.. .. Généralités,

. .. Méthode-du-krigeage,

.. .. Influence,

, Influence de substrats composites sur la tenue mécanique d'un assemblage collé

.. .. Conclusions,

, Plusieurs méthodes existent afin d'évaluer la robustesse de la surface de réponse obtenue

L. Dans-cette-partie and . Valeur, Afin de garantir que la solution interpolée décrit de manière fidèle la "vraie" surface de réponse, on peut effectuer tous les calculs pour connaître, en tout point du domaine, la "vraie" valeur issue du modèle de ruine. Il est évident que d'un point de vue industriel cette solution n'est pas envisageable, vraie" est définie comme le résultat de la prévision de la rupture calculée à l'aide du modèle

, Une seconde surface est alors construite avec une population réduite (n ? p) de points de mesure, consiste à retirer des points de mesure utilisés pour générer la première surface de réponse avec n points de mesure

, Une éprouvette collée tubulaire bout à bout présente alors un fort intérêt pour mener ce type d'étude puisque la surface collée reste relativement importante comme l'ont montré Arnaud

, Des sollicitations en torsion, et en traction/torsion combinées ou découplées sont également possibles. L'intérêt majeur avec cette géométrie d'éprouvette est de pouvoir étudier l'influence d'un chargement multi-axial non-proportionnel. L'ajout de becs réduisant le phénomène d'effets de bords a été étudié par Arnaud et al. (ACC14) qui a montré un fort potentiel pour l'identification du comportement d'un joint de colle en complément de l'essai Arcan modifié utilisé classiquement. Le travail de conception réalisé permet d'envisager l'analyse du comportement en fatigue d'un assemblage collé. En effet, le montage de sollicitation de l'éprouvette tubulaire permet une sollicité complexe de celle-ci

. Bibliographie,

A. Fallahi, A. , and A. Baladi, The Effects of Materials Properties & Angle Junction on Stress Concentration at Interface of Dissimilar Materials, Advanced Materials Research, issue.7, pp.887-892, 2011.

R. D. Adams and J. Coppendale, Measurement of the Elastic Moduli Resonant Bar Technique, Journal Mechanical Engincering Science, vol.18, 1976.

N. Arnaud, R. Créac'hcadec, and J. , Cognard : A tension/compressiontorsion test suited to analyze the mechanical behaviour of adhesives under non-proportional loadings, International Journal of Adhesion and Adhesives, vol.53, pp.3-14, 2014.

N. Arnaud, R. Créac'hcadec, and J. Y. , Cognard : Identification of the Elastic-Plastic Behavior of Adhesively Bonded Structures Under Multi-Axial Loadings : Comparison of a Modified Arcan Test and a Tension/Compression-Torsion Test, The Journal of Adhesion, vol.91, issue.8, 2015.

R. D. Adams, J. Coppendale, and N. Peppiatt, Stress analysis of axisymmetric butt joints loaded in torsion and tension, The Journal of Strain Analysis for Engineering Design, vol.13, issue.1, pp.1-10, 1978.

R. D. , Adams : Testing of bonded joints. Industrial applications of adhesive bonding, pp.69-87, 1987.

M. Arnaud and X. Emery, Estimation et interpolation spatiale, Hermes sci édition, 2000.

R. D. Adams and J. A. Harris, The influence of local geometry on the strength of adhesive joints, International Journal of Adhesion and Adhesives, vol.7, issue.2, pp.69-80, 1987.

L. Alfonso, Characterization and modeling of multi-material assemblies under mixed quasi-static loadings for the design of automotive structures, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01453047

R. D. Adams and V. Mallick, A Method for the Stress Analysis of Lap Joints, The Journal of Adhesion, vol.38, pp.199-217, 1992.

W. Althof and . Neumann, Verfahren zur Ermittlung von SchubspannungsGleitungs-Diagrammen von Konstruktions. Klebstoffen in dünnen Klebschichten, 1974.

R. D. Adams and N. A. Peppiatt, Stress Analysis of Adhesive Bonded Tubular Lap Joints, vol.9, pp.1-18, 1977.

, Arnovljevic : Das Verteilungsgesetz der Tiefspannungen in axial beanspruchten Verbundstaben, Z. F. Archund-Ing-Wesen, vol.55, p.415, 1909.

, ASTM : Adhesively bonded joints : Testing, analysis and Design, volume STP 981, 1988.

