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A consistent model coupling adhesion, friction, and unilateral contact. (English) Zbl 0949.74008
Summary: We present a model considering unilateral contact, Coulomb friction, and adhesion. In the framework of continuum thermodynamics, the contact zone is treated as a material boundary, and the local constitutive laws are derived by choosing two specific surface potentials: the free energy and the dissipation potential. Because of non-regular properties of these potentials, convex analysis is used to derive the local behavior laws from the state and the complementary laws. The adhesion is characterized by an internal variable \(\beta\) which represents the intensity of adhesion. The continuous transition from a total adhesive condition in a possible pure frictional one is enforced by using elasticity coupled with damage for the interface. Non-penetration conditions and Coulomb law are strictly imposed without using any penalty. The variational formulation for quasistatic problems is written as the coupling between an implicit variational inequality, a variational inequality, and a differential equation. We propose an incremental formulation, and give an existence result under a condition on the friction coefficient. A numerical method is derived from the incremental formulation, and various algorithms are implemented: they solve a sequence of minimization problems under constraints. The model is used to simulate a micro-indentation experiment conducted to characterize the behavior of fiber/matrix interface in a ceramic composite. Finally, we discuss the identification of constitutive parameters.

MSC:
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74A15 Thermodynamics in solid mechanics
74E30 Composite and mixture properties
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[1] Allix, O.; Ladevèze, P., Inerlaminar interface modelling for prediction of delamination, Composite struct., 21, 235-242, (1992)
[2] Allix, O.; Ladevèze, P., Damage analysis of interlaminar fracture specimens, Composite struct., 31, 61-74, (1995)
[3] Cangémi, L., Frottement et adhérence : modèle, traitement numérique et application à l’interface fibre/matrice, ()
[4] Cangémi, L.; Cocu, M.; Raous, M., Adhesion and friction model for the fiber/matrix interface of a composite, (), 157-163
[5] Chaboche, J.L.; Girard, R.; Levasseur, P., On the interface debonding models, International journal of damage mechanics, 6, 220-257, (1997)
[6] Chaboche, J.L.; Girard, R.; Levasseur, P., Numerical analysis of composite systems by using interphase/interface models, Comput. mech., 20, 3-11, (1997) · Zbl 0888.73059
[7] Chabrand, P.; Dubois, F.; Raous, M., Programmation mathématique pour le contact avec frottement et comparaison avec d’autres méthodes, (), 429-434
[8] Chabrand, P.; Dubois, F.; Raous, M., Various numerical methods for solving unilateral contract problems with friction, Math. comput. model, 28, 4-8, 97-108, (1998) · Zbl 1002.74592
[9] Cocu, M., Existence of solutions of Signorini problems with friction, Int. J. engrg. sci., 22, 567-575, (1984) · Zbl 0554.73096
[10] Cocu, M.; Cangemi, L.; Raous, M., Approximation results for a class of quasistatic contact problems including adhesion and friction, (), 211-218
[11] Cocu, M.; Pratt, E.; Raouos, M., Formulation and approximation of quasistatic frictional contact, Int. J. engrg. sci., 34, 7, 783-798, (1996) · Zbl 0900.73684
[12] Daher, N.; Maugin, G.A., The method of virtual power in continuum mechanics, Application to media presenting singular surfaces and interfaces, Acta mechanica, 60, 217-240, (1986) · Zbl 0594.73004
[13] Eldund, U., Surface adhesive joint description with coupled elastic-plastic damage behavior and numerical applications, Comput. methods appl. mech. engrg., 115, 253-276, (1993)
[14] Frémond, M., Equilibre des structures qui adhèrent à leur support, C.R. acad. sci. Paris, 295, Série II, 913-916, (1982) · Zbl 0551.73096
[15] Frémond, M., Adhérence des solides, Journal de Mécanique théorique et appliquée, 6, 3, 383-407, (1987) · Zbl 0645.73046
[16] Ganghoffer, J.-F.; Schultz, J.; Brillard, A., Modèles asymptotiques de joints collés par un adhésif viscoplastique, C.R. acad. sci. Paris, 321, Série II, 43-46, (1995) · Zbl 0838.73067
[17] Hutchinson, J.W.; Jensen, H.K., Models of fiber debonding and pull-out in brittle composites with friction, Mech. mater., 9, 139-163, (1990)
[18] Klarbring, A., Derivation and analysis of rate boundary problems of frictional contact, Europ. J. mech. A/solids, 9, 1, 53-85, (1990) · Zbl 0699.73074
