Y. Abdin, A. Jain, I. Verpoest, and S. Lomov, Mean-eld based micro-mechanical modelling of short wavy ber reinforced composites, Composites: Part A, vol.91, p.472483, 2016.

N. Achour, Modélisation Multi-échelles et analyse expérimentale du comportement de composites à matrice thermoplastique renforcée en bres de verre sous sollicitations dynamiques modérées, 2017.

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, p.297305, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01206545

W. Albouy, De la contribution de la visco-élasto-plasticité au comportement en fatigue des composites à matrice thermoplastique et thermodurcissable, 2013.

O. Allix, P. Ladevèze, and E. Vittecoq, Modelling and identication of the mechanical behaviour of composite laminates in compression, Composites Science and Technology, vol.51, p.3542, 1994.

M. Arif, Damage mechanisms is short glass ber reinforced polyamide-66 under quasi-static and fatigue loading: Eect of relative humidity and injection molding induced microstructure, Arts et Métiers Paristech, 2014.

M. Arif, F. Meraghni, Y. Chemisky, N. Despringre, and G. Robert, In situ damage mechanisms investigation of PA66/GF30 composite: Eect of relative humidity, Composites: Part B, vol.58, p.487495, 2014.

E. Arruda, M. Boyce, and R. Jayachandran, Eects of strain rate, temperature and thermomechanical coupling on the nite strain deformation of glassy polymers, Mechanics of Materials, vol.19, p.193212, 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, p.72617275, 2007.

A. Asadi and J. Raghavan, Inuence of time-dependent damage on creep of multidirectional polymer composite laminates, Composites: Part B, vol.42, p.489498, 2011.

A. Asadi and J. Raghavan, Model for prediction of simultaneous time-dependent damage evolution in multiple plies of multidirectional polymer composite laminates and its inuence on creep, Composites: Part B, vol.79, p.359373, 2015.

P. Badel, S. Gautier, E. Vidal-sallé, and P. Boisse, Rate constitutive equations for computational analyses of textile composite reinforcement mechanical behaviour during forming, Composites: Part A, vol.40, p.9971007, 2009.

A. Benaarbia, Analyse énergétique du comportement thermomécanique du PA6.6 chargé de bres de verre, 2014.

A. Benaarbia, A. Chrysochoos, and G. Robert, Kinetics of stored and dissipated energies associated with cyclic loadings of dry polyamide 6.6 specimens, Polymer Testing, vol.34, p.155167, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00957767

A. Benaarbia, A. Chrysochoos, and G. Robert, Thermomechanical behavior of PA6.6 composites subjected to low cycle fatigue, Composites: Part B, vol.76, p.5264, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01060991

Y. Benveniste, A new approach to the application of Mori-Tanaka's theory in composite materials, Mechanics of Materials, vol.6, p.147157, 1987.

Y. Benveniste, G. Dvorak, and T. Chen, Stress elds in composites with coated inclusions, Mechanics of Materials, vol.7, p.305317, 1989.

Y. Benveniste, G. Dvorak, and T. Chen, On diagonal and elastic symmetry of the approximate eective stiness tensor of heterogeneous media, Journal of the Mechanics and Physics of Solids, vol.39, issue.7, p.927946, 1991.

Y. Benveniste, G. Dvorak, and T. Chen, On eective properties of composites with coated cylindrically orthotropic bers, Mechanics of Materials, vol.12, p.289297, 1991.

B. Berthel, Mesures thermographiques de champs de dissipation accompagnant la fatigue à grand nombre de cycles des aciers, 2007.
URL : https://hal.archives-ouvertes.fr/tel-00410074

J. Berthelot, Matériaux composite comportement mécanique et analyse des structures, 1999.

R. Berthelsen, R. Denzer, P. Oppermann, and A. Menzel, Computational homogenisation for thermoviscoplasticity: application to thermally sprayed coatings, Computational Mechanics, vol.60, p.739766, 2017.

M. Bhattacharyya, A. Fau, U. Nackenhorst, D. Néron, and P. Ladevèze, A model reduction technique in space and time for fatigue simulation, Multiscale Modeling of Heterogeneous Structures, p.183203, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02306384

A. Blanche, Eets dissipatifs en fatigue à grand et très grand nombre de cycles, 2012.

M. Boubakar, F. Trivaudey, D. Perreux, and L. Vang, A meso-macro nite element modelling of laminate structures-Part I: time-independent behaviour, Composite Structures, vol.58, p.271286, 2002.

M. Boubakar, L. Vang, F. Trivaudey, and D. Perreux, A meso-macro nite element modelling of laminate structures Part II: time-dependent behaviour, Composite Structures, vol.60, p.275305, 2003.

