. Aussi and . Fait-le-choix-d, adopter une approche de type saut de cycles Dans le but de valider notre modèle et son identification, nous avons proposé une comparaison des résultats obtenus par la simulation d'un élément de volume avec les résultats d'un calcul par éléments finis sur une éprouvette lisse. Enfin, nous terminons par une application sur une structure plus complexe : une plaque trouée

R. Biliographiques and . Abry, In situ monitoring of damage in CFRP laminates by means of ac and dc measurement, Comportement en fatigue de pièces épaisses en matériaux composites, pp.855-864, 2001.

. Alberola, Uniirectional fibre-reinforced polymers: analytical morphology approach and mechanical modelling based on the percolation concept, Polymer, vol.40, issue.2, pp.315-3284, 1999.
DOI : 10.1016/S0032-3861(98)00195-5

D. Allen, Homogenization principles and their application to continuum damage mechanics, Composites Science and Technology, vol.61, issue.15, pp.2223-2230, 2001.
DOI : 10.1016/S0266-3538(01)00116-6

L. Allix, O. Allix, and P. Ladevèze, Interlaminar interface modelling for the prediction of delamination, Composite Structures, vol.22, issue.4, pp.235-242, 1992.
DOI : 10.1016/0263-8223(92)90060-P

E. Aussedat-yahia, Comportement et endommagement du composite tissé Carbone/PMR15 soumis à des chargements mécaniques et thermiques, 1997.

K. Aveston, J. Aveston, and A. Kelly, Theory of multiple fracture of fibrous composites, Journal of Materials Science, vol.18, issue.3, pp.352-362, 1973.
DOI : 10.1007/BF00550155

. Bader, The mecanisms of initiation and development of damage in multi-axial fibre-reinforced plastic laminates, ICM 3. Proceedings, 1979.

B. Bader, M. Bader, and L. Boniface, Damage development during quasi-static and cyclic loading in GRP and CFRP laminates containing 90 ? plies, Fifth International Conference on Composite Materials, pp.221-232, 1985.

P. Bailey, J. Bailey, and A. Parvizi, On fibre debonding effects and the mechanism of transverse-ply failure in cross-ply laminates of glass fibre/thermoset composites, Journal of Materials Science, vol.31, issue.3, pp.649-659, 1981.
DOI : 10.1007/BF02402782

B. Bathias, C. Bathias, and J. Baïlon, La fatigue des matériaux et des structures, 1980.

J. Berthelot, Matériaux composites, 1999.

L. Berthelot, . Corre, J. Berthelot, L. Corre, and J. , Statistical analysis of the progression of transverse cracking and delamination in cross-ply laminates, Composites Science and Technology, vol.60, issue.14, pp.2659-2669, 2000.
DOI : 10.1016/S0266-3538(00)00140-8

. Berthelot, Transverse cracking of cross-ply laminates: Part 1. Analysis, Composites Part A: Applied Science and Manufacturing, vol.27, issue.10, pp.989-1001, 1996.
DOI : 10.1016/1359-835X(96)80002-A

S. Blassiau, Modélisation des phénomènes microstructuraux au sein d'un composite unidirectionnel carbone/epoxy et prediction de durée de vie : contrôle et classification de réservoirs bobinés, 2005.

. Blassiau, Micromechanisms of load transfer in a unidirectional carbon fibre-reinforced epoxy composite due to fibre failures: Part 3. Multiscale reconstruction of composite behaviour, Composite Structures, vol.83, issue.3, pp.312-323, 2008.
DOI : 10.1016/j.compstruct.2007.05.004

URL : https://hal.archives-ouvertes.fr/hal-00130644

. Boisse, A new approach in non-linear mechanics: The large time increment method, International Journal for Numerical Methods in Engineering, vol.15, issue.3, pp.647-663, 1990.
DOI : 10.1002/nme.1620290312

O. Boniface, L. Boniface, and S. Ogin, Application of the Paris Equation to the Fatigue Growth of Transverse Ply Cracks, Journal of Composite Materials, vol.14, issue.7, pp.735-754, 1989.
DOI : 10.1177/002199838902300706

. Boniface, Observation on transverse ply crack growth in (0 ? /90 ? 2 ) s CFRP laminate under monotonic and cyclic loading, Sixth International Conference on Composite Materials (ICCM 6) and Second European Conference on Composite Materials (ECCM 2), pp.3156-3165, 1987.

