Z. Ren and Q. Zheng, A Quantitative study of minimum sizes of representative volume elements of cubic polycrystals???numerical experiments, Journal of the Mechanics and Physics of Solids, vol.50, issue.4, pp.881-893, 2002.
DOI : 10.1016/S0022-5096(01)00102-8

J. C. Joris, M. A. René-de-brost, C. V. Crisfield, and . Verhoosel, Nonlinear Finite element Analysis of solids and structures. Wiley series in computational mechanics, 2012.

R. Peerlings, Enhanced damage modelling for fracture and fatigue, 1999.

F. Risler and C. Rey, Iterative accelerating algorithms with krylov sub-spaces for the solution to large-scale non-linear problems, Numerical Algorithms, vol.23, issue.1, pp.1-30, 2000.
DOI : 10.1023/A:1019187614377

C. Robert and C. Mareau, A comparison between different numerical methods for the modeling of polycrystalline materials with an elastic???viscoplastic behavior, Computational Materials Science, vol.103, pp.134-144, 2015.
DOI : 10.1016/j.commatsci.2015.03.028

C. Robert, N. Saintier, T. Palin-luc, and F. Morel, Micro-mechanical modelling of high cycle fatigue behaviour of metals under multiaxial loads, Mechanics of Materials, vol.55, pp.112-129, 2012.
DOI : 10.1016/j.mechmat.2012.08.006

H. Rognon, Comportement en fatigue sous environnement vibratoire : Prise en compte de la plasticité au sein des méthodes spectrales, 2013.

H. Rognon, Méthode d'estimation rapide de la tenue en fatigue oligocyclique d'une structure dans le cadre de la plasticité confinée : application aux assemblages soudés pour la construction navale, 2013.

D. Ryckelynck, A priori hyperreduction method: an adaptive approach, Journal of Computational Physics, vol.202, issue.1, pp.346-366, 2005.
DOI : 10.1016/j.jcp.2004.07.015

D. Ryckelynck, Hyper-reduction of mechanical models involving internal variables, International Journal for Numerical Methods in Engineering, vol.1, issue.3, pp.75-89, 2009.
DOI : 10.1002/nme.2406

URL : https://hal.archives-ouvertes.fr/hal-00732247

D. Ryckelynck and D. M. Benziane, Multi-level A Priori Hyper-Reduction of mechanical models involving internal variables, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.17-20, pp.17-201134, 2010.
DOI : 10.1016/j.cma.2009.12.003

URL : https://hal.archives-ouvertes.fr/hal-00461492

D. Ryckelynck, F. Chinesta, E. Cueto, and A. Ammar, On thea priori model reduction: Overview and recent developments, Archives of Computational Methods in Engineering, vol.43, issue.5, pp.91-128, 2006.
DOI : 10.1007/BF02905932

D. Ryckelynck, L. Hermanns, F. Chinesta, and E. Alarcon, An efficient ???a priori??? model reduction for boundary element models, Engineering Analysis with Boundary Elements, vol.29, issue.8, pp.29796-801, 2005.
DOI : 10.1016/j.enganabound.2005.04.003

URL : https://hal.archives-ouvertes.fr/hal-00020778

D. Ryckelynck, K. Lampoh, and S. Quilicy, Hyper-reduced predictions for lifetime assessment of elasto-plastic structures, Meccanica, vol.65, issue.3, pp.309-317, 2016.
DOI : 10.1007/s11012-015-0244-7

URL : https://hal.archives-ouvertes.fr/hal-01295849

D. Ryckelynck and D. Missoum-benziane, Multi-level A Priori Hyper-Reduction of mechanical models involving internal variables, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.17-20, pp.17-201134, 2010.
DOI : 10.1016/j.cma.2009.12.003

URL : https://hal.archives-ouvertes.fr/hal-00461492

D. Ryckelynck, D. Missoum-benziane, S. Cartle, and J. Besson, A robust adaptive model reduction method for damage simulations, Computational Materials Science, vol.50, issue.5, pp.1597-1605, 2011.
DOI : 10.1016/j.commatsci.2010.11.034

URL : https://hal.archives-ouvertes.fr/hal-00585356

D. Ryckelynck, F. Vincent, and S. Cantournet, Multidimensional a priori hyperreduction of mechanical models involving internal variables, Computer Methods in Applied Mechanics and Engineering, vol.225, pp.28-43, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00705783