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.86, p.86112, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01006931

J. Chaboche, Damage induced anisotropy: on the diculties associated with the active/passive unilateral condition, International Journal of Damage Mechanics, vol.1, issue.2, p.148171, 1992.

J. Chaboche, P. Kanouté, and A. Roos, On the capabilities of mean-eld approaches for the description of plasticity in metal matrix composites, International Journal of Plasticity, vol.21, p.14091434, 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, p.151, 2017.

D. Chatziathanasiou, Y. Chemisky, G. Chatzigeorgiou, and F. Meraghni, Modeling of coupled phase transformation and reorientation in shape memory alloys under nonproportional thermomechanical loading, International Journal of Plasticity, vol.82, pp.192-224, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01360902

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, p.1839, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01515204

G. Chatzigeorgiou, N. Charalambakis, Y. Chemisky, and F. Meraghni, Thermomechanical Behavior of Dissipative Composite Materials, 2018.

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, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01196237

G. Chatzigeorgiou, F. Meraghni, and A. Javili, Generalized interfacial energy and size eects in composites, Journal of Mechanics and Physics of Solids, vol.106, p.257282, 2017.

F. Chinesta, A. Ammar, and E. Cueto, Proper generalized decomposition of multiscale models, Numerical Methods in Engineering, vol.83, issue.8-9, p.11141132, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01007223

A. Chrysochoos and H. Louche, An infrared image processing to analyse the caloric eects accompanying strain localisation, International Journal of Engineering Science, vol.38, p.17591788, 2000.

J. Cognard and P. Ladevèze, A large time increment approach for cyclic viscoplasticity, International Journal of Plasticity, vol.9, p.141157, 1993.

D. Cojocaru and A. Karlsson, A simple numerical method of cycle jumps for cyclically loaded structures, International Journal of Fatigue, vol.28, p.16771689, 2006.

G. Couégnat, Approche multiéchelle du comportement mécanique de matériaux composites à renfort tissé, 2008.

L. Delannay, I. Doghri, and O. Pierard, Prediction of tension-compression cycles in multiphase steel using a modied incremental mean-eld model, International Journal of Solids and Structures, vol.44, p.72917306, 2007.

K. Derrien, J. Fitoussi, G. Guo, and D. Batiste, Prediction of the eective damage properties and failure properties of nonlinear anisotropic discontinuous reinforced composites, Computer Methods in Applied Mechanics and Engineering, vol.185, p.93107, 2000.

R. Desmorat, Décomposition de Kelvin et concept de contraintes eectives multiples pour les matériaux anisotropes, Comptes Rendus Mécanique, vol.337, p.733738, 2009.

R. Desmorat, F. Gatuingt, and F. Ragueneau, Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials, Engineering Fracture Mechanics, vol.74, p.15391560, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00994382

N. Despringre, Analyse et modélisation des mécanismes d'endommagement et de déformation en fatigue multiaxiale de matériaux composites : polyamide renforcé par des bres courtes, Arts et Métiers ParisTech, 2015.

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, p.7788, 2016.

F. Detrez, S. Cantournet, and R. Seguela, Plasticity/damage coupling in semicrystalline polymers prior to yielding: Micromechanisms and damage law identication, Polymer, vol.52, 2011.

B. Dimitrijevic and K. Hackl, A method for gradient enhancement of continuum damage models, vol.28, p.4352, 2008.

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, p.16811712, 2003.

A. Drosdov, Cyclic thermo-viscoplasticity of high density polyethylene, International Journal of Solids and Structures, vol.47, p.15921602, 2010.

A. Drosdov, Cyclic viscoplasticity of semicrystalline polymers, Mechanics Research Communications, vol.37, p.2831, 2010.

A. Drosdov and J. Christiansen, Cyclic viscoplasticity of solid polymers: The eects of strain rate and amplitude of deformation, Polymer, vol.48, p.30033012, 2007.

A. Drosdov, J. Christiansen, R. Klitkou, and C. Potamiche, Viscoelasticity and viscoplasticity of polypropylene/polyethylene blends, International Journal of Solids and Structures, vol.47, p.24982507, 2010.

A. Drosdov, R. Klitkou, and J. Christiansen, Cyclic viscoplasticity of semicrystalline polymers with nite deformations, Mechanics of Materials, vol.56, p.5364, 2013.

A. Drosdov, C. Sanporean, and J. Christiansen, Mechanical response of HEMA gel under cyclic deformation: Viscoplasticity and swelling-induced recovery, International Journal of Solids and Structures, vol.52, p.220234, 2015.