. Burcham, Investigation of the microcracking behavior of bismaleimide composites during thermal aging, Polymer Composites, vol.2, issue.6, pp.507-517, 1995.
DOI : 10.1002/pc.750160609

. Camanho, . Dàvilla, P. Camanho, and C. Dàvilla, Mixed-mode decohesion finite elements for the simulation of delamination in composite materials, NASA/TM, pp.2002-211, 2002.

. Caron, Multi-particle modelling for the prediction of delamination in multi-layered materials, Composites Science and Technology, vol.66, issue.6, pp.755-765, 2006.
DOI : 10.1016/j.compscitech.2004.12.022

. Caron, . Ehrlacher, J. Caron, and A. Ehrlacher, Modelling of fatigue microcracking kinetics in crossply composites and experimental validation, International Conference on fatigue of composites, pp.378-385, 1997.
DOI : 10.1016/S0266-3538(98)00173-0

R. Biliographiques, . Caron, J. Ehrlacher-]-caron, and A. Ehrlacher, Modelling the kinetics of transverse cracking in composite laminates, Comportement en fatigue de pièces épaisses en matériaux composites pastel-00677076, pp.1261-1270, 1997.

J. Chaboche, Le concept de contrainte effective appliqué à l'elasticité et la viscoplasticité en présence d'endommagement anisotrope, Colloque EUROMECH 115, pp.737-760, 1979.

J. Chaboche, Damage induce anisotropy : On the difficulties associed with the active/passive unilateral condition, International Journal of damage mechanics, vol.1, 1992.

J. Chaboche, Mécanique de l'endommagement, anisotropie et désactivation du dommage, 1994.

. Chaboche, Macroscopic modelling of inelastic and damage processes with unilateral effects in thermostructural composite materials, ASME Winter Annual Meeting. Proceedings, 1994.

C. Chou, P. Chou, and R. Croman, Degradation and Sudden- Death Models of Fatigue of Graphite/ Epoxye-Laminates, Composite Materials : Testing and Design, pp.431-454, 1979.

H. Cox, The elasticity and strength of paper and other fibrous materials, British Journal of Applied Physics, vol.3, issue.3, pp.72-79, 1952.
DOI : 10.1088/0508-3443/3/3/302

C. Daniel, I. Daniel, and A. Charewicz, Fatigue damage mechanisms and residual properties of graphite/epoxy laminates, Engineering Fracture Mechanics, vol.25, issue.5-6, pp.793-808, 1986.
DOI : 10.1016/0013-7944(86)90042-1

V. Degriek, . Paepegem, J. Degriek, and W. Van-paepegem, Fatigue damage modeling of fibre-reinforced composite materials: Review, Applied Mechanics Reviews, vol.54, issue.4, pp.279-300, 2001.
DOI : 10.1115/1.1381395

. Diao, Simulation of fatigue performance of cross-ply composite laminates, Applied Composite Materials, vol.7, issue.6, pp.391-406, 1995.
DOI : 10.1007/BF00133682

D. Diaz, C. Diaz, A. Caron, and J. , Prediction of the onset of mode III delamination in carbon-epoxy laminates, Composite Structures, vol.72, issue.4, pp.438-445, 2006.
DOI : 10.1016/j.compstruct.2005.01.014

E. Engrand, A Boundary Layer Approach to the Calculation of Transverse Stresses along the Free Edges of a Symmetric Laminated Plate of Arbitrary Width Under In-plane Loading, Composite Structures, vol.198, pp.247-261, 1981.
DOI : 10.1007/978-94-009-8120-1_17

. Feng, Development of a method for predicting the fatigue life of CFRP components, International Conference on Comportement en fatigue de pièces épaisses en matériaux composites 221, 1997.