[19] Klarbring, A., Derivation of a model of adhesively bonded joints by the asymptotic expansion method, Int. J. engrg. sci., 29, 4, 493-512, (1991) · Zbl 0762.73069
[20] Klarbring, A.; Bjorkman, G., A mathematical programming approach to contact problems with friction and varying contact surface, Comput. structures, 30, 5, 1185-1198, (1988) · Zbl 0677.73078
[21] Lebon, F.; Raous, M., Multibody contact problems including friction in structure assembly, Comput. struct., 42, 5, 925-934, (1992) · Zbl 0775.73272
[22] Leguillon, D., Un exemple d’intéraction singularité-couche limite pour la modélisation de la fracture dans LES composites, C.R. acad. sci. Paris, 319, 161-166, (1994), Série II · Zbl 0804.73044
[23] Lemaitre, J., Formulation de l’endommagement des interfaces, C.R. acad. sci. Paris, 315, Série II, 1047-1050, (1992) · Zbl 0761.73086
[24] Leroy, F.H.; Raous, M., Etude et modélisation de l’essai de micro-indentation sur composite SIC/SIC, ONERA report no. 22.810, (1997)
[25] Licht, C., Comportement asymptotique d’une bande dissipative mince de faíble rigidité, C.R. acad. sciences Paris, 317, Série I, 429-433, (1993) · Zbl 0781.73059
[26] Licht, C.; Michaille, G., Une modélisation du comportement d’un joint collé élastique, C.R. acad. sci. Paris, 322, 295-300, (1996), Série I · Zbl 0863.73019
[27] Licht, C.; Pratt, E.; Raous, M., Remarks on a numerical method for unilateral contact including friction, (), 129-144 · Zbl 0762.73076
[28] Marshall, D.B., An indentation method for measuring matrix fiber frictional stresses in ceramic composites, J. am. soc., 67, 12, C259-C260, (1984)
[29] Martin, E.; Piquenol, N.; Quensset, J.-M., Influence des conditions de couplage fibre-matrice sur le comportement à la rupture d’un microcomposite fragile-fragile, ()
[30] Martinez, D.; Gupta, V., Energy criterion for crack deflection at an interface between two orthotropic media, J. mech. phys. solids, 42, 8, 1247-1271, (1994) · Zbl 0837.73053
[31] Michel, J.C.; Suquet, P.; Thébaud, F., Une modélisation du rôle des interfaces dans le comportement des composites à matrice métallique, Revue européenne des eléments finis, 3, 4, 573-595, (1994) · Zbl 0924.73261
[32] Mroz, Z.; Stupkiewicz, S., Hysteretic effects and progressive delamination at composite interfaces, (), 247-264
[33] Needlman, A., A continuum model for void nucleation by inclusion debonding, J. appl. mech., 54, 525-531, (1987) · Zbl 0626.73010
[34] Needlman, A., An analysis of tensile decohesion along an interface, J. mechanics phys. solids, 33, 3, 289-324, (1990)
[35] M. Raous, Quasistatic Signorini problem with Coulomb friction and coupling to adhesion, in: P. Panagiotopoulus, P. Wriggers, eds., Contact Problem: Theory, Methods, Applications, CISM Collection (Springer Verlag, Vienna) in press. · Zbl 0942.74052
[36] Péres, P., Analyse théorique et expérimentale du rôle des paramètres de microstructure sur le comportement des composites à matrice fragile, ()
[37] Raous, M.; Cangémi, L.; Cocu, M., Un modèle couplant adhérence et frottement pour le contact entre deux solides déformables, C.R. acad. sci. Paris, 325, 503-509, (1997), Série II b · Zbl 0896.73051
[38] Raous, M.; Chabrand, P.; Lebon, F., Numerical methods for frictional contact problems and applications, Journal de Mécanique théorique et appliquée, 7, supplement 1, 111-128, (1988), special issue · Zbl 0679.73048
[39] Raous, M.; Barbarin, S., Preconditioned conjugate gradient method for a unilateral problem with friction, (), 423-432
[40] Sanchez-Palencia, E., Passage à la limite de l’élasticité tridimensionnelle à la théorie asymptotique des coques minces, C.R. acad. sci. Paris, 311, 909-916, (1990), Série II · Zbl 0701.73080
[41] Shetty, D.K., Shear-lag analysis of fiber push-out (indentation) tests for establishing interfacial friction stress in ceramic matrix composites, J. am. ceram. soc., 71, 2, C107-C109, (1988)
[42] Strömberg, N.; Johansson, L.; Klarbring, A., Derivation and analysis of a generalized standard model for contact, friction and wear, Int. J. solids and struct., 33, 13, 1817-1836, (1996) · Zbl 0926.74012
[43] Stupkiewicz, S., Fiber sliding model accounting for interfacial micro-dilatancy, Mech. mater., 22, 65-84, (1996)
[44] Truong Dinh Tien, J.-M., Contact avec adhérence, Thèse université Paris, 6, (1990)
[45] Tvergaard, V., Effect of fiber debonding in a whisker-reinforced metal, Mater. sci. engrg., A125, 203-213, (1990)
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