Y. Duan, A. Saigal, R. Greif, and M. Zimmerman, A Uniform Phenomenological Constitutive Model for Glassy and Semicrystalline Polymers, Polymer Engineering & Science, vol.41, p.13221328, 2001.

Y. Duan, A. Saigal, R. Greif, and M. Zimmerman, Impact Behavior and Modeling of Engineering Polymers, Polymer Engineering & Science, vol.43, p.112124, 2003.

M. Ekh, A. Menzel, K. Runesson, and P. Steinmann, Anisotropic damage with the MCR eect coupled to plasticity, International Journal of Engineering Science, vol.41, p.15351551, 2003.

J. Eshelby, The determination of the elastic eld of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society of London A, vol.241, p.376396, 1226.

N. Feld, F. Coussa, and B. Delattre, A novel approach for the strain rate dependent modelling of woven composites, Composite Structures, vol.192, p.568576, 2018.

F. Feyel, Multiscale FE2 elastoviscoplastic analysis of composite structures, Computational Materials Science, vol.16, p.344354, 1999.

F. Feyel, A multilevel nite element method (FE2) to describe the response of highly non-linear structures using generalized continua, Computer Methods in Applied Mechanics and Engineering, vol.192, p.32333244, 2003.

F. Feyel and J. Chaboche, FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long bre SiC/Ti composite materials, Computer Methods in Applied Mechanics and Engineering, vol.183, p.309330, 2000.

E. Gamstedt and B. Sjögren, Micromechanisms in tension-compression fatigue of composite laminates containing transverse plies, Composites Science and Technology, vol.59, p.167178, 1999.

D. Garoz, F. Gilabert, R. Sevenois, S. Spronk, and W. Van-paepegem, Material parameter identication of the elementary ply damage mesomodel using virtual micro-mechanical tests of a carbon ber epoxy system, Composite Structures, vol.181, p.391404, 2017.

A. Gavazzi and D. Lagoudas, On the numerical evaluation of Eshelby's tensor and its application to elastoplastic brous composites, Computational Mechanics, vol.7, p.1319, 1990.

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

P. Germain, Sur certaines dénitions liées à l'énérgie en mécanique de solides, International Journal of Engineering Science, vol.20, issue.2, p.245259, 1982.

P. Germain, Q. Nguyen, and P. Suquet, Continuum thermodynamics, vol.50, p.10101020, 1983.
URL : https://hal.archives-ouvertes.fr/hal-00105630

G. , Approche multimodèle pour la conception de structures composites à renfort tissé, 2013.

A. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I. Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, vol.99, p.215, 1977.
DOI : 10.2172/7351470
URL : https://www.osti.gov/servlets/purl/7351470

S. Haouala and I. Doghri, Modeling and algorithms for two-scale time homogenization of viscoelastic-viscoplastic solids under large numbers of cycles, International Journal of Plasticity, vol.70, p.98125, 2015.

Z. Hashin, Failure Criteria for Unidirectional Fiber Composites, Journal of Applied Mechanics, vol.47, issue.2, p.329334, 1980.
DOI : 10.1115/1.3153664

Z. Hashin and A. Rotem, A Fatigue Failure Criterion for Fibre Reinforced Materials, Journal of Composite Materials, vol.7, p.448464, 1973.
DOI : 10.21236/ad0760146
URL : http://www.dtic.mil/dtic/tr/fulltext/u2/760146.pdf

W. He, Y. Wu, Y. Xu, and T. Fu, A thermodynamically consistent nonlocal damage model for concrete materials with unilateral eects, Computer Methods in Applied Mechanics and Engineering, vol.297, p.371391, 2015.
DOI : 10.1016/j.cma.2015.09.010

R. Hill, A theory of the yielding and plastic ow of anisotropic metals, Proceedings of the Royal Society of London A, vol.193, p.281297, 1033.

R. Hill, A self-consistent mechanics of composite materials, Journal of the Mechanics and Physics of Solids, vol.13, p.21322, 1965.
DOI : 10.1016/0022-5096(65)90010-4

R. Hill, The essential structure of constitutive laws for metal composites and polycrystals, Journal of Materials Science and Engineering, vol.15, issue.2, p.7995, 1967.

C. Hochard, P. Aubourg, and J. Charles, Modelling of the mechanical behaviour of woven-fabric CFRP laminates up to failure, Composites Science and Technology, vol.61, p.221230, 2001.

C. Hochard, J. Payan, and C. Bordreuil, A progressive rst ply failure model for woven ply CFRP laminates under static and fatigue loads, International Journal of Fatigue, vol.28, p.12701276, 2006.