Y. Fish, J. Fish, and Q. Yu, Computational mechanics of fatigue and life predictions for composite materials and structures, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.43, pp.4827-4849, 2002.
DOI : 10.1016/S0045-7825(02)00401-2

. Fukunaga, Probabilistic Failure Strength Analyses of Graphite/Epoxy Cross-Ply Laminates, Journal of Composite Materials, vol.18, issue.4, pp.339-356, 1984.
DOI : 10.1177/002199838401800403

. Gamstedt, . Sjören, E. Gamstedt, and B. Sjören, An experimental investigation of the sequence effect in block amplitude loading of cross-ply composite laminates, International Journal of Fatigue, vol.24, issue.2-4, pp.437-446, 2002.
DOI : 10.1016/S0142-1123(01)00099-8

. Gamstedt, . Sjören, E. Gamstedt, and B. Sjören, Micromechanisms in tension-compression fatigue of composite laminates containing transverse plies, Composites Science and Technology, vol.59, issue.2, pp.167-178, 1999.
DOI : 10.1016/S0266-3538(98)00061-X

. Garret, . Bailey, K. Garret, and J. Bailey, Multiple transverse fracture in 90 ? cross-ply laminates of a glass fiber-reinforced polyester, Journal of Composite Materials, vol.12, pp.157-168, 1977.

P. Germain, Cours de Mécanique des Milieux Coninus, 1973.

P. Ghidossi, Contribution à l'étude de l'effet des conditions d'usinage d'éprouvettes en composite à matrice polymère sur leur réponse mécanique, 2003.

. Halpin, Characterization of Composites for the Purpose of Reliability Evaluation, ASTM STP 521, 1973.
DOI : 10.1520/STP36479S

Z. Hashin, Analysis of cracked laminates: a variational approach, Mechanics of Materials, vol.4, issue.2, pp.121-136, 1985.
DOI : 10.1016/0167-6636(85)90011-0

Z. Hashin, Analysis of Orthogonally Cracked Laminates Under Tension, Journal of Applied Mechanics, vol.54, issue.4, pp.872-849, 1987.
DOI : 10.1115/1.3173131

R. Hashin, Z. Hashin, and A. Rotem, A Fatigue Failure Criterion for Fiber Reinforced Materials, Journal of Composite Materials, vol.7, issue.4, pp.448-464, 1977.
DOI : 10.1177/002199837300700404

J. Hedgepeth, Stress concentrations in filamentary structures, NASA/TND 882, 1961.

V. Hedgepeth, . Dyke, J. Hedgepeth, and P. Van-dyke, Local stress concentrations in imperfect filamentary composite materials, Journal of Composite Materials, vol.1, pp.294-309, 1967.

. Henaff-gardin, Doubly periodic matrix cracking in composite laminates Part 1: General in-plane loading, Composite Structures, vol.36, issue.1-2, pp.113-130, 2002.
DOI : 10.1016/S0263-8223(96)00071-2

L. Henaff-gardin, C. Henaff-gardin, and M. Lafarie-frenot, The use of a characteristic damage variable in the syudy of transverse cracking development under fatigue loading in cross-ply laminates, International journal of solids and structures, vol.24, pp.389-395, 2002.

R. Biliographiques-[-henaff-gardin, Prediction of cracking evolution under uniaxial fatigue loading in cross-ply composite laminates, Comportement en fatigue de pièces épaisses en matériaux composites pastel-00677076 International Conference on fatigue of composites, pp.189-196, 1997.

R. Highsmith, A. Highsmith, and K. Reifsnider, Stiffness-Reduction Mechanisms in Composite Laminates, Damage in composite materials, pp.103-117, 1982.
DOI : 10.1520/STP34323S

. Hochard, 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.
DOI : 10.1016/S0266-3538(00)00199-8

C. Huchette, Sur la complémentarité des approches expérimentales et numériques pour la modélisation des mécanismes d'endommagement dans les composites stratifiés, 2005.

. Huchette, Identification et modélisation de l'influence de l'endommagement intralaminaire sur la propagation de délaminage dans les composites, Compte-rendu des 16 eme Journées Nationales sur les Composite, 2009.

L. Kachanov, On creep rutpure time, Proc. Acad. Sci, pp.26-31, 1958.

M. Kawai, Damage mechanics for off-axis fatigue behavior of unidirectionnal carbon fiber-reinforced composites at room and high temperatures, International Conference on Composite materials. Proceedings of the Twelfth International Conference on Composite Materials (ICCM 12), 1999.

