Y. Abdin, A. Jain, I. Verpoest, and S. Lomov, Mean-field based micromechanical modelling of short wavy fiber reinforced composites, Composites Part A : Applied Science and Manufacturing, vol.91, pp.472-483, 2015.

J. Aboudi, Micromechanics-based thermoviscoelastic constitutive equations for rubber-like matrix composites at finite strains, International Journal of Solids and Structures, vol.41, issue.20, pp.5611-5629, 2004.

J. Aboudi, M. Pindera, A. , and S. , Higher-order theory for periodic multiphase materials with inelastic phases, International Journal of Plasticity, vol.19, issue.6, pp.805-847, 2003.

N. Achour, G. Chatzigeorgiou, F. Meraghni, Y. Chemisky, and J. Fitoussi, Implicit implementation and consistent tangent modulus of a viscoplastic model for polymers, International Journal of Mechanical Sciences, vol.103, pp.297-305, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01206545

A. Kassem and G. , Micromechanical material models for polymer composites through advanced numerical simulation techniques, 2009.

G. Allaire, Homogenization and two-scale convergence, SIAM Journal on Mathematical Analysis, vol.23, pp.1482-1518, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01111805

D. Anagnostou, G. Chatzigeorgiou, Y. Chemisky, and F. Meraghni, Hierarchical micromechanical modeling of the viscoelastic behavior coupled to damage in SMC and SMC-hybrid composites, Composites Part B : Engineering, vol.151, pp.8-24, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01812711

G. Anzelotti, G. Nicoletto, R. , and E. , Mesomechanic strain analysis of twill-weave composite lamina under unidirectional in-plane tension, Full-field Measurements in Composites Testing and Analysis, vol.39, pp.1294-1301, 2008.

M. Arif, F. Meraghni, Y. Chemisky, N. Despringre, R. et al., In situ damage mechanisms investigation of pa66/gf30 composite : Effect of relative humidity, Composites Part B : Engineering, vol.58, pp.487-495, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01513629

E. Arruda, M. Boyce, J. , and R. , Effects of strain rate, temperature and thermomechanical coupling on the finite strain deformation of glassy polymers, Mechanics of Materials, vol.19, issue.2, pp.193-212, 1995.

T. Asada and N. Ohno, Fully implicit formulation of elastoplastic homogenization problem for two-scale analysis, International Journal of Solids and Structures, vol.44, issue.22, pp.7261-7275, 2007.

S. Avri, F. Pierron, M. Sutton, Y. , and J. , Identification of elastovisco-plastic parameters and characterization of lüders behavior using digital image correlation and the virtual fields method, Mechanics of Materials, vol.40, issue.9, pp.729-742, 2008.

B. Bednarcyk, B. Stier, J. Simon, S. Reese, and E. Pineda, , 2015.

, Meso-and micro-scale modeling of damage in plain weave composites, Composite Structures, vol.121, pp.258-270

A. Bensoussan, J. Lions, and G. Papanicolaou, Asymptotic methods for periodic structures, 1978.

Y. Benveniste, A new approach to the application of mori-tanaka's theory in composite materials, Mechanics of Materials, vol.6, issue.2, pp.147-157, 1987.

Y. Benveniste, G. Dvorak, C. , and T. , Stress fields in composites with coated inclusions, Mechanics of Materials, vol.7, issue.4, pp.305-317, 1989.

Y. Benveniste, G. Dvorak, C. , and T. , On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media, Journal of the Mechanics and Physics of Solids, vol.39, issue.7, pp.927-946, 1991.

R. Berthelsen, R. Denzer, P. Oppermann, and A. Menzel, Computational homogenisation for thermoviscoplasticity : application to thermally sprayed coatings, Computational Mechanics, vol.60, pp.739-766, 2017.

A. Bertram and A. Krawietz, On the introduction of thermoplasticity, Acta Mechanica, vol.223, issue.10, pp.2257-2268, 2012.

P. Boisse, N. Hamila, E. Guzman-maldonado, A. Madeo, G. Hivet et al., The bias-extension test for the analysis of in-plane shear properties of textile composite reinforcements and prepregs : a review, International Journal of Material Forming, vol.10, issue.4, pp.473-492, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01313827

M. Boubakar, F. Trivaudey, D. Perreux, and L. Vang, A meso-macro finite element modelling of laminate structures -Part I : Time-independent behaviour, Journal of Composite Structures, vol.58, issue.2, pp.271-286, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00014069

M. Boubakar, L. Vang, F. Trivaudey, and D. Perreux, A meso-macro finite element modelling of laminate structures : Part ii : time-dependent behaviour, Composite Structures, vol.60, issue.3, pp.275-305, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00014073

Z. Boufaida, Analyse des propriétés mécaniques de composites taffetas verre/matrice acrylique en relation avec les propriétés d'adhésion des fibres sur la matrice, 2015.

L. Brassart, I. Doghri, and L. Delannay, Homogenization of elasto-plastic composites coupled with a nonlinear finite element analysis of the equivalent inclusion problem, International Journal of Solids and Structures, vol.47, issue.5, pp.716-729, 2010.