C. Hochard and Y. Thollon, A generalized damage model for woven ply laminates under static and fatigue loading conditions, International Journal of Fatigue, vol.32, pp.158-165, 2010.
DOI : 10.1016/j.ijfatigue.2009.02.016

O. Homan, The Brittle Strength of Orthotropic Materials, Journal of Composite Materials, vol.1, 1967.

J. Huang and D. Griths, Return mapping algorithms and stress predictors for failure analysis in geomechanics, Journal of Engineering Mechanics, vol.135, issue.4, p.276284, 2009.
DOI : 10.1061/(asce)0733-9399(2009)135:4(276)

A. Karallis and M. Boyce, A general anisotropic yield criterion using bounds and transformation weighting tensor, Journal of the Mechanics and Physics of Solids, vol.41, issue.12, p.19591886, 1993.

M. Kawai, Y. Masuko, and T. Sagawa, O-axis tensile creep rupture of unidirectional CFRP laminates at elevated temperature, Composites: Part A, vol.37, p.257269, 2006.
DOI : 10.1016/j.compositesa.2005.08.002

A. 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, p.581601, 2006.

B. Kiefer, T. Waenschmidt, L. Sprave, and A. Menzel, A gradient-enhanced damage model coupled to plasticity-multi-surface formulation and algorithmic concepts, International Journal of Damage Mechanics, 2017.
DOI : 10.1177/1056789516676306

A. Krairi, Multiscale modeling of the damage and failure of homogeneous and shortber reinforced thermoplastics under monotonic and fatigue loadings, 2015.

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, p.163181, 2014.
DOI : 10.1016/j.ijplas.2014.04.010

A. Krairi, I. Doghri, and G. Robert, Multiscale high cycle fatigue models for neat and short ber reinforced thermoplastic polymers, International Journal of Fatigue, vol.92, p.179192, 2016.
DOI : 10.1016/j.ijfatigue.2016.06.029

A. Krasnobrizha, Modelisation des mechanismes d'hysteresis des composites tissés a l'aide d'un modèle collaboratif elasto-plastique endommageable à derivees fractionnaires, 2015.

A. Krasnobrizha, P. Rozycki, L. Gornet, and P. Cosson, Hysteresis behaviour modelling of woven composite using a collaborative elastoplastic damage model with fractional derivatives, Composite Structures, vol.158, p.101111, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01580754

P. Ladevèze, A damage computational method for composite structures, Computers & Structures, vol.44, p.7987, 1992.

P. Ladevèze, On reduced models in nonlinear solid mechanics, European Journal of Mechanics-A/Solids, vol.60, p.227237, 2016.

P. Ladevèze and E. L. Dantec, Damage modelling of the elementary ply for laminated composites, Composites Science and Technology, vol.43, p.257267, 1992.

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, 1991.

R. Lakes, Viscoelastic Solids, 1999.

J. Läufer, V. Becker, and W. Wagner, Gradient enhancement of a transversely isotropic continuum damage model, Composite Structures, vol.181, p.138144, 2017.

A. Launay, M. Maitournam, Y. Marco, and I. Raoult, Multiaxial fatigue models for short glass ber reinforced polyamide Part I: Nonlinear anisotropic constitutive behavior for cyclic response, International Journal of Fatigue, vol.47, p.382389, 2013.

A. Launay, M. Maitournam, Y. Marco, and I. Raoult, Multiaxial fatigue models for short glass bre reinforced polyamide. Part II: Fatigue life estimation, International Journal of Fatigue, vol.47, 2013.

A. Launay, M. Maitournam, Y. Marco, I. Raoult, and F. Szmytka, Cyclic behaviour of short glass bre reinforced polyamide: Experimental study and constitutive equations, International Journal of Plasticity, vol.27, p.12671293, 2011.

A. Launay, Y. Marco, M. Maitournam, and I. Raoult, Modelling the inuence of temperature and relative humidity on the time-dependent mechanical behaviour of a short glass bre reinforced polyamide, Mechanics of Materials, vol.56, p.110, 2013.

W. Lawrimore, I. I. , D. Francis, J. Bouvard, Y. Hammi et al., A mesomechanics parametric nite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model, Mechanics of Materials, vol.96, p.8395, 2016.

N. Laws and J. Brockenbrough, The eect of micro-crack systems on the loss of stiness of brittle solids, International Journal of Solids and Structures, vol.23, p.12471268, 1987.

N. Laws, G. Dvorak, and M. Hejazi, Stiness changes in unidirectional composites caused by crack systems, Mechanics of Materials, vol.2, p.123137, 1983.

E. and L. Dantec, Contribution à la modélisation du comportement mécanique des composites stratiés, 1989.

H. Lee and S. Pyo, Micromechanics-based elastic damage modeling of particulate composites with weakened interfaces, International Journal of Solids and Structures, vol.44, p.83908406, 2007.