. Kawai, . Honda, M. Kawai, and N. Honda, Off-axis fatigue behavior of a carbon/epoxy cross-ply laminate and predictions considering inelasticity and in situ strength of embedded plies, International Journal of Fatigue, vol.30, issue.10-11, pp.1743-1755, 2008.
DOI : 10.1016/j.ijfatigue.2008.02.009

. Kawai, . Kato, M. Kawai, and K. Kato, Effects of R-ratio on the off-axis fatigue behavior of unidirectional hybrid GFRP/Al laminates at room temperature, International Journal of Fatigue, vol.28, issue.10, pp.1226-1238, 2006.
DOI : 10.1016/j.ijfatigue.2006.02.020

. Kawai, . Taniguchi, M. Kawai, and T. Taniguchi, Off-axis fatigue behavior of plain weave carbon/epoxy fabric laminates at room and high temperatures and its mechanical modeling, Composites Part A: Applied Science and Manufacturing, vol.37, issue.2, pp.243-256, 2006.
DOI : 10.1016/j.compositesa.2005.07.003

. Kiewel, . Aktaa, H. Kiewel, J. Aktaa, and D. Munz, Application of an extrapolation method in thermocyclic failure analysis, Computer Methods in Applied Mechanics and Engineering, vol.182, issue.1-2, pp.55-71, 2000.
DOI : 10.1016/S0045-7825(99)00085-7

. Kim, Strength evaluation and failure analysis of unidirectional composites using Monte-Carlo simulation, Materials Science and Engineering: A, vol.340, issue.1-2, pp.33-40, 2003.
DOI : 10.1016/S0921-5093(02)00159-4

. Krajcinovic, . Fonseka, D. Krajcinovic, and G. Fonseka, The Continuous Damage Theory of Brittle Materials, Part 1: General Theory, Journal of Applied Mechanics, vol.48, issue.4, 1981.
DOI : 10.1115/1.3157739

R. Borderie, Computational modelling of concrete and reinforced concrete based on damage mechanics, Third International Conference of Computational Plasticity, pp.681-692, 1992.

P. Ladevèze, Sur la mécanique de l'endommagement des composites, Comptes-rendus des JNC 5, pp.667-683, 1986.

. Ladevèze, P. Ledantec-]-ladevèze, and E. Ledantec, Damage modelling of the elementary ply for laminated composites, Composites Science and Technology, vol.43, issue.3, pp.257-267, 1992.
DOI : 10.1016/0266-3538(92)90097-M

. Ladevèze, P. Lemaitre-]-ladevèze, and J. Lemaitre, Damage effective stress in quasi-unilateral condition, IUTAM Congress, 1984.

. Ladevèze, P. Lubineau-]-ladevèze, and G. Lubineau, On a damage mesomodel for laminates, Composites Science and Technology, vol.61, issue.15, pp.2149-2158, 2001.
DOI : 10.1016/S0266-3538(01)00109-9

. Lafarie-frenot, M. Henaff-gardin-]-lafarie-frenot, and C. Henaff-gardin, Analyse locale de la fissuration des plis à 90° de stratifiés croisés carbone/epoxy, Comptes Rendus des 7 eme Journées Nationales sur les Composites, 1990.

. Lafarie-frenot, Matrix cracking induced by cyclic ply stresses in composite laminates, Composites Science and Technology, vol.61, issue.15, pp.2327-2336, 2001.
DOI : 10.1016/S0266-3538(01)00125-7

M. Lafarie-frenot and N. Ho, Influence of free edge intralaminar stresses on damage process in CFRP laminates under thermal cycling conditions, Composites Science and Technology, vol.66, issue.10, pp.1354-1365, 2006.
DOI : 10.1016/j.compscitech.2005.09.006

D. Laroche, Accumulation d'endommagement dans le carbone époxyde détecté par emission acoustique, 1980.

B. Laws, 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.
DOI : 10.1016/0020-7683(87)90104-1

D. Laws, N. Laws, and G. Dvorak, The loss of stiffness of cracked laminates, pp.119-127, 1985.

D. Laws, N. Laws, and G. Dvorak, Progressive Transverse Cracking In Composite Laminates, Journal of Composite Materials, vol.22, issue.10, pp.900-916, 1988.
DOI : 10.1177/002199838802201001

M. Levesque, L'essai de traction de matériaux composites à fibres continues, 2000.

. Li, On matrix crack saturation in composite laminates, Composites Part B: Engineering, vol.34, issue.5, pp.473-480, 2003.
DOI : 10.1016/S1359-8368(03)00020-9

H. Lim, S. Lim, and C. Hong, Prediction of Transverse Cracking and Stiffness Reduction in Cross-Ply Laminated Composites, Journal of Composite Materials, vol.20, issue.5, pp.695-713, 1989.
DOI : 10.1177/002199838902300704

R. Biliographiques and . Macquire, Experimental and theorical damage acumulation in glass-epoxy tubes under torsion loading, Comportement en fatigue de pièces épaisses en matériaux composites pastel-00677076, pp.174-193, 1992.

