Comptes Rendus
no. 7-8
Surface mechanics: facts and numerical models
Interface models coupling adhesion and friction
[Modèles dʼinterface couplant adhésion et frottement]
Michel Raous1
1 LMA, 31, chemin Joseph-Aiguier, 13402 Marseille cedex 20, France
Comptes Rendus. Mécanique, Volume 339 (2011) no. 7-8, pp. 491-501.

On passe ici en revue de manière concise les modèles dʼinterface couplant frottement et adhésion, où lʼadhésion est considérée comme un endommagement dʼinterface. Les modèles de zones cohésives les plus utilisés sont présentés et discutés. Un cadre général pour ces lois est donné sous la forme dʼune formulation unifiée récemment proposée par Del Piero et Raous. Comme exemple dʼapplication, on établit que la loi RCCM (Raous–Cangémi–Cocou–Monerie) est un cas particulier de cette formulation générale. Les formes variationnelles et quelques méthodes de résolution associées sont rappelées dans le contexte de la mécanique non régulière à la fois pour des problèmes quasi-statiques et pour des problèmes dynamiques. Quelques exemples dans des domaines dʼapplication variés sont donnés. Enfin, quelques problèmes ouverts et des recherches en cours dans ce champ thématique sont évoqués.

Interface models coupling friction and adhesion, where adhesion is regarded as interface damage, are briefly reviewed. The most widely used cohesive zone models are presented and discussed. A general framework for these laws, recently developed by Del Piero and Raous in the form of a unified model, is outlined. As an example, it is here established that the RCCM (Raous–Cangémi–Cocou–Monerie) model is a specific case in this general framework. The variational formulation and some associated solvers are briefly recalled in the context of non-smooth mechanics in the cases of both quasi-static and dynamic problems. A few examples in various fields of application are given. Lastly, some open problems and ongoing researches in this field are presented and discussed.

Publié le :
DOI : 10.1016/j.crme.2011.05.007
Keywords: Contact, Adhesion, Friction, Interface, Non-smooth mechanics
Mot clés : Contact, Adhésion, Frottement, Interface, Mécanique non régulière
Michel Raous 1

1 LMA, 31, chemin Joseph-Aiguier, 13402 Marseille cedex 20, France 
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Michel Raous. Interface models coupling adhesion and friction. Comptes Rendus. Mécanique, Volume 339 (2011) no. 7-8, pp. 491-501. doi : 10.1016/j.crme.2011.05.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.05.007/

[1] G. Del Piero; M. Raous A unified model for adhesive interfaces with damage, viscosity, and friction, Eur