J. Lemaitre, Coupled elasto-plasticity and damage constitutive equations, Computer Methods in Applied Mechanics and Engineering, vol.51, p.3149, 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.

K. Levenberg, A method for the solution of certain non-linear problem in least squares, Quarterly of Applied Mathematics, vol.2, p.164168, 1944.

S. Li, On the unit cell for micromechanical analysis of bre-reinforced composites, Proceedings of the Royal Society of London A, vol.455, p.815838, 1983.

S. Li, General unit cells for micromechanical analyses of unidirectional composites, Composites: Part A, vol.32, p.815826, 2001.

S. Li and A. Wongsto, Unit cells for micromechanical analyses of particle-reinforced composites, Mechanics of Materials, vol.36, p.543572, 2004.

H. Lin, L. Brown, and A. Long, Modelling and Simulating Textile Structures Using TexGen, Advanced Materials Research, vol.331, p.4447, 2011.

S. Lomov, A. Gusakov, G. Huysmans, A. Prodromou, and I. Verpoest, Textile geometry preprocessor for meso-mechanical models of woven composites, Composites Science and Technology, vol.60, p.20832095, 2000.

S. Lomov, G. Huysmans, Y. Luo, R. Parnas, A. Prodromou et al., Textile composites: modelling strategies, Composites: Part A, vol.32, pp.1379-1394, 2001.

S. Lomov, D. Ivanov, I. Verpoest, M. Zako, T. Kurashiki et al., Meso-FE modelling of textile composites: Road map, data ow and algorithms, Composites Science and Technology, vol.67, p.18701891, 2007.

Z. Mahboob, Y. Chemisky, F. Meraghni, and H. Bougherara, Mesoscale modelling of tensile response and damage evolution in natural bre reinforced laminates, Composites: Part B, vol.119, p.168183, 2017.

A. Malpot, Etude du comportement en fatigue d'un composite à matrice polyamide renforcé d'un tissu de bres de verre pour application automobile, 2016.

A. Malpot, F. Touchard, and S. Bergamo, Eect of relative humidity on mechanical properties of a woven thermoplastic composite for automotive application, Polymer Testing, vol.48, p.160168, 2015.

A. Malpot, F. Touchard, and S. Bergamo, Inuence of moisture on the fatigue behaviour of a woven thermoplastic composite used for automotive application, Materials & Design, vol.98, p.1219, 2016.

A. Malpot, F. Touchard, and S. Bergamo, An investigation of the inuence of moisture on fatigue damage mechanisms in a woven glass-bre-reinforced PA66 composite using acoustic emission and infrared thermography, Composites: Part B, vol.130, p.1120, 2017.

L. Marcin, Modélisation du comporetement, de l'endommagement et de la rupture de matériaux composites à renforts tissés pour le dimentionnement robuste de structures, 2010.

D. W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, Journal of the Society for Industrial and Applied Mathematics, vol.11, issue.2, p.431441, 1963.

A. Maurel-pantel, . Baquet, J. Bikard, N. Bouvard, and . Billon, A thermomechanical large deformation constitutive model for polymers based on material network description: Application to a semi-crystalline polyamide 66, International Journal of Plasticity, vol.67, p.102126, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01083213

F. Meraghni and M. Benzeggagh, Micromechanical modelling of matrix degradation in randomly oriented discontinuous-bre composites, Composites Science and Technology, vol.55, p.171186, 1995.

F. Meraghni, C. Blakeman, and M. Benzeggagh, Eect of interfacial decohesion on stiness reduction in a random discontinuous-bre composite containing matrix microcracks, Composites Science and Technology, vol.56, p.541555, 1996.

F. Meraghni, Y. Chemisky, B. Piotrowski, R. Echchor, N. Bourgeois et al., Parameter identication of a thermodynamic model for superelastic shape memory alloys using analytical calculation of the sensitivity matrix, European Journal of Mechanics-A/Solids, vol.45, p.226237, 2014.

F. Meraghni, F. Desrumaux, and M. Benzeggagh, Implementation of a constititive micromechanical model for damage analysis in glass mat reinforced composite structures, Composites Science and Technology, vol.62, p.20872097, 2002.

F. Meraghni, H. Nouri, N. Bourgeois, C. Czarnota, and P. Lory, Parameters identication of fatigue damage model for short glass ber reinforced polyamide (PA6-GF30) using digital image correlation. Procedia Engineering, vol.10, p.21102116, 2011.

M. Meuwissen, C. Oomens, F. Baaijens, R. Petterson, and J. ,

. Janssen, Determination of the elasto-plastic properties of aluminium using a mixed numerical-experimental method, Journal of Materials Processing Technology, vol.75, pp.204-211, 1998.