. Manders, Statistical analysis of multiple fracture in 0???/90???/0??? glass fibre/epoxy resin laminates, Journal of Materials Science, vol.153, issue.10, pp.2876-2889, 1983.
DOI : 10.1007/BF00700768

. Mercier, Introduction à la science des matériaux, Traité des matériaux, 1999.

. Miner, Fatigue damage detection in graphite/epoxy composites using sonic infrared imaging technique, Composites Sciences and Technology, vol.64, pp.657-666, 2004.

K. Miner, Cumulative damage in fatigue, Journal of Applied Mechanics, vol.67, pp.159-164, 1945.

J. Nairn, Comprehensive Composite Materials, 2000.

H. Nairn, J. Nairn, and . Hu, The initiation and growth of delaminations induced by matrix microcracks in laminated composites, International Journal of Fracture, vol.41, issue.1, pp.1-24, 1992.
DOI : 10.1007/BF00013005

. Nairn, A critical evaluation of theories for predicting microcracking in composite laminates, Journal of Materials Science, vol.6, issue.18, pp.5099-5111, 1993.
DOI : 10.1007/BF00361186

J. Nairn, Some new variational mechanics results on composite microcracking, pp.14-18, 1995.

T. Nuismer, R. Nuismer, and S. Tan, Constitutive Relations of a Cracked Composite Lamina, Journal of Composite Materials, vol.22, issue.4, pp.306-321, 1988.
DOI : 10.1177/002199838802200401

. Ogihara, Effects of stacking sequence on microscopic fatigue damage development in quasi-isotropic CFRP laminates with interlaminar-toughened layers, Composites Science and Technology, vol.59, issue.9, pp.1387-1398, 1998.
DOI : 10.1016/S0266-3538(98)00180-8

. Okabe, Numerical modeling of progressive damage in fiber reinforced plastic cross-ply laminates, Composites Science and Technology, vol.68, issue.10-11, pp.2282-2289, 2008.
DOI : 10.1016/j.compscitech.2008.04.021

. Parvizi, Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates, Journal of Materials Science, vol.8, issue.1, pp.195-201, 1978.
DOI : 10.1007/BF00739291

J. Payan, Étude du comportement de composites stratifiés sous chargement statique et de fatigue, 2004.

H. Payan, J. Payan, and C. Hochard, Damage modelling of laminated carbon/epoxy composites under static and cyclic loadings, International journal of solids and structures, vol.24, pp.299-306, 2002.

E. Petitpas, Comportement et endommagement des matériaux composites stratifiés, 1993.

R. Biliographiques and . Petitpas, La fatigue des stratifiés carbone/résine : étude du mode de fissuration transverse, Communication au groupe Fragilité/Rupture, pp.14-18, 1987.

V. Philippidis, T. Philippidis, and A. Vassilopoudos, Fatigue of composite laminates under off-axis loading, International Journal of Fatigue, vol.21, issue.3, pp.253-362, 1999.
DOI : 10.1016/S0142-1123(98)00073-5

. Pipes, . Pagano, R. Pipes, and N. Pagano, Interlaminar Stress in Composite Laminates under Uniform Axial Tension, Journal of Composite Materials, vol.7, 1970.

E. Puppo, A. Puppo, and H. Evensen, Interlaminar Shear in Laminated Composites Under Generalized Plane Stress, Journal of Composite Materials, vol.3, issue.2, pp.204-220, 1970.
DOI : 10.1177/002199837000400206

Y. Rabotnov, Creep rupture, Proceedings of the XII International Congress on Applied Mechanics, 1968.
DOI : 10.1007/978-3-642-85640-2_26

J. Rebiere, Evolution de l'endommagement par fissuration et délaminage dans les stratifiés croisés à l'aide d'une approche variationnelle, Proceedings de la conférence Matériaux, 2002.

K. Reifsnider, Some fundamental aspects of fatigue and fracture response of composite materials, Proceedings of the 14 th Meeting of Society of Engineering Science, pp.373-384, 1977.