S. Baillargeon, Le krigeage : revue de la théorie et application à l'interpolation spatiale de données de précipitations, 2005.

J. Besson, G. Cailletaud, J. Chaboche, and S. Forest, Mécanique non linéaire des matériaux. Coll. etud édition, 2001.

R. Bryant and W. Dukes, The measurement of the shear strength of adhesive joints in torsion The measurement of the shear strength of adhesive joints in torsion, British Journal of Applied Physics, vol.16, issue.101, 1965.

J. Berthelot, Mécanique des Matériaux et Structures Composites, 2013.

J. J. Bikerman, Effect of impurities on polyethylene recycling, Journal of Applied Chemistry, vol.11, pp.81-85, 1961.

J. A. Barnes, M. Kumosa, and D. Hull, Theoretical and Experimental Evaluation of the Iosipescu Shear Test, Composites Science and Technology, vol.28, pp.251-268, 1987.

C. John, . Brewer, A. Paul, and . Lagace, Quadratic Stress Criterion for Initiation of Delamination NGINEERS, Journal of composite materials, vol.22, pp.1141-1155, 1988.

K. Bodjona, L. Lessard, ;. Barthlott, C. Neinhuis, . Jetter et al., Nonlinear static analysis of a composite bonded/bolted single-lap joint using the meshfree radial point interpolation method, Composite Structures, vol.134, issue.2, pp.169-174, 1996.

A. Barroso, F. París, and V. Manti?, Representativity of the singular stress state in the failure of adhesively bonded joints between metals and composites, Composites Science and Technology, vol.69, pp.1746-1755, 2009.

G. Bresson, Collage fiable pour l'espace : influence de la qualité des procédés et dimensionnement des assemblages, L'université bordeaux 1, 2011.

T. Kevin and O. Brien, Characterization of delamination onset and growth in a composite laminate, Damage in Composite in Materials, pp.140-167, 1982.

L. Banks-sills, Application of the finite element method to linear elastic fracture mechanics, Applied Mechanics Review, vol.44, issue.10, pp.447-461, 1991.

D. Bogy and K. Wang, Stress singularities at interface corners in bonded dissimilar isotropic elastic materials, International Journal of Solids and Structures, vol.7, issue.8, pp.993-1005, 1971.

Z. Chen, R. D. Adams, and F. M. Lucas, International Journal of Adhesion & Adhesives The use of the J -integral vector to analyse adhesive bonds with and without a crack, International Journal of Adhesion and Adhesives, vol.31, issue.1, pp.48-55, 2011.

N. Carrere, C. Badulescu, J. Y. Cognard, and D. Leguillon, 3D models of specimens with a scarf joint to test the adhesive and cohesive multi-axial behavior of adhesives, International Journal of Adhesion and Adhesives, vol.62, pp.154-164, 2015.

]. J. +-14, C. Cognard, J. Badulescu, R. Maurice, N. Créac'hcadec et al., On modelling the behaviour of a ductile adhesive under low temperatures, International Journal of Adhesion and Adhesives, vol.48, pp.119-129, 2014.

D. Chen and S. Cheng, Torsional stress in tubular lap joints, International Journal of Solids and Structures, vol.29, issue.7, pp.845-853, 1991.

. Y. Ccds-+-11]-j, R. Cognard, L. F. Créac'hcadec, F. G. Silva, P. Teixeira et al., Experimental Analysis on the Influence of Hydrostatic Stress on the Behaviour of an Adhesives Using a Pressure Vessel, The Journal of Adhesion, vol.87, issue.7, pp.1-16, 2011.

W. K. Chiu, P. D. Chalkley, and R. Jones, Effect of temperature on the shear stress strain behaviour of structural adhesives (FM73), vol.53, pp.483-489, 1994.

J. Y. Cognard, R. Créac'hcadec, L. Sohier, and P. Davies, Analysis of the nonlinear behavior of adhesives in bonded assemblies-Comparison of TAST and Arcan tests, International Journal of Adhesion and Adhesives, vol.28, issue.8, pp.393-404, 2008.