J. Michel, H. Moulinec, and P. Suquet, Eective properties of composite materials with periodic microstructure: a computational approach, Computer Methods in Applied Mechanics and Engineering, vol.172, p.109143, 1999.

B. Miled, I. Doghri, L. Brassart, and L. Delannay, Micromechanical modeling of coupled viscoelastic-viscoplastic composites based on an incrementally ane formulation, International Journal of Solids and Structures, vol.50, p.17551769, 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, p.33813394, 2011.

S. Moreau, A. Chrysochoos, J. Muracciole, and B. Wattrisse, Analysis of thermoelastic eects accompanying the deformation of PMMA and PC polymers, Comptes Rendus Mécanique, vol.333, p.648653, 2005.

T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with mistting inclusions, Acta Metallurgica, vol.21, p.571574, 1973.

A. Muliana, Nonlinear viscoelastic-degradation model for polymeric based materials, International Journal of Solids and Structures, vol.51, p.122132, 2014.

T. Mura, Micromechanics of defects in solids, 1987.

M. Nasri, Réduction dimensionnelle pour la simulation de la fatigue des métaux, 2017.

S. Nemat-nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials, 1999.

Q. Nguyen, E. Vidal-sallé, P. Boisse, C. Park, J. Saouab et al., Mesoscopic scale analyses of textile composite reinforcement compaction, Composites: Part B, vol.44, p.231241, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00785596

H. Nouri, Modélisation et identication de lois de comportement avec endommagement en fatigue polycyclique de matériaux composites à matrice thermoplastique, Arts et Métiers ParisTech, 2009.

H. Nouri, F. Meraghni, and P. Lory, Fatigue damage model for injection-molded short glass bre reinforced thermoplastics, International Journal of Fatigue, vol.31, p.934942, 2009.

M. Ortiz and J. Simo, An analysis of a new class of integration algorithms for elasto-plastic constitutive relations, International Journal for Numerical Methods in Engineering, vol.23, p.353366, 1986.

V. Oshmyan, S. Patlazhan, and Y. Remond, The Eect of Structural Changes and Nonlinear Character of Plastic Flow on Low Strains in Semicrystalline Polymers, Polymer Science, vol.47, p.346351, 2005.

V. Oshmyan, S. Patlazhan, and Y. Remond, Principles of Structural-Mechanical Modeling of Polymers and Composites, Polymer Science, vol.48, p.10041013, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00097029

N. Ottosen and M. Ristinmaa, Failure and initial yield criteria, The Mechanics of Constitutive Modeling, p.145193, 2005.

N. Ottosen and M. Ristinmaa, Introduction to time-dependent material behavior, The Mechanics of Constitutive Modeling, p.357378, 2005.

C. Ovalle-rodas, F. Zaïri, and M. Naït-abdelaziz, A nite strain thermo-viscoelastic constitutive model to describe the self-heating in elastomeric materials during lowcycle fatigue, Journal of the Mechanics and Physics of Solids, vol.64, p.396410, 2014.

C. Ovalle-rodas, F. Zaïri, M. Naït-abdelaziz, and P. Charrier, A thermo-viscohyperelastic model for the heat build-up during low-cycle fatigue of lled rubbers: Formulation, implementation and experimental verication, International Journal of Plasticity, vol.79, p.217236, 2016.

J. Payan, Etude du comportement de composites stratiés sous chargement statique et de fatigue, 2004.

J. Payan and C. Hochard, Damage modelling of laminated carbon epoxy composites under static and fatigue loadings, International Journal of Fatigue, vol.24, p.299306, 2002.

D. Perreux and D. Lazuardi, The eect of residual stress on the non-linear behaviour of composite laminates Part II. Layer, laminate non-linear models and the eect of stress on the model parameters residual, Composites Science and Technology, vol.61, p.177190, 2001.

D. Perreux and C. Oytana, Continuum damage mechanics for microcracked composites, Composites Engineering, vol.3, p.115122, 1993.
DOI : 10.1016/0961-9526(93)90036-j

C. Peyrac, T. Jollivet, N. Leray, F. Lefebvre, O. Westphal et al., Self-Heating Method for Fatigue Limit Determination on Thermoplastic Composites. Procedia Engineering, vol.133, p.129135, 2015.
DOI : 10.1016/j.proeng.2015.12.639
URL : https://doi.org/10.1016/j.proeng.2015.12.639

O. Pierard and I. Doghri, An enhanced ane formulation and the corresponding numerical algorithms for the mean-eld homogenization of elasto-viscoplastic composites, International Journal of Plasticity, vol.22, p.131157, 2006.