L. Brassart, L. Stainier, I. Doghri, and L. Delannay, Homogenization of elasto-(visco) plastic composites based on an incremental variational principle, International Journal of Plasticity, vol.36, pp.86-112, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01006931

R. Brenner and P. Suquet, Overall response of viscoelastic composites and polycrystals : exact asymptotic relations and approximate estimates, International Journal of Solids and Structures, vol.50, issue.10, pp.1824-1838, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00788677

R. Brent, W. Gregory, S. Philip, D. , and J. , Development and validation of a genetic l-system programming framework for topology optimization of multifunctional structures, Computers and Structures, vol.218, pp.152-169, 2019.

J. Chaboche, P. Kanoute, R. , and A. , On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites, International Journal of Plasticity, vol.21, issue.7, pp.1409-1434, 2005.

N. Charalambakis, G. Chatzigeorgiou, Y. Chemisky, and F. Meraghni, Mathematical homogenization of inelastic dissipative materials : a survey and recent progress, Continuum Mechanics and Thermodynamics, vol.30, pp.1-51, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02390365

G. Chatzigeorgiou, N. Charalambakis, Y. Chemisky, and F. Meraghni, Periodic homogenization for fully coupled thermomechanical modeling of dissipative generalized standard materials, International Journal of Plasticity, vol.81, pp.18-39, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01515204

G. Chatzigeorgiou, N. Charalambakis, Y. Chemisky, and F. Meraghni, , 2018.

, Thermomechanical Behavior of Dissipative Composite Materials

G. Chatzigeorgiou, Y. Chemisky, and F. Meraghni, Computational micro to macro transitions for shape memory alloy composites using periodic homogenization, Smart Materials and Structures, vol.24, issue.3, p.35009, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01196237

G. Chatzigeorgiou, F. Meraghni, J. , and A. , Generalized interfacial energy and size effects in composites, Journal of the Mechanics and Physics of Solids, vol.106, pp.257-282, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01556870

F. Chinesta, A. Ammar, and E. Cueto, Proper Generalized Decomposition of Multiscale Models, International Journal for Numerical Methods in Engineering, vol.83, issue.8-9, pp.1114-1132, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01007222

M. Christian, H. Martina, F. , and W. , A phase field model for rate-independent crack propagation : Robust algorithmic implementation based on operator splits, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.45, pp.2765-2778, 2010.

B. D. Coleman and M. E. Gurtin, Thermodynamics with Internal State Variables, The Journal of Chemical Physics, vol.47, issue.2, pp.597-613, 1967.

M. Cremonesi, D. Néron, P. Guidault, and P. Ladevèze, A pgdbased homogenization technique for the resolution of nonlinear multiscale problems, Computer Methods in Applied Mechanics and Engineering, vol.267, pp.275-292, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01403834

. Bibliographie,

C. Czarnota, K. Kowalczyk-gajewska, A. Salahouelhadj, M. Martiny, and S. Mercier, Modeling of the cyclic behavior of elastic-viscoplastic composites by the additive tangent mori-tanaka approach and validation by finite element calculations, International Journal of Solids and Structures, pp.96-117, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01513622

L. Delannay, I. Doghri, and O. Pierard, Prediction of tension-compression cycles in multiphase steel using a modified incremental mean-field model, International Journal of Solids and Structures, vol.44, issue.22, pp.7291-7306, 2007.

N. Despringre, Y. Chemisky, K. Bonnay, and F. Meraghni, Micromechanical modeling of damage and load transfer in particulate composites with partially debonded interface, Composite Structures, vol.155, pp.77-88, 2016.

F. Detrez, S. Cantournet, and R. Seguela, Plasticity/damage coupling in semi-crystalline polymers prior to yielding : Micromechanisms and damage law identification, Polymer, vol.52, issue.9, pp.1998-2008, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00592106

G. Dillon and M. Buggy, Damage development during flexural fatigue of carbon fibre-reinforced peek, Composites, vol.26, issue.5, pp.355-370, 1995.

M. Dittmann, F. Aldakheel, J. Schulte, . Wriggers, and C. Hesch, Variational phase-field formulation of non-linear ductile fracture, Computer Methods in Applied Mechanics and Engineering, vol.342, pp.71-94, 2018.

I. Doghri, L. Brassart, L. Adam, and J. Gérard, A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites, International Journal of Plasticity, vol.27, issue.3, pp.352-371, 2011.

I. Doghri and A. Ouaar, Homogenization of two-phase elasto-plastic composite materials and structures : Study of tangent operators, cyclic plasticity and numerical algorithms, International Journal of Solids and Structures, vol.40, issue.7, pp.1681-1712, 2003.

H. Dong, J. Cui, Y. Nie, Y. , and Z. , Second-Order Two-Scale Computational Method for Nonlinear Dynamic Thermo-Mechanical Problems of Composites with Cylindrical Periodicity, Communications in Computational Physics, vol.21, issue.4, pp.1173-1206, 2017.

A. Drago and M. Pindera, Micro-macromechanical analysis of heterogeneous materials : Macroscopically homogeneous vs periodic microstructures, Composites Science and Technology, vol.67, issue.6, pp.1243-1263, 2007.