J. Y. Cognard, R. Créac'hcadec, L. Sohier, and D. Leguillon, Influence of adhesive thickness on the behaviour of bonded assemblies under shear loadings using a modified TAST fixture, International Journal of Adhesion and Adhesives, vol.30, issue.5, pp.257-266, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00489162

S. Hwu-chyanbin-et-jian and . Hu, Stress intensity factors and energy release rates of delaminations in composite laminates, Engineering Fracture Mechanics, vol.42, issue.6, pp.977-988, 1992.

P. Chauvet, Aide-mémoire de la géostatistique linéaire, 2008.

G. Cherepanov, Crack propagation in continuous media, Journal of Applied Mathematics and Mechanics, vol.31, issue.3, pp.503-512, 1967.

T. Choon and . Chon, Analysis of Tubular Lap Joint in Torsion, Journal Composite Materials, vol.16, pp.268-284, 1982.

J. L. Clarke, Structural design of polymer composites eurocomp design code and handbook, vol.35, 1996.

N. Carrere, E. Martin, and D. Leguillon, Comparison between models based on a coupled criterion for the prediction of the failure of adhesively bonded joints, Engineering Fracture Mechanics, vol.138, pp.185-201, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01213277

M. Callies and D. Quéré, On water repellency. Soft Matter, vol.1, issue.1, p.55, 2005.

R. Créac, Hcadec : Analyse et modélisation du comportement non linéaire d ' assemblages collés pour application marine, 2008.

T. A. Cruse, Strength of Notched Composites, Journal of Composite Materials, vol.7, pp.218-229, 1973.

R. Créac'hcadec, L. Sohier, C. Cellard, and B. Gineste, A stress concentration-free bonded arcan tensile compression shear test specimen for the evaluation of adhesive mechanical response, International Journal of Adhesion and Adhesives, vol.61, pp.81-92, 2015.

C. John, . Davis-;-ludovic, B. Dufour, F. Bourel, G. Lauro et al., Gregory Haugou et Nicolas Leconte : International Journal of Adhesion & Adhesives A viscoelastic -viscoplastic model with non associative plasticity for the modelling of bonded joints at high strain rates, Statistics and data analysis in geology. Statistics and Data Analysis in Geology, vol.70, pp.304-314, 1986.

E. Darque-cerreti and B. Monasse, Assemblage des matériaux par collage. Techniques de l'ingénieur, vol.33, 2008.

E. Dragoni and L. Goglio, Adhesive stresses in axially-loaded tubular bonded joints -Part I : Critical review and finite element assessment of published models, International Journal of Adhesion and Adhesives, vol.47, pp.35-45, 2013.

J. Dundurs and M. S. Lee, Stress concentration at a sharp edge in contact problems, Journal of Elasticity, vol.2, issue.2, pp.109-112, 1972.

S. Ding, L. Meekisho, and M. Kumosa, Analysis of stress singular fields at a bimaterial wedge corner, Engineering Fracture Mechanics, vol.49, issue.4, pp.569-585, 1994.

V. B-v-derjaguin, Y. Muller, and . Toporov, Effect of contact deformation on the adhesion of particles, Journal of colloid and interface science, vol.52, issue.3, pp.105-108, 1975.

A. Doitrand, Endommagement à l'échelle mésoscopique et son influence sur la tenue mécanoique des matériaux composites tissés, 2017.

D. C. Drucker and W. Prager, Soil Mechanics and Plastic Analysis or Limit Design, Quarterly of Applied Mathematics, vol.10, issue.2, pp.157-165, 1952.

F. Lucas, P. J. Silva, R. D. Das-neves, A. Adams, and J. Wang, Spelt : Analytical models of adhesively bonded joints-Part II : Comparative study, International Journal of Adhesion and Adhesives, vol.29, issue.3, pp.331-341, 2009.

F. Lucas, P. J. Silva, R. D. Das-neves, and J. Adams, Spelt : Analytical models of adhesively bonded joints-Part I : Literature survey, International Journal of Adhesion and Adhesives, vol.29, issue.3, pp.319-330, 2009.

L. F. Silva, R. A. Silva, J. A. Chousa, and A. M. Pinto, Alternative Methods to Measure the Adhesive Shear Displacement in the Thick Adherend Shear Test, Journal of Adhesion Science and Technology, vol.22, issue.1, pp.15-29, 2008.

D. A. Dillard, H. K. Singh, D. J. Pohlit, and J. M. Starbuck, Observations of Decreased Fracture Toughness for Mixed Mode Fracture Testing of Adhesively Bonded Joints, Journal of Adhesion Science and Technology, vol.23, pp.1515-1530, 2009.