O. Pierard, C. Friebel, and I. Doghri, Mean-eld homogenization of multi-phase thermo-elastic composites a general framework and its validation, Composites Science and Technology, vol.64, p.15871603, 2004.
DOI : 10.1016/j.compscitech.2003.11.009

O. Pierard, C. Gonzalez, J. Segurado, J. Llorca, and I. Doghri, Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions, International Journal of Solids and Structures, vol.44, p.69456962, 2007.
DOI : 10.1016/j.ijsolstr.2007.03.019
URL : https://doi.org/10.1016/j.ijsolstr.2007.03.019

O. Pierard, J. Llorca, J. Segurado, and I. Doghri, Micromechanics of particlereinforced elasto-viscoplastic composites: Finite element simulations versus ane homogenization, International Journal of Plasticity, vol.23, p.10411060, 2007.
DOI : 10.1016/j.ijplas.2006.09.003

P. , P. Castañeda, and J. Willis, The eect of spacial distribution on the eective behavior of composite materials and cracked media, Journal of the Mechanics and Physics of Solids, vol.43, issue.12, p.19191951, 1995.

P. Potluri and T. Sagar, Compaction modelling of textile preforms for composite structures, Composite Structures, vol.86, p.177185, 2008.
DOI : 10.1016/j.compstruct.2008.03.019

F. Praud, G. Chatzigeorgiou, J. Bikard, and F. Meraghni, Phenomenological multimechanisms constitutive modelling for thermoplastic polymers, implicit implementation and experimental validation, Mechanics of Materials, vol.114, p.929, 2017.
DOI : 10.1016/j.mechmat.2017.07.001
URL : https://hal.archives-ouvertes.fr/hal-01575686

F. Praud, G. Chatzigeorgiou, Y. Chemisky, and F. Meraghni, Micromechanical modelling of viscoelastic-viscoplastic-damage behaviour for polyamide woven fabric composites under cyclic loading, European Conference on Composite Materials ECCM17, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01365023

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

F. Praud, G. Chatzigeorgiou, Y. Chemisky, and F. Meraghni, Modélisation multiéchelle des composites tissés à matrice thermoplastique sous chargements cycliques non proportionnels, Journées Nationales sur les Composites JNC20, 2017.

A. Puck and W. Schneider, On failure mechanisms and failure criteria of lamentwound glass-bre/resin composites, Plastics and Polymers, vol.37, p.3343, 1969.

A. Puck and H. Schürmann, Failure analysis of FRP laminates by means of physically based phenomenological models, Composites Science and Technology, vol.58, p.10451067, 1998.

M. Qi, A. Giraud, J. Colliat, and J. Shao, A numerical damage model for initially anisotropic materials, International Journal of Solids and Structures, p.245256, 2016.
DOI : 10.1016/j.ijsolstr.2016.08.021
URL : https://hal.archives-ouvertes.fr/hal-01383686

M. Qidwai, D. Hartl, and D. Lagoudas, Numerical implementation of an SMA thermomechanical constitutive model using return mapping algorithms, Shape Memory Alloys: Modeling and Engineering Applications, p.189231

. Springer, , 2008.

M. Qidwai and D. Lagoudas, Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms, International Journal for Numerical Methods in Engineering, vol.47, p.11231168, 2000.

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

E. Sanchez-palencia, Comportement local et macroscopique d'un type de milieux physiques hétérogènes, International Journal of Engineering Science, vol.12, issue.4, p.331351, 1974.
DOI : 10.1016/0020-7225(74)90062-7
URL : http://dml.cz/bitstream/handle/10338.dmlcz/103951/AplMat_27-1982-2_4.pdf

R. Schapery, On the characterization of nonlinear viscoelastic materials, Polymer Engineering & Science, vol.9, issue.4, p.295310, 1969.

F. Schirmaier, J. Weiland, L. Kärger, and F. Henning, A new ecient and reliable algorithm to determine the fracture angle, Composites Science and Technology, vol.100, 1925.
DOI : 10.1016/j.compscitech.2014.05.033

H. Shahsavari, R. Naghdabadi, M. Baghani, and S. Sohrabpour, A viscoelasticviscoplastic constitutive model considering damage evolution for time dependent materials: Application to asphalt mixes, International Journal of Damage Mechanics, vol.25, issue.7, p.921942, 2016.

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

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

J. Simo and M. Ortiz, A unied approach to nite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations, Computer Methods in Applied Mechanics and Engineering, vol.49, issue.2, p.221245, 1985.

D. Spring and G. Paulino, A growing library of three-dimensional cohesive elements for use in ABAQUS, Engineering Fracture Mechanics, vol.126, 2014.