. Reifsnider, K. Stinchcomb-]-reifsnider, and W. Stinchcomb, A Critical-Element Model of the Residual Strength and Life of Fatigue-Loaded Composite Coupons, Composite Materials : Fatigue and Fracture, Thomas Haln.H Ed., ASTM STP 907, pp.298-313, 1986.
DOI : 10.1520/STP19992S

T. Rossignol, J. Rossignol, and A. Thionnet, Une nouvelle technique de d??tection des endommagements dans les composites bas??e sur l'utilisation des micro-ondes et des circuits microrubans r??sonants, Comptes Rendus M??canique, vol.334, issue.12, pp.719-724, 2006.
DOI : 10.1016/j.crme.2006.10.003

. Scarponi, . Briotti, C. Scarponi, and G. Briotti, Ultrasonic technique for the evaluation of delaminations on CFRP, GFRP, KFRP composite materials, Composites Part B: Engineering, vol.31, issue.3, pp.237-243, 2000.
DOI : 10.1016/S1359-8368(99)00076-1

. Schilling, X-ray computed microtomography of internal damage in fiber reinforced polymer matrix composites, Composites Science and Technology, vol.65, issue.14, pp.2071-2078, 2005.
DOI : 10.1016/j.compscitech.2005.05.014

. Sedrakian, A numerical model of fatigue behaviour for composite plates : application to a three point bending test, International Conference on fatigue of composites La Socété Française de Métallurgie et des Matériaux. Proceedings, pp.415-423, 1997.

. Sedrakian, Contribution of industrial composite parts to fatigue behaviour simulation, International Journal of Fatigue, vol.24, issue.2-4, pp.307-318, 2002.
DOI : 10.1016/S0142-1123(01)00086-X

R. Biliographiques, . Shokrieh, . Lessard, M. Shokrieh, and L. Lessard, Multiaxial fatigue behaviour of unidirectional plies based on uniaxial fatigue experiments -1. modelling, Comportement en fatigue de pièces épaisses en matériaux composites pastel-00677076, pp.201-207, 1997.

S. Sidoroff, F. Sidoroff, and B. Subagio, Fatigue damage modelling of composite materials from bending tests, Second European Conference on Composite Materials (ECCM-II), pp.4-32, 1987.

. Sihn, Experimental studies of thin-ply laminated composites, Composites Science and Technology, vol.67, issue.6, pp.996-1008, 2007.
DOI : 10.1016/j.compscitech.2006.06.008

. Smith, A comparison of transverse cracking phenomena in (0/90) s and (90/0) s CFRP lamintes, Applied Composite Materials, vol.5, issue.1, pp.11-23, 1998.
DOI : 10.1023/A:1008847528988

. Spearing, . Beaumont, . Spearing, and L. Beaumont, Fatigue damage mechanics of composite materials Part III: Prediction of post-fatigue strength, Composites Science and Technology, vol.44, issue.4, pp.299-307, 1992.
DOI : 10.1016/0266-3538(92)90067-D

W. Stinchcomb, Nondestructive evaluation of damage accumulation processes in composite laminates, Composites Science and Technology, vol.25, issue.2, pp.103-118, 1986.
DOI : 10.1016/0266-3538(86)90037-0

R. Talreja, Transverse Cracking and Stiffness Reduction in Composite Laminates, Journal of Composite Materials, vol.19, issue.4, pp.355-375, 1985.
DOI : 10.1177/002199838501900404

R. Talreja, Stiffness properties of composite laminates with matrix cracking and interior delamination, Engineering Fracture Mechanics, vol.25, issue.5-6, pp.751-762, 1986.
DOI : 10.1016/0013-7944(86)90038-X

. Tang, An appropriate stiffness degradation parameter to monitor fatigue damage evolution in composites, International Journal of Fatigue, vol.26, issue.4, pp.421-427, 2004.
DOI : 10.1016/j.ijfatigue.2003.07.003

A. Thionnet, Prévision d'endommagement sous chargements quasi-statiques et cycliques des structures composites stratifiées, 1991.

. Thionnet, A theoretical and experimental study to point out the notion of loading mode in damage mechanics : Application to the identification and validation of a fatigue damage modelling for laminates composites, International journal of solids and structures, vol.24, pp.147-154, 2002.