F. M. Lucas, T. N. Silva, M. A. Rodrigues, M. F. Figueiredo, and J. A. De-moura, Chousal : Effect of Adhesive Type and Thickness on the Lap Shear Strength, The Journal of Adhesion, vol.82, pp.1091-1115, 2006.

R. T. Gürdal, P. Haftka, and . Hajela, Design and optimisation of laminated composite materials, 1999.

B. Gineste, Assemblages de structures en materiaux composites par stratification d'un element de liaison caracterisation de l'endommagement, 1993.

L. Gornet, S. Kamran-ali, L. Sohier, M. S. , J. Y. Cognard et al., Modelling of the mechanical behaviour of nomex cores using tensile shear tests under out-of-plane loadings, 14th European Conference on Composite Materials, 2010.

M. Goland and E. Reissner, The stresses in cemented joints, Journal of Applied Mechanics, vol.66, issue.A17, 1944.

Y. Gilibert and A. Rigolot, Théorie élastique de l'assemblage collé à double recouvrement : utilisation de la méthode des développements asymptotiques raccordés au voisinage des extrémités, Materials and Structures, vol.18, issue.5, pp.363-387, 1985.

Y. Gratton, Le krigeage : la méthode optimale d'interpolation spatiale. Les articles de l'Institut d'Analyse Géographique, pp.1-4, 2002.

M. Greiveldinger, Mecanismes d'Adhésion Sur Tôles Grasses, 2000.

A. A. Griffith, The phenomena of flow and rupture in solids, Philosophical Transactions of the Royal Society A, vol.221, pp.163-198, 1920.

H. L. Groth, Stress singularities and fracture at interface corners in bonded joints, International Journal of Adhesion and Adhesives, vol.8, issue.2, pp.107-113, 1988.

J. A. Harris and R. A. Adams, Strength prediction of bonded single lap joints by non-linear finite element methods, International Journal of Adhesion and Adhesives, vol.4, issue.2, pp.65-78, 1984.

S. Hedan, Mesures par voie optique de champs cinématiques pour l'étude du comportement de plaques élastiques fissurées et chargées en mode I, formulation des déplacements 2D par confrontation numérique-expérience en statique, analyse des effets 3D en dynamique, 2008.

R. W. , Hertzberg : Deformation and fracture mechanics of engineering materials, Wiley édition, 1989.

M. Herbreteau, P. Jouannigot, . Weisbecker, . Coradi, and . Martin, a New Push-Out Procedure for the Evaluation of Interfacial Properties of Sic / Sic Composites. ECCM15 -15TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, pp.24-28, 2012.

W. E. Howell, NASA TECHNICAL MEMORANDUM NASA TM X-71995 BONDED COMPOSITE-TO-METAL SCARF JOINT PERFORMANCE IN AN AIRCRAFT LANDING GEAR DRAG STRUT, 1974.

M. Hajianmaleki, S. Mohammad, and . Qatu, Mechanics of Composite Beams. Advances in Composite Materials -Analysis of Natural and ManMade Materials, pp.527-546, 2011.

L. J. Hart-smith, , 1973.

L. J. Hart-smith, Analysis and design of advanced composite bounded joints, 1974.

S. Hell, P. Weißgraeber, J. Felger, W. Becker-;-a-ilioni, N. Badulescu et al., A viscoelastic-viscoplastic model to describe creep and strain rate e ff ects on the mechanical behaviour of adhesively-bonded assemblies, International Journal of Adhesion and Adhesives, vol.117, pp.112-126, 2014.

A. Iloni, P. Y. Le-gac, C. Badulescu, D. Thévenet, and P. Davies, Prediction of mechanical behaviour of a bulk epoxy adhesive in marine environnement, Journal of Adhesion, 2017.

C. E. Inglis, Stresses in a plate due to the presence of cracks and sharp corners, Trans. Inst. Naval Arch, vol.55, pp.219-239, 1913.

T. Iwamoto, T. Nagai, and T. Sawa, Experimental and computational investigations on strain rate sensitivity and deformation behavior of bulk materials made of epoxy resin structural adhesive, International Journal of Solids and Structures, vol.47, issue.2, pp.175-185, 2010.

G. R. Irwin, Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate, Journal of Applied Mechanics, vol.24, pp.361-364, 1957.