P. Suquet, Elements of homogenization for inelastic solid mechanics, Lecture Notes in Physics, vol.272, 1987.

A. Tchalla, S. Belouettar, A. Makradi, and H. Zahrouni, An ABAQUS toolbox for multiscale nite element computation, Composites: Part B, vol.52, p.323333, 2013.
DOI : 10.1016/j.compositesb.2013.04.028

E. Tikarrouchine, G. Chatzigeorgiou, F. Praud, B. Piotrowski, Y. Chemisky et al., Three-dimensional FE2 method for the simulation of non-linear, ratedependent response of composite structures, Composite Structures, vol.193, p.165179, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01762458

E. Tikarrouchine, F. Praud, G. Chatzigeorgiou, B. Piotrowski, Y. Chemisky et al., Modélisation multi-échelle non-linéaire par homogénéisation périodique et analyses par EF2: application aux composites à matrice élastoviscoplastique endommageable, Journées Nationales sur les Composites JNC20, 2017.

S. Tsai and E. Wu, A general theory of strength for anisotropic materials, Journal of Composite Materials, vol.5, p.5880, 1971.

P. Vannucci, General anisotropic elasticity, Anisotropic Elasticity, 1973.
DOI : 10.1007/978-981-10-5439-6_2

D. Vasiukov, S. Panier, and A. Hachemi, Non-linear material modeling of berreinforced polymers based on coupled viscoelasticity-viscoplasticity with anisotropic continuous damage mechanics, Composite Structures, vol.132, p.527535, 2015.

I. Verpoest and S. Lomov, Virtual textile composites software WiseTex: Integration with micro-mechanical, permeability and structural analysis, Composites Science and Technology, vol.65, p.25632574, 2005.

B. Vieille, W. Albouy, and L. Taleb, Viscoelastic viscoplastic model for aeronautical thermoplastic laminates at high temperature: Validation on high stress gradient structures, Composites: Part B, vol.90, p.278286, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01954220

G. Voyiadjis and A. Samadi-dooki, Constitutive modeling of large inelastic deformation of amorphous polymers: Free volume and shear transformation zone dynamics, Journal of Applied Physics, vol.119, issue.22, p.225104, 2016.

T. Waenschmidt, C. Polindara, A. Menzel, and S. Blanco, A gradient-enhanced large-deformation continuum damage model for bre-reinforced materials, Computer Methods in Applied Mechanics and Engineering, vol.268, p.801842, 2014.

W. , A statistical distribution function of wide applicability, Journal of Applied Mechanics, vol.18, p.293297, 1951.

J. Wiegand, N. Petrinic, and B. Elliott, An algorithm for determination of the fracture angle for the three-dimensional Puck matrix failure criterion for UD composites, Composites Science and Technology, vol.68, p.25112517, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00504131

H. William, Numerical recipes in Fortran: The art of scientic computing, 1989.

L. Wu, L. Adam, I. Doghri, and L. Noels, An incremental-secant mean-eld homogenization method with second statistical moments for elasto-visco-plastic composite materials, Mechanics of Materials, vol.114, p.180200, 2017.

L. Wu, L. Noels, L. Adam, and I. Doghri, A combined incremental-secant mean-eld homogenization scheme with per-phase residual strains for elasto-plastic composites, International Journal of Plasticity, vol.51, p.80102, 2013.

C. Yu, G. Kang, and K. Chen, A hygro-thermo-mechanical coupled cyclic constitutive model for polymers with considering glass transition, International Journal of Plasticity, vol.89, p.2965, 2017.

C. Yu, G. Kang, K. Chen, and F. Lu, A thermo-mechanically coupled nonlinear viscoelastic-viscoplastic cyclic constitutive model for polymeric materials, Mechanics of Materials, vol.105, p.115, 2017.

F. Zaïri, M. Naït-abdelaziz, J. Gloaguen, A. Bouaziz, and J. Lefebvre, Micromechanical modelling and simulation of chopped random ber reinforced polymer composites with progressive debonding damage, International Journal of Solids and Structures, vol.45, p.52205236, 2008.

P. Zerbe, B. Schneider, E. Moosbrugger, and M. Kaliske, A viscoelastic-viscoplasticdamage model for creep and recovery of a semicrystalline thermoplastic, International Journal of Solids and Structures, p.340350, 2017.

Q. Zhu, J. Shao, and D. Kondo, A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction eects, European Journal of Mechanics-A/Solids, vol.30, p.316325, 2011.

J. Zouhaier, F. Meraghni, J. Fitoussi, and D. Batiste, Multi-scales modelling of dynamic behaviour for discontinuous bre SMC composites, Composites Science and Technology, vol.69, p.97103, 2009.