G. Drosopoulos, P. Wriggers, and G. Stavroulakis, A multi-scale computational method including contact for the analysis of damage in composite materials, Computational Materials Science, vol.95, pp.522-535, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01403838

A. D. Drozdov and J. Christiansen, Cyclic viscoplasticity of solid polymers : The effects of strain rate and amplitude of deformation, Polymer, vol.48, issue.10, pp.3003-3012, 2007.

Y. Duan, A. Saigal, R. Greif, and M. Zimmerman, A uniform phenomenological constitutive model for glassy and semi crystalline polymers, 2001.

, Polymer engineering and science, vol.41, pp.1322-1328

F. El-halabi, D. González, A. Chico, and M. Doblaré, Fe2 multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition, Computer Methods in Applied Mechanics and Engineering, vol.257, pp.183-202, 2013.

H. I. Ene, On linear thermoelasticity of composite materials, International Journal of Engineering Science, vol.21, issue.5, pp.443-448, 1983.

J. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, pp.376-396, 1226.

F. Feyel, Multiscale fe2 elastoviscoplastic analysis of composite structures, Computational Materials Science, vol.16, issue.1, pp.344-354, 1999.

F. Feyel and J. Chaboche, Fe2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials, Computer Methods in Applied Mechanics and Engineering, vol.183, issue.3, pp.309-330, 2000.

F. Feyel and J. Chaboche, Fe2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials, Computer Methods in Applied Mechanics and Engineering, vol.183, issue.3, pp.309-330, 2000.

F. Fisher and L. Brinson, Viscoelastic interphases in polymer-matrix composites : theoretical models and finite-element analysis, Composites Science and Technology, vol.61, issue.5, pp.731-748, 2001.

R. Fleischhauer, M. Bo?i?, and M. Kaliske, A novel approach to computational homogenization and its application to fully coupled two-scale thermomechanics, Computational Mechanics, vol.58, issue.5, pp.769-796, 2016.

S. Forest, Micromorphic approach for gradient elasticity, viscoplasticity, and damage, Journal of Engineering Mechanics, vol.135, pp.117-131, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00368014

G. Francfort, Homogenization and linear thermoelasticity, SIAM Journal on Mathematical Analysis, vol.14, issue.4, pp.696-708, 1983.

E. Gamstedt and B. Sjögren, Micromechanisms in tensioncompression fatigue of composite laminates containing transverse plies, Composites Science and Technology, vol.59, issue.2, pp.167-178, 1999.

D. Garoz-gómez, F. Villegas, R. Sevenois, S. Spronk, and W. Van-paepegem, Material parameter identification of the elementary ply damage mesomodel using virtual micro-mechanical tests of a carbon fiber epoxy system, Composite Structures, vol.181, pp.391-404, 2017.

A. Gavazzi and D. Lagoudas, On the numerical evaluation of eshelby's tensor and its application to elastoplastic fibrous composites, Computational Mechanics, vol.7, issue.1, pp.13-19, 1990.

P. Germain, Cours de mécanique des milieux continus, Tome I : Théorie Générale, 1973.

P. Germain, Sur certaines définitions liées à l'énergie en mécanique des solides, International Journal of Engineering Science, vol.20, issue.2, pp.245-259, 1982.

P. Germain, Q. S. Nguyen, and P. Suquet, Continuum thermodynamics, Journal of Applied Mechanics, vol.50, pp.1010-1020, 1983.
URL : https://hal.archives-ouvertes.fr/hal-00105630

S. Ghosh, K. Lee, and P. Raghavan, A multi-level computational model for multi-scale damage analysis in composite and porous materials, International Journal of Solids and Structures, vol.38, issue.14, pp.2335-2385, 2001.

G. Gibert, B. Prabel, A. Gravouil, J. , and C. , A 3d automatic mesh refinement x-fem approach for fatigue crack propagation, Finite Elements in Analysis and Design, vol.157, pp.21-37, 2019.

M. Grmela and G. Lebon, Hamiltonian extended thermodynamics, Journal of Physics A : Mathematical and General, vol.23, issue.14, pp.3341-3351, 1990.

C. Guillaume, Multiscale modeling of the mechanical behavior of woven composite materials, 2008.

R. Hill, Elastic properties of reinforced solids : Some theoretical principles, Journal of the Mechanics and Physics of Solids, vol.11, issue.5, pp.357-372, 1963.

R. Hill, A self-consistent mechanics of composite materials, Journal of the Mechanics and Physics of Solids, vol.13, issue.4, pp.213-222, 1965.

R. Hill, The essential structure of constitutive laws for metal composites and polycrystals, Journal of the Mechanics and Physics of Solids, vol.15, issue.2, pp.79-95, 1967.

R. Hill and E. Orowan, A theory of the yielding and plastic flow of anisotropic metals, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol.193, pp.281-297, 1033.

T. Hobbiebrunken, M. Hojo, T. Adachi, C. De-jong, and B. Fiedler, Evaluation of interfacial strength in cf/epoxies using fem and in-situ experiments, The 11th US-Japan Conference on Composite Materials, vol.37, pp.2248-2256, 2006.

C. Hochard, P. Aubourg, C. , and J. , Modelling of the mechanical behaviour of woven-fabric cfrp laminates up to failure, Composites Science and Technology, vol.61, issue.2, pp.221-230, 2001.