J. Jumel, M. K. Budzik, N. Salem, and M. E. Shanahan, Instrumented end notched flexure -Crack propagation and process zone monitoring. Part I : Modelling and analysis, International Journal of Solids and Structures, vol.50, issue.2, pp.297-309, 2013.

J. Jumel, M. K. Budzik, N. Salem, and M. E. Shanahan, Instrumented end notched flexure -Crack propagation and process zone monitoring. Part I : Modelling and analysis, International Journal of Solids and Structures, vol.50, issue.2, pp.297-309, 2013.

G. R. Johnson and W. H. Cook, FRACTURE CHARACTERISTICS OF THREE METALS SUBJECTED TO VARIOUS STRAINS, vol.21, pp.31-48, 1985.

J. P. Jeandrau, Analysis and design data for adhesively bonded joints, International Journal of Adhesion and Adhesives, vol.11, issue.2, pp.71-79, 1991.

S. Joannes, Caractérisation mécanique et outil d'aide au dimensionnement des collages structuraux, 2007.

K. L. Jerina and P. C. Paris, Fatigue and Fracture Mechanics, Fatigue and Fracture Mechanics, chapitre Fractures, p.347, 2000.

V. K. Kryzhanovskii, V. V. Burlov, A. D. Semenova, . V. Yu, and . Zhorova, Improved method for determining the glass transition temperature of highly cross-linked polymers by thermomechanical means, Polymer Science Series D, vol.5, issue.3, pp.190-194, 2012.

A. J. Kinloch, Adhesion and Adhesives, 1987.

S. Kumar and M. A. Khan, An elastic solution for adhesive stresses in multimaterial cylindrical joints, International Journal of Adhesion and Adhesives, vol.64, pp.142-152, 2016.

S. Krenk, Energy release rate of symmetric adhesive joints, Engineering Fracture Mechanics, vol.43, issue.4, pp.549-559, 1992.

. D-g-krige, A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand, Journal of the Chemical, pp.201-215, 1952.

R. B. Jr and . Krieger, Stiffness Characteristics of Structural Adhesives for Stress Analysis in Hostile. Environment, 1975.

R. Krueger, Virtual crack closure technique : History , approach , and applications, Applied Mechanics Review, vol.57, issue.2, pp.109-143, 2004.

E. W. Kuenzi and G. H. , Stevens : Determination of Mechanical Properties of Adhesives for Use in the design of bonded joints, 1963.

S. Kumar and J. P. Scanlan, On axisymmetric adhesive joints with graded interface stiffness, International Journal of Adhesion and Adhesives, vol.41, pp.57-72, 2013.

E. Paul, M. L. Labossiere, and . Dunn, Fracture initiation at threedimensional bimaterial interface corners, Journal of the Mechanics and Physics of Solids, vol.49, issue.3, pp.609-634, 1998.

J. B. Leblond, Mécanique de la rupture fragile et ductile. Hermes sci édition, 2003.

D. Leguillon, Strength or toughness ? A criterion for crack onset at a notch, European Journal of Mechanics, A/Solids, vol.21, issue.1, pp.61-72, 2002.

G. Lelias, E. Paroissien, F. Lachaud, J. Morlier, S. Schwartz et al., An extended semi-analytical formulation for fast and reliable mode I/II stress analysis of adhesively bonded joints, International Journal of Solids and Structures, vol.62, pp.18-38, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01514904

F. Lapique and K. Redford, Curing effects on viscosity and mechanical properties of a commercial epoxy resin adhesive, International Journal of Adhesion and Adhesives, vol.22, issue.4, pp.337-346, 2002.

E. Lubkin and J. L. , Reisssner : Stress distribution and design data for adhesive lap joints between circular tubes, Transactions ASME, vol.78, pp.1213-1221, 1956.

R. Mahnken, Simulation of strength difference for adhesive materials in finite deformation elasto-plasticity, Comput. Methods Appl. Mech. Engrg, vol.194, pp.4097-4114, 2005.

R. Mahnken, Simulation of strength difference coupled to softening in elasto-plasticity for adhesive materials, International Journal of Adhesion and Adhesives, vol.32, pp.1-14, 2012.