M. Thionnet, A. Thionnet, and M. , Mécanique et comportement des milieux continus, Concepts Généraux, Editions Ellipses, vol.1, 2004.

M. Thionnet, A. Thionnet, and C. Martin, A new constructive method using the theory of invariants to obtain material behavior laws, International Journal of Solids and Structures, vol.43, issue.2, pp.325-345, 2006.
DOI : 10.1016/j.ijsolstr.2005.05.021

URL : https://hal.archives-ouvertes.fr/hal-00157256

. Thionnet, Mécanique et comportement des milieux continus, Applications et théorie des invariants, Editions Ellipses, vol.2, 2004.

A. Thionnet and J. Renard, Meso-macro approach to transverse cracking in laminated composites using Talreja's model, Composites Engineering, vol.3, issue.9, pp.851-871, 1993.
DOI : 10.1016/0961-9526(93)90044-K

R. Thionnet, A. Thionnet, and J. Renard, Une étude théorique et expérimentale pour mettre en évidence la notion de mode en mécanique de l'endommagement, pp.349-364, 2001.

D. Valentin, Etude par émission acoustique de l'endommagement sous sollicitations mécaniques des composites carbone-époxy, 1983.

. Valentin, D. Valentin, and A. Bunsell, A Study of Damage Accumulation in Carbon Fibre Reinforced Epoxy Resin Structures During Mechanical Loading Monitored By Acoustic Emission, Journal of Reinforced Plastics and Composites, vol.1, issue.4, pp.314-334, 1982.
DOI : 10.1177/073168448200100403

. Van-paepegem, . Degriek, W. Van-paepegem, and J. Degriek, Modelling strategies for fatigue damage behaviour fibre-reinforced polymer composites, European Journal of Mechanical and Environmental Engineering, vol.46, issue.4, pp.217-227, 2001.

. Van-paepegem, . Degriek, W. Van-paepegem, and J. Degriek, A new coupled approach of residual stifness and strength for fatigue of fibre-reinfored composites, International journal of solids and structures, vol.24, pp.747-762, 2002.

B. Varna, J. Varna, and L. Berglund, A Model for Prediction of the Transverse Cracking Strain in Cross-Ply Laminates, Journal of Reinforced Plastics and Composites, vol.11, issue.7, pp.708-728, 1992.
DOI : 10.1177/073168449201100701

. Vieillevigne, Modelling of the fatigue behaviour of an unidirectional glass epoxy composite submitted to fatigue loadings, International Conference on fatigue of composites La Société Française de Métallurgie et des Matériaux. Proceedings, pp.424-430, 1997.

D. Violeau, Une stratégie de calcul pour l'analyse à l'échelle "micro" des endommagements jusqu'à rupture des composites stratifiés, 2007.

C. Wang, A. Wang, and F. Crossman, Initiation and Growth of Transverse Cracks and Edge Delamination in Composite Laminates Part 1. An Energy Method, Journal of Composite Materials, vol.14, issue.1, pp.71-87, 1980.
DOI : 10.1177/002199838001400106

. Wevers, Processing of transient signals from damage in CFRP composite materials monitored with embedded intensity-modulated fiber optic sensors, NDT & E International, vol.39, issue.3, pp.229-235, 2006.
DOI : 10.1016/j.ndteint.2005.07.008

J. Whitney, Fatigue Characterization of Composite Materials, In : Fatigue of Fibrous Materials, Lauratis KN. Ed., ASTM STP, vol.723, pp.133-151, 1981.
DOI : 10.1520/STP27618S

E. Wu, Application of Fracture Mechanics to Anisotropic Plates, Journal of Applied Mechanics, vol.34, issue.4, pp.1003-1010, 1967.
DOI : 10.1115/1.3607864

R. Biliographiques and L. Xu, Interaction between matrix cracking and edge delamination in composite laminates, Comportement en fatigue de pièces épaisses en matériaux composites pastel-00677076, pp.469-478, 1994.

L. Ye and B. Yang, A boundary layer approach to interlaminar stresses in composite with curved edges, Journal of Reinforced Plastics and Composites, vol.7, pp.179-198, 1988.

. Yokozeki, Consecutive matrix cracking in contiguous plies of composite laminates, International Journal of Solids and Structures, vol.42, issue.9-10, pp.2785-2802, 2005.
DOI : 10.1016/j.ijsolstr.2004.09.040