C. Hochard, J. Payan, and C. Bordreuil, A progressive first ply failure model for woven ply cfrp laminates under static and fatigue loads, The Third International Conference on Fatigue of Composites, vol.28, pp.1270-1276, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00106918

C. Hochard and Y. Thollon, A generalized damage model for woven ply laminates under static and fatigue loading conditions, Fourth International Conference on Fatigue of Composites (ICFC4), vol.32, pp.158-165, 2010.

T. Jiang and J. Shao, On the incremental approach for nonlinear homogenization of composite and influence of isotropization, Computational Materials Science, vol.46, issue.2, pp.447-451, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00412002

D. Jou, J. Casas-vázquez, and G. Lebon, Extended irreversible thermodynamics revisited (1988-98), Reports on Progress in Physics, vol.62, issue.7, pp.1035-1142, 1999.

A. Kalamkarov and A. Kolpakov, Analysis, design and optimization of composite structures, 1997.

A. S. Khan, O. Lopez-pamies, and R. Kazmi, Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures, International Journal of Plasticity, vol.22, issue.4, pp.581-601, 2006.

H. Khatam and M. Pindera, Plasticity-triggered architectural effects in periodic multilayers with wavy microstructures, International Journal of Plasticity, vol.26, issue.2, pp.273-287, 2010.

B. Kiefer, T. Waffenschmidt, L. Sprave, and A. Menzel, A gradientenhanced damage model coupled to plasticity-multi-surface formulation and algorithmic concepts, International Journal of Damage Mechanics, vol.27, issue.2, pp.253-295, 2018.

V. Kouznetsova, M. G. Geers, and W. A. Brekelmans, Multiscale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, International Journal for Numerical Methods in Engineering, vol.54, issue.8, pp.1235-1260, 2002.

A. Krairi and I. Doghri, A thermodynamically-based constitutive model for thermoplastic polymers coupling viscoelasticity, viscoplasticity and ductile damage, International Journal of Plasticity, vol.60, pp.163-181, 2014.

A. Krairi and I. Doghri, A thermodynamically-based constitutive model for thermoplastic polymers coupling viscoelasticity, viscoplasticity and ductile damage, International Journal of Plasticity, vol.60, pp.163-181, 2014.

A. Krasnobrizha, Modelling of the hysteretic behavior of woven composite using a collaborative elastoplastic damaged model with fractional derivatives, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01684162

A. Krasnobrizha, P. Rozycki, P. Cosson, and L. Gornet, Modélisation des mécanismes d´hystérésis des composites tissés à l´aide d´un modèle collaboratif élasto-plastique endommageable à dérivées fractionnaires, Matériaux & Techniques, vol.104, issue.4, p.407, 2016.

S. Kruch and J. Chaboche, Multi-scale analysis in elasto-viscoplasticity coupled with damage, International Journal of Plasticity, vol.27, issue.12, pp.2026-2039, 2011.

C. Kuhn, T. Noll, and R. Müller, On phase field modeling of ductile fracture, vol.39, pp.35-54, 2016.

P. Ladeveze and E. Ledantec, Damage modelling of the elementary ply for laminated composites, Composites Science and Technology, vol.43, issue.3, pp.257-267, 1992.

P. Ladeveze, O. Loiseau, and D. Dureisseix, A micro-macro and parallel computational strategy for highly heterogeneous structures, International Journal for Numerical Methods in Engineering, vol.52, pp.121-138, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00322459

P. Ladeveze and A. Nouy, On a multiscale computational strategy with time and space homogenization for structural mechanics, Multiscale Computational Mechanics for Materials and Structures, vol.192, issue.28, pp.3061-3087, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00366648

P. Ladeveze, A. Nouy, and O. Loiseau, A multiscale computational approach for contact problems, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.43, pp.4869-4891, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00366657

P. Ladeveze, J. Passieux, and D. Néron, The latin multiscale computational method and the proper generalized decomposition, Multiscale Models and Mathematical Aspects in Solid and Fluid Mechanics, vol.199, issue.21, pp.1287-1296, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00414447

D. Lagoudas, A. Gavazzi, and H. Nigam, Elastoplastic behavior of metal matrix composites based on incremental plasticity and the mori-tanaka averaging scheme, Computational Mechanics, vol.8, issue.3, pp.193-203, 1991.

A. Launay, M. Maitournam, Y. Marco, I. Raoult, and F. Szmytka, Cyclic behaviour of short glass fibre reinforced polyamide : Experimental study and constitutive equations, International Journal of Plasticity, vol.27, issue.8, pp.1267-1293, 2011.

A. Launay, M. Maitournam, Y. Marco, and I. Raoult, Multiaxial fatigue models for short glass fiber reinforced polyamide -part i : Nonlinear anisotropic constitutive behavior for cyclic response, International Journal of Fatigue, vol.47, pp.382-389, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00778277

A. Launay, Y. Marco, M. Maitournam, and I. Raoult, Modelling the influence of temperature and relative humidity on the time-dependent mechanical behaviour of a short glass fibre reinforced polyamide, Mechanics of Materials, vol.56, pp.1-10, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00778275

N. Laws and J. Brockenbrough, The effect of micro-crack systems on the loss of stiffness of brittle solids, International Journal of Solids and Structures, vol.23, issue.9, pp.1247-1268, 1987.

J. Lemaitre, Coupled elasto-plasticity and damage constitutive equations, Computer Methods in Applied Mechanics and Engineering, vol.51, issue.1, pp.31-49, 1985.

J. Lemaitre and J. Chaboche, Mechanics of solid materials, 1990.

J. Lemaitre and R. Desmorat, Engineering damage mechanics : ductile, creep, fatigue and brittle failure, 2005.

S. Li, On the unit cell for micromechanical analysis of fibre-reinforced composites, Proceedings of the Royal Society of London A, vol.455, pp.815-838, 1983.

S. Li, General unit cells for micromechanical analyses of unidirectional composites, Composites : Part A, vol.32, pp.815-826, 2000.

H. Lin, L. Brown, and A. Long, Modelling and simulating textile structures using texgen, Advances in Textile Engineering, vol.331, pp.44-47, 2011.

T. Linse, G. Hütter, and M. Kuna, Simulation of crack propagation using a gradient-enriched ductile damage model based on dilatational strain. Engineering Fracture Mechanics, vol.95, pp.13-28, 2012.

B. Love and R. Batra, Determination of effective thermomechanical parameters of a mixture of two elastothermoviscoplastic constituents, International Journal of Plasticity, vol.22, issue.6, pp.1026-1061, 2006.

Z. Mahboob, Y. Chemisky, F. Meraghni, and H. Bougherara, Mesoscale modelling of tensile response and damage evolution in natural fibre reinforced laminates, Composites Part B : Engineering, vol.119, pp.168-183, 2017.

A. Malpot, Fatigue Behaviour of a Woven Glass-Fibre-Reinforced Polyamide COmposite for Automotive Application. Theses, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01505589

A. Malpot, F. Touchard, and S. Bergamo, Effect of relative humidity on mechanical properties of a woven thermoplastic composite for automotive application, Polymer Testing, vol.48, pp.160-168, 2015.

J. Marigo, P. Mialon, J. Michel, and P. Suquet, Plasticité et homogénéisation : un exemple de prévision des charges limites d'une structure hétérogène périodique, Journal de Mecanique Theorique et Appliquee, vol.6, issue.1, pp.47-75, 1987.

J. Mediavilla, R. Peerlings, and M. Geers, An integrated continuous-discontinuous approach towards damage engineering in sheet metal forming processes, Engineering Fracture Mechanics, vol.73, issue.7, pp.895-916, 2006.

F. Meraghni and M. Benzeggagh, Micromechanical modelling of matrix degradation in randomly oriented discontinuous-fibre composites, Composites Science and Technology, vol.55, issue.2, pp.171-186, 1995.

F. Meraghni, F. Desrumaux, and M. Benzeggagh, Implementation of a constitutive micromechanical model for damage analysis in glass mat reinforced composite structures, Composites Science and Technology, vol.62, issue.16, pp.2087-2097, 2002.

S. Mercier and A. Molinari, Homogenization of elastic-viscoplastic heterogeneous materials : Self-consistent and mori-tanaka schemes, International Journal of Plasticity, vol.25, issue.6, pp.1024-1048, 2009.

. Bibliographie,

S. Mercier and A. Molinari, Homogenization of elastic-viscoplastic heterogeneous materials : Self-consistent and mori-tanaka schemes, International Journal of Plasticity, vol.25, issue.6, pp.1024-1048, 2009.

S. Mercier, A. Molinari, S. Berbenni, and M. Berveiller, Comparison of different homogenization approaches for elastic-viscoplastic materials, Modelling and Simulation in Materials Science and Engineering, vol.20, issue.2, p.24004, 2012.

J. Michel, H. Moulinec, and P. Suquet, Effective properties of composite materials with periodic microstructure : a computational approach, Computer Methods in Applied Mechanics and Engineering, vol.172, issue.1, pp.109-143, 1999.

B. Miled, I. Doghri, L. Brassart, and L. Delannay, Micromechanical modeling of coupled viscoelastic-viscoplastic composites based on an incrementally affine formulation, International Journal of Solids and Structures, vol.50, issue.10, pp.1755-1769, 2013.

B. Miled, I. Doghri, and L. Delannay, Coupled viscoelastic-viscoplastic modeling of homogeneous and isotropic polymers : Numerical algorithm and analytical solutions, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.47, pp.3381-3394, 2011.

S. Moreau, A. Chrysochoos, J. Muracciole, and B. Wattrisse, Analysis of thermoelastic effects accompanying the deformation of pmma and pc polymers, Comptes Rendus Mécanique, vol.333, issue.8, pp.648-653, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00008145

T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, vol.21, issue.5, pp.571-574, 1973.

F. Murat and L. Tartar, H-convergence, in Topics in the mathematical modelling of composite materials, Progress in Nonlinear Differential Equations and their Applications, vol.31, pp.21-43, 1997.