O. Mario, Etude du vieillissement des assemblages structuraux acier / aluminium : influence de l ' environnement sur le dimensionnement, 2007.
URL : https://hal.archives-ouvertes.fr/tel-00273203

G. Matheron, Le krigeage universel, 1969.

J. Maurice, Characterization and modeling of the 3D elastic-plastic behavior of structural adhesive filmd for aeronautical applications

N. Moës, A. Gravouil, and T. Belytschko, Non-planar 3D crack growth by the extended finite element and level sets-Part I : Mechanical model, International Journal for Numerical Methods in Engineering, vol.53, issue.11, pp.2549-2568, 2002.

J. W. Mcbain and D. G. Hopkins, On Adhesives and Adhesive Action, Journal of Physical Chemistry, vol.29, issue.2, pp.188-204, 1925.

D. Morin, . Haugou, . Bennani, and . Lauro, Identification of a new failure criterion for toughened epoxy adhesive, Engineering Fracture Mechanics, vol.77, issue.17, pp.3481-3500, 2010.

A. Moradi, D. Leguillon, and N. Carrère, Influence of the adhesive thickness on a debonding -An asymptotic model, Engineering Fracture Mechanics, vol.114, pp.55-68, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00978658

R. Mahnken and M. Schlimmer, Simulation of strength difference coupled to softening in elasto-plasticity for adhesive materials, International Journal for Numerical Methods in Engineering, vol.63, pp.1461-1477, 2005.

S. Murakami, Y. Sekiguchi, C. Sato, E. Yokoi, and T. Furusawa, Strength of cylindrical butt joints bonded with epoxy adhesives under combined static or high-rate loading, International Journal of Adhesion and Adhesives, vol.67, pp.86-93, 2015.

H. Nayeb-hashemi, J. N. Rossettos, and A. P. Melo, Multiaxial fatigue life evaluation of tubular adhesively bonded joints, International Journal of Adhesion and Adhesives, vol.17, issue.1, pp.55-63, 1997.

O. Nemes, . Lachaud, and . Mojtabi, Contribution to the study of cylindrical adhesive joining, International Journal of Adhesion and Adhesives, vol.26, issue.6, pp.474-480, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00967373

T. Nao-aki-noda, R. Miyazaki, T. Li, Y. Uchikoba, and . Sano, Adhesives Debonding strength evaluation in terms of the intensity of singular stress at the interface corner with and without fi ctitious crack, International Journal of Adhesion and Adhesives, vol.61, pp.46-64, 2015.

A. Öchsner, M. Stasiek, G. Mishuris, and J. Grácio, A new evaluation procedure for the butt-joint test of adhesive technology : Determination of the complete set of linear elastic constants, International Journal of Adhesion and Adhesives, vol.27, issue.8, pp.703-711, 2007.

E. Paroissien, Contribution aux assemblages hybrides (boulonnées/collés) -Application aux jonctions aéronautiques, 2007.

N. Pugno and A. Carpinteri, Tubular Adhesive Joints Under Axial Load, vol.70, p.832, 2003.

A. Parvizi, K. W. Garrett, and J. E. Bailey, Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates, Journal of Materials Science, vol.13, pp.195-201, 1978.

. E-paroissien, . Gaubert, and . Lachaud, Elasto-plastic analysis of bonded joints with macro-elements, Journal of Adhesion Science and Technology, vol.27, issue.13, pp.1464-1498, 2013.

S. J. Park and K. M. Liechti, Rate-Dependent Large Strain Behavior of a Structural Adhesive, Mechanics of Time-Dependent Materials, vol.7, pp.143-164, 2003.

I. S. Raju, Calculation of strain-energy release rates with higher order and singular finite elements, Engineering Fracture Mechanics, vol.28, issue.3, pp.251-274, 1987.

E. D. Reedy and T. R. Guess, Interface corner failure analysis of joint strength : Effect of adherend stiffness, International journal of Fracture, vol.88, pp.305-314, 1997.

. J-r-rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, Journal of Applied Mechanics, vol.35, pp.379-386, 1968.

E. F. Rybicki and M. F. Kanninen, A finite element calculation of stress intensity facors by a modified crack closure integral, Engineering Fracture Mechanics, vol.9, issue.1, pp.931-938, 1977.

. Schindel, ;. Bidinelli, M. K. Salem, J. Budzik, M. Jumel et al., Investigation of the crack front process zone in the double cantilever beam test with backface strain monitoring technique, Pratique du collage industriel. Lavoisier édition, vol.98, pp.272-283, 1992.