D. Ryckelynck, Hyperréduction a priori en dynamique non-linéaire à large bande, Giens, 2005.

D. Ryckelynck, R??duction a priori de mod??les thermom??caniques, Comptes Rendus M??canique, vol.330, issue.7, pp.499-505, 2002.
DOI : 10.1016/S1631-0721(02)01487-0

K. Sai, Modèles à grand nombre de variables internes et méthodes numériques associées, 1993.

J. Salençon, Mécanique des milieux continus. Éditions de l'École Polytechnique, 2007.

B. Sarbandi, S. Cartle, J. Besson, and D. Ryckelynck, Truncated Integration for Simultaneous Simulation of Sintering Using a Separated Representation, Archives of Computational Methods in Engineering, vol.12, issue.1, pp.455-463, 2010.
DOI : 10.1007/s11831-010-9055-0

URL : https://hal.archives-ouvertes.fr/hal-00542499

S. Savalle and J. P. Culié, Méthodes de calcul associées aux lois de comportement cyclique et d'endommagement, La recherche Aérospatiale, vol.5, pp.263-278, 1978.

J. Schwartz, O. Fandeur, and C. Rey, Fatigue crack initiation modeling of 316LN steel based on non local plasticity theory, Procedia Engineering, vol.2, issue.1, pp.1353-1362, 2010.
DOI : 10.1016/j.proeng.2010.03.147

URL : https://hal.archives-ouvertes.fr/hal-00752010

J. Schwartz, O. Fandeur, and C. Rey, Numerical approach of cyclic behaviour of 316LN stainless steel based on a polycrystal modelling including strain gradients, International Journal of Fatigue, vol.55, pp.202-212, 2013.
DOI : 10.1016/j.ijfatigue.2013.07.003

J. Schwartz, Approche non locale en plasticité cristalline : application à l'étude du comportement mécanique de l'acier AISI 316LN en fatigue oligocyclique, 2011.

J. C. Simo and R. L. Taylor, Consistent tangent operators for rate-independent elastoplasticity, Computer Methods in Applied Mechanics and Engineering, vol.48, issue.1, pp.101-118, 1985.
DOI : 10.1016/0045-7825(85)90070-2

S. Sirisup, G. Karniadakis, D. Xiu, and I. Kevrekidis, Equation-free/Galerkin-free POD-assisted computation of incompressible flows, Journal of Computational Physics, vol.207, issue.2, pp.568-587, 2005.
DOI : 10.1016/j.jcp.2005.01.024

L. Sirovich, Turbulence and the dynamics of coherent structures. part 1 : Coherent structures, Quarterly of Applied Mathematics, issue.3, pp.561-571, 1987.

L. Sirovich, Turbulence and the dynamics of coherent structures. part 2 : Symmetries and transformations, Quarterly of Applied Mathematics, issue.3, pp.573-582, 1987.

L. Sirovich, Turbulence and the dynamics of coherent structures. part 3 : Dynamics and scaling, Quarterly of Applied Mathematics, issue.3, pp.583-590, 1987.

L. Sirovich and M. Kirby, Low-dimensional procedure for the characterization of human faces, Journal of the Optical Society of America A, vol.4, issue.3, pp.519-524, 1987.
DOI : 10.1364/JOSAA.4.000519

L. Sirovich and H. Park, Turbulent thermal convection in a finite domain: Part I. Theory, Physics of Fluids A: Fluid Dynamics, vol.297, issue.3, pp.1649-1658, 1990.
DOI : 10.1103/PhysRevLett.44.572

K. V. Spiliopoulos and K. D. Panagiotou, A direct method to predict cyclic steady states of elastoplastic structures, Computer Methods in Applied Mechanics and Engineering, vol.223, issue.224, pp.223-224186, 2012.
DOI : 10.1016/j.cma.2012.03.004

K. V. Spiliopoulos, A direct method to predict cyclic steady states of elastoplastic structures Inelastic Analysis of Structures under Variable Loads, pp.213-232, 2000.

K. V. Spiliopoulos, A Simplified Method to Predict the Steady Cyclic Stress State of Creeping Structures, Journal of Applied Mechanics, vol.69, issue.2, pp.149-153, 2002.
DOI : 10.1115/1.1430234

K. V. Spiliopoulos and K. D. Panagiotou, Simplified Methods for the Steady State Inelastic Analysis of Cyclically Loaded Structures, Comput. Methods Appl. Mech.Engrg, pp.223-224186, 2012.
DOI : 10.1007/978-94-010-9421-4_14

G. Strang, Linear algebra and its applications, 2006.

C. Teodosiu, J. Raphanel, and L. Tabourot, Finite element simulation of the large elastoplastic deformation of multicrystals, 5th MECAMAT Int. Seminar on Large Plastic Deformations : Fundamental Aspects and Applications to Metal Forming, pp.153-168, 1993.

M. J. Turner, R. W. Clough, C. H. Martin, and L. J. Topp, Stiffness and Deflection Analysis of Complex Structures, Journal of the Aeronautical Sciences, vol.23, issue.9, pp.805-824, 1956.
DOI : 10.2514/8.3664

K. and D. Van, Sur la résistance à la fatigue des métaux. Sciences et Techniques de l'armement, mémorial de l'artillerie française, p.3, 1973.

E. Vasseur, P. Navidi, and S. Hariri, Direct determination of limiting cycle during cyclic loading, Computational Materials Science, vol.7, issue.1-2, pp.11-15, 1996.
DOI : 10.1016/S0927-0256(96)00053-5

URL : https://hal.archives-ouvertes.fr/hal-00111528

N. Verdon, C. Allery, C. Béghein, A. Hamdouni, and D. Ryckelynck, Reduced-order modelling for solving linear and non-linear equations, International Journal for Numerical Methods in Biomedical Engineering, vol.2, issue.1, pp.43-58, 2011.
DOI : 10.1002/cnm.1286

URL : https://hal.archives-ouvertes.fr/hal-00541925

N. Verdon, C. Allery, D. Ryckelynck, and A. Hamdouni, An adaptive ROM approach for solving transfer equations, Revue europ??enne de m??canique num??rique, vol.15, issue.5, pp.589-605, 2005.
DOI : 10.3166/remn.15.589-605

URL : https://hal.archives-ouvertes.fr/hal-00312311

N. Verdon, Un système dynamique d'ordre réduit basé sur une approche APR- POD pour l'étude de l'interaction écoulement turbulent-particules, 2007.

S. Volkwein, Optimal control of a phase-eld model using proper orthogonal decomposition, Z. Angew. Math. Mech

P. Wriggers, Nonlinear Finite Element Methods, 2008.

J. Yvonnet and Q. He, The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains, Journal of Computational Physics, vol.223, issue.1, pp.341-368, 2007.
DOI : 10.1016/j.jcp.2006.09.019

URL : https://hal.archives-ouvertes.fr/hal-00693621

J. Zarka and J. Casier, Elastic-plastic response of a structure subjected to cyclic loading : practical rules, Mechanics Today, vol.6, pp.93-198, 1979.

J. Zarka, J. Frelat, G. Inglebert, and P. Kasmai-navidi, A new approach in inelastic analysis of structures, CADLM, 1990.

J. Zarka and H. Karaouni, New Rules to Be Included in Codes and Standards to Represent Multiaxial Variable Amplitudes Loadings on Structures, 10th International Conference on Nuclear Engineering, Volume 4, 2002.
DOI : 10.1115/ICONE10-22029

URL : https://hal.archives-ouvertes.fr/hal-00117706

J. Zarka and H. Karaouni, Fatigue analysis of structures during random loadings, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00114472

J. Zarka and P. K. Navidi, Simplified dynamical analysis of inelastic structures, Nuclear Engineering and Design, vol.92, issue.1, pp.89-103, 1986.
DOI : 10.1016/0029-5493(86)90101-9

J. Zarka and A. Pecker, Participation à la mise au point d'une méthode d'analyse simplifiée, 1988.

J. Zghal, Etude du comportement en fatigue à grand nombre de cycles d'un acier à haute limite d'élasticité HC360LA : Endommagement, plasticité et phénomènes dissipatifs associés, École Nationale Supérieure d'Arts et Métiers, 2016.

O. C. Zienkiewicz, The Finite Element Method in Structural and Continuum Mechanics, 1967.