B. Birkhäuser,

A. Nasri, Dimensional reduction for the simulation of metal fatigue. Theses, Ecole nationale supérieure d'arts et métiers -ENSAM, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01533317

S. Nemat-nasser and M. Hori, Micromechanics : Overall properties of heterogeneous materials, 1999.

S. Nezamabadi, J. Yvonnet, H. Zahrouni, and M. Potier-ferry, A multilevel computational strategy for handling microscopic and macroscopic instabilities, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.27, pp.2099-2110, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00692235

S. Nezamabadi, H. Zahrouni, J. Yvonnet, and M. Potier-ferry, A multiscale finite element approach for buckling analysis of elastoplastic long fiber composites, International Journal for Multiscale Computational Engineering, vol.8, pp.287-301, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01468352

H. Nouri and F. Meraghni, Modélisation et identification de lois de comportement avec endommagement en fatigue polycyclique de matériaux composites à matrice thermoplastique, 2008.

H. Nouri, F. Meraghni, L. , and P. , Fatigue damage model for injectionmolded short glass fibre reinforced thermoplastics, International Journal of Fatigue, vol.31, issue.5, pp.934-942, 2009.
URL : https://hal.archives-ouvertes.fr/pastel-00005669

A. Nouy and P. Ladeveze, Multiscale computational strategy with time and space homogenization : a radial-type approximation technique for solving micro problems, Int. J. Multiscale Comput. Engrg, p.170, 2004.

A. Nouy and P. Ladeveze, Proper generalized decomposition for multiscale and multiphysics problems, Archives of Computational Methods in Engineering, vol.17, issue.4, pp.351-372, 2010.

E. Obert, F. Daghia, P. Ladevèze, and L. Ballere, Micro and meso modeling of woven composites : Transverse cracking kinetics and homogenization, Composite Structures, vol.117, pp.212-221, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01581253

C. Oliver-leblond, H. Dumontet, and D. Kondo, A micro-mechanics based strain gradient damage model : formulation and solution for the torsion of a cylindrical bar, European Journal of Mechanics -A/Solids, vol.56, pp.19-30, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01223772

N. Ottosen and M. Ristinmaa, The Mechanics of Constitutive Modeling. The Mechanics of Constitutive Modeling, 2005.

I. Özdemir, W. A. Brekelmans, and M. G. Geers, Fe2 computational homogenization for the thermo-mechanical analysis of heterogeneous solids, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.3, pp.602-613, 2008.

V. Papadopoulos and M. Tavlaki, The impact of interfacial properties on the macroscopic performance of carbon nanotube composites. a fe2-based multiscale study, Composite Structures, vol.136, pp.582-592, 2016.

P. Pascal, Damage detection in PA 66/6|Glass woven fabric using ultrasonic techniques towards durability prediction of automotive parts. Theses, Ecole nationale supérieure d'arts et métiers -ENSAM, 2018.

O. Pierard, C. Friebel, and I. Doghri, Mean-field homogenization of multi-phase thermo-elastic composites : a general framework and its validation, Composites Science and Technology, vol.64, issue.10, pp.1587-1603, 2004.

O. Pierard, C. González, J. Segurado, J. Llorca, and I. Doghri, Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions, International Journal of Solids and Structures, vol.44, issue.21, pp.6945-6962, 2007.

E. Pierres, M. Baietto, and A. Gravouil, Experimental and numerical analysis of fretting crack formation based on 3d x-fem frictional contact fatigue crack model, Comptes Rendus Mécanique, vol.339, issue.7, pp.532-551, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00616930

J. Pina, V. Kouznetsova, and M. Geers, Thermo-mechanical analyses of heterogeneous materials with a strongly anisotropic phase : the case of cast iron, International Journal of Solids and Structures, vol.63, pp.153-166, 2015.

B. Piotrowski, T. Ben-zineb, E. Patoor, and A. Eberhardt, Modeling of niobium precipitates effect on the ni47ti44nb9 shape memory alloy behavior, International Journal of Plasticity, vol.36, pp.130-147, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01203110

P. Castañeda, P. Suquet, and P. , Nonlinear composites, Advances in Applied Mechanics, vol.34, pp.171-302, 1997.

P. Castañeda, P. Willis, and J. , The effect of spatial distribution on the effective behavior of composite materials and cracked media, Journal of the Mechanics and Physics of Solids, vol.43, issue.12, pp.1919-1951, 1995.

P. Ponte-castañeda, The effective mechanical properties of nonlinear isotropic composites, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.45-71, 1991.

F. Praud, Multi-scale modelling of thermoplastic-based woven composites, cyclic and time-dependent behaviour. Theses, Ecole nationale supérieure d'arts et métiers -ENSAM, 2018.
URL : https://hal.archives-ouvertes.fr/tel-01936624

F. Praud, G. Chatzigeorgiou, J. Bikard, and F. Meraghni, Phenomenological multi-mechanisms constitutive modelling for thermoplastic polymers, implicit implementation and experimental validation, Mechanics of Materials, vol.114, pp.9-29, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01575686

F. Praud, G. Chatzigeorgiou, Y. Chemisky, and F. Meraghni, Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites, Composite Structures, vol.182, pp.223-236, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01634479

A. Puck and H. Schürmann, Failure analysis of frp laminates by means of physically based phenomenological models, Composites Science and Technology, vol.62, issue.12, pp.1633-1662, 2002.

M. Qi, A. Giraud, J. Colliat, and J. Shao, A numerical damage model for initially anisotropic materials, International Journal of Solids and Structures, pp.245-256, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01383686

J. Qu and M. Cherkaoui, Fundamentals of micromechanics of solids, 2006.

K. Reifsnider and R. Jamison, Fracture of fatigue-loaded composite laminates, International Journal of Fatigue, vol.4, issue.4, pp.187-197, 1982.