Y. P. Shi and S. Cheng, Analysis of Adhesive-Bonded Cylindrical Lap Joints Subjected to Axial Load, Journal of Engineering Mechanics, vol.119, issue.3, 1993.

G. Stamoulis, ;. G. Carrere, N. Stamoulis, J. Y. Carrere, P. Cognard et al., Investigating the influence of material non-linearity in the fracture properties of ductile adhesives submitted to mixed-mode loading, International Journal of Adhesion and Adhesives, vol.179, pp.147-159, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01727698

S. Schmauder, M. Meyer, F. Hellmut, and . Fischmeister, Correlation Between Dundurs ' Parameters and Elastic Constants, Z. Metallkd, vol.83, issue.1, pp.524-528, 1992.

M. Shahverdi, P. Anastasios, T. Vassilopoulos, and . Keller, Composites : Part A Mixed-mode quasi-static failure criteria for adhesivelybonded pultruded GFRP joints, COMPOSITES PART A, vol.59, pp.45-56, 2014.

E. Scott, . Stapleton, M. Anthony, and . Waas, Macroscopic Finite Element for a Single Lap Joint. 50th Structures, Structural Dynamics, and Materials Conference, pp.1-12, 2009.

E. Scott, A. M. Stapleton, N. Waas, L. John, and . Field, Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element, vol.49, pp.1740-1749, 2011.

. Luis-f-trimin, Evaluation of Numerical Methods to Model Structural Adhesive Response and Failure in Tension and Shear Loading, Journal dynamic behavior material, vol.2, pp.122-137, 2016.

A. Uguen, Influence de l 'endommagement plan sur le comportement hors-plan des composites stratifiés et des assemblages collés, 2017.

M. Vogler, G. Ernst, and R. Rolfes, Invariant based transversely-isotropic material and failure model for fiber-reinforced polymers, Computers, Materials and Continua, vol.16, issue.1, pp.25-49, 2010.

]. B. +-16, S. Valès, R. Marguet, L. Créac'hcadec, J. Sohier et al., Numerical study of the local behaviour of adhesive bonds under dynamic loading, Journal of Adhesion Science and Technology, vol.30, issue.12, pp.1319-1339, 2016.

H. Whitworth, O. Aluko, and . Tomlinson, Application of the point stress criterion to the failure of composite pinned joints, Engineering Fracture Mechanics, vol.75, pp.1829-1839, 2008.

P. Weißgraeber and W. Becker, Finite Fracture Mechanics model for mixed mode fracture in adhesive joints, International Journal of Solids and Structures, vol.50, pp.2383-2394, 2013.

M. E. Waddoups, J. R. Eisenmann, and B. E. Kaminiski, Advanced Composite MaterialsMacroscopic Fracture Mechanics of Advanced Composite Materials, Journal Composite Materials, vol.5, pp.447-454, 1971.

H. M. Westergaard, Westergaard1939-BearingPressures-and-Cracks.pdf, 1939.

J. Whitney and R. J. , Nuismer : Stress fracture criteria for laminated composites containing stress concentrations, Journal Composite Materials, vol.8, pp.253-265, 1974.

P. Weißgraeber, N. Stein, and W. Becker, A general sandwich-type model for adhesive joints with composite adherends, International Journal of Adhesion and Adhesives, vol.55, pp.56-63, 2014.

J. Wang and A. Stein, Bin Bo Gao et Yong Ge : A review of spatial sampling, Spatial Statistics, vol.2, issue.1, pp.1-14, 2012.

L. Wierzbicki and T. Xue, On the effect of the third invariant of the stress devitor on ductile fracture. Impact and crashworthiness, vol.136, 2005.

X. X. Yu, A. D. Crocombe, and G. Richardson, Material modelling for rate-dependent adhesives, International Journal of Adhesion and Adhesives, vol.21, issue.3, pp.197-210, 2001.

Y. Y. Yan, N. Gao, and W. Barthlott, Mimicking natural superhydrophobic surfaces and grasping the wetting process : A review on recent progress in preparing superhydrophobic surfaces, Advances in Colloid and Interface Science, vol.169, issue.2, pp.80-105, 2011.

S. E. Yamada and C. T. Sun, Analysis of Laminate Strength and Its Distribution, Journal Composite Materials, vol.12, pp.275-284, 1978.