J. Renard and M. Marmonier, Etude de l'initiation de l'endommagement dans la matrice d'un matériau composite par une méthode d'homogénisation, Aerospace Science and Technology, vol.9, pp.37-51, 1987.

W. Ruijter, Analysis of mechanical properties of woven textile composites as a function of textile geometry, 2009.

D. Ryckelynck, K. Lampoh, and S. Quilicy, Hyper-reduced predictions for lifetime assessment of elasto-plastic structures, Meccanica, vol.51, issue.2, pp.309-317, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01295849

M. Saleh, G. Lubineau, P. Potluri, P. Withers, and C. Soutis, , 2016.

, Micro-mechanics based damage mechanics for 3d orthogonal woven composites : Experiment and numerical modelling, Composite Structures, vol.156, pp.115-124

E. Sanchez-palencia, Comportements local et macroscopique d'un type de milieux physiques heterogenes, International Journal of Engineering Science, vol.12, issue.4, pp.331-351, 1974.

E. Sanchez-palencia, Non-homogeneous media and vibration theory, Lecture Notes in Physics, vol.127, 1978.

S. Schindler, J. Mergheim, M. Zimmermann, J. C. Aurich, and P. Steinmann, Numerical homogenization of elastic and thermal material properties for metal matrix composites (mmc), Continuum Mechanics and Thermodynamics, vol.29, issue.1, pp.51-75, 2017.

J. Schröder, M. Labusch, and M. Keip, Algorithmic two-scale transition for magneto-electro-mechanically coupled problems : Fe2-scheme : Localization and homogenization, Computer Methods in Applied Mechanics and Engineering, vol.302, pp.253-280, 2016.

D. Scida, Z. Aboura, M. Benzeggagh, and E. Bocherens, A micromechanics model for 3d elasticity and failure of woven-fibre composite materials, Composites Science and Technology, vol.59, issue.4, pp.505-517, 1999.
URL : https://hal.archives-ouvertes.fr/hal-02126064

A. Sengupta, P. Papadopoulos, and R. L. Taylor, A multiscale finite element method for modeling fully coupled thermomechanical problems in solids, International Journal for Numerical Methods in Engineering, vol.91, pp.1386-1405, 2012.

A. Seupel, G. Hütter, and M. Kuna, An efficient fe-implementation of implicit gradient-enhanced damage models to simulate ductile failure, Engineering Fracture Mechanics, vol.199, pp.41-60, 2018.

M. Sherburn, Geometric and mechanical modelling of textiles, 2007.

L. Shuguang and W. Anchana, Unit cells for micromechanical analyses of particle-reinforced composites, Mechanics of Materials, vol.36, issue.7, pp.543-572, 2004.

J. Simo and T. Hughes, Computational Inelasticity, 1998.

R. Smit, W. Brekelmans, and H. Meijer, Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling, Computer Methods in Applied Mechanics and Engineering, vol.155, issue.1, pp.181-192, 1998.

D. Sornin and K. Saanouni, About elastoplastic nonlocal formulations with damage gradients, International Journal of Damage Mechanics, vol.20, issue.6, pp.845-875, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00623528

P. Suquet, Analyse limite et homogeneisation. Comptes Rendus de l'Académie des Sciences, vol.295, pp.1355-1358, 1983.

. Bibliographie,

P. Suquet, Local and global aspects in the mathematical theory of plasticity. Plasticity today : modelling, methods and applications, pp.279-310, 1985.

P. M. Suquet, Elements of homogenization for inelastic solid mechanics, Lecture Notes in Physics, vol.272, pp.193-278, 1987.

C. Swan, Techniques for stress-and strain-controlled homogenization of inelastic periodic composites, Computer Methods in Applied Mechanics and Engineering, vol.117, issue.3, pp.249-267, 1994.

A. Tabiei and W. Yi, Comparative study of predictive methods for woven fabric composite elastic properties, Composite Structures, vol.58, issue.1, pp.149-164, 2002.

L. Tartar, Non linear constitutive relations and homogenization, Contemporary Developments in Continuum Mechanics and Partial Differential Equations, vol.30, pp.472-484, 1978.

A. Tchalla, S. Belouettar, A. Makradi, and H. Zahrouni, An abaqus toolbox for multiscale finite element computation, Composites Part B : Engineering, vol.52, pp.323-333, 2013.

I. Temizer, On the asymptotic expansion treatment of two-scale finite thermoelasticity, International Journal of Engineering Science, vol.53, pp.74-84, 2012.

I. Temizer and P. Wriggers, Homogenization in finite thermoelasticity, Journal of the Mechanics and Physics of Solids, vol.59, issue.2, pp.344-372, 2011.

K. Terada and N. Kikuchi, A class of general algorithms for multi-scale analyses of heterogeneous media, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.40, pp.5427-5464, 2001.

E. Tikarrouchine, G. Chatzigeorgiou, Y. Chemisky, and F. Meraghni, Fully coupled thermo-viscoplastic analysis of composite structures by means of multi-scale three-dimensional finite element computations, International Journal of Solids and Structures, vol.164, pp.120-140, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01985854

E. Tikarrouchine, G. Chatzigeorgiou, F. Praud, P. Piotrowski, Y. Chemisky et al., Three-dimensional fe2 method for the simulation of non-linear, rate-dependent response of composite structures, Composite Structures, vol.193, pp.165-179, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01762458

D. Tumbajoy-spinel, ,. Feulvarch, J. Bergheau, and G. Kermouche, 2d axisymmetric x-fem modeling of the hertzian cone crack system, Comptes Rendus Mécanique, vol.341, issue.9, pp.715-725, 2013.

D. Vasiukov, S. Panier, and A. Hachemi, Non-linear material modeling of fiber-reinforced polymers based on coupled viscoelasticity-viscoplasticity with anisotropic continuous damage mechanics, Composite Structures, vol.132, pp.527-535, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01717141

L. Wang, J. Wu, C. Chen, C. Zheng, B. Li et al., Progressive failure analysis of 2d woven composites at the meso-micro scale, Composite Structures, vol.178, pp.395-405, 2017.

W. Weibull, A statistical distribution function of wide applicability, Journal of Applied Mechanics, vol.18, pp.293-297, 1033.

R. Xu, C. Bouby, H. Zahrouni, T. Ben-zineb, H. Hu et al., 3d modeling of shape memory alloy fiber reinforced composites by multiscale finite element method. Composite Structures, vol.200, pp.408-419, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01950633

Q. Yu and J. Fish, Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales : a coupled thermo-viscoelastic example problem, International Journal of Solids and Structures, vol.39, issue.26, pp.6429-6452, 2002.

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

L. Zhou, M. Chen, C. Liu, and H. Wu, A multi-scale stochastic fracture model for characterizing the tensile behavior of 2d woven composites, Composite Structures, vol.204, pp.536-547, 2018.

Q. Zhu, J. Shao, and D. Kondo, A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction effects, European Journal of Mechanics -A/Solids, vol.30, issue.3, pp.316-325, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00734535

!. %&'-()*-+-;-*-+-' and . #$*-*-&-;-!*-+-$,

&. &+-'-", !. , +. , %. , *. et al., &+* 3 ! #$' + #+ )! %&! 2 "! + &+* &* "' &#"&+ ' + )+ ' 5&* "#* &9 :&* "' &%#, vol.789

#. , !. &>, and -. )'-*-'-6!-+*-"'-&%*-+-$!,

. &%&-+-'-+-&%, ! (+ ' "&+! "+ +

+. &#, 9E)!* * )(,! ' -)C)' ( * ,(+ + ' ")("=%! ")+ ' &FG?

+. >-f, +. Fg?b, %. , *. ;-+-#$'--)%-!-*-*, and *. %&*,

. &i-e+-%!-%9-;-*-+-' and . #$*-*-&&+-*-;-!&'-()*-!*-!, &4* "6* % &+ ! )#+ )! &#

!. &#, &' + &&"+#"&+ ' + ),&%3 )(+ ! ' # "* =

!. , 5' &#" * &+ ' -) 5#%"((4(+%)#+ ' * +! 2 "! #,& !%' 2 2 ,! + &+ = &%! 2 "! #(+ &> K6! &#")! + &")+ ' &&)

!. +%&, , vol.3

*. +m+-!-%, &. &&+-!-)#+-)!-&(+, !. <#"-;-+-&=+)('-#!-"&+-!-)#+-)!, !. +%"+-*-&-$&&-!, &. +%-;-!-+-&+-=-&%&*-"'-&%#-;-!-+-(+"*-' et al., , vol.2

&. and !. &&-+-'-".-+,

*. and &. #$*-*-&-!/0c-!-"#&&)&+-$!-;-c$",

&. and C. ,

=. %+, &#* 0/ 1 ! "#$6&%"+ $ ! ' "%' #$

. !-%'-#++-$-;-!-*-*!-&,

. &+-!-)#+-)!-&9?$#-;-+-+-'-"*&+-!-+-4='-+-4!-+-&+-$-!, &+ ! )#+ )! 2 2 #+ &6=' + ! "%)#' 4+ $!

#. #+-)!-"2+-$!-'-2-"!-#(+%+-$*-"#*#"&+-'-+-)+-'-5*-r&9-?$#"&'-%!-%#"&+-'-+-)+-&3#-;-&*-=+6"+-$&#*-&>, &+ ' + )+ ' 5* R&

+. %%#-;-6'-%r'-+-$-!-*-*-*-'-q+-'-"+-#$'--)'-+-$k'-+-*-;-*-+-' and . &#*-#-;-+-+-'-"*&+-!-+-4='-&-*-'-%+-"&-;-*-+-+-$,

#. #s&amp;%&amp;&apos;-+-=5&quot;*-)+-&apos;-&quot;9?$&apos;-&amp;#-;-+-+-&apos;-&quot;*&amp;+-!-+-4=&apos;-&amp;%-*-&quot;=%&quot;#&quot;-;-!-&amp;#*-&amp;r*-*&amp;+, &+ ! )#+ )! CR$"& $&&<$' 6' +%' 2 2 ! ++ = &"2"* ' !6$5, ! *%' &+ ! ' 6)+ ' "&"2' + ! *5! ' 6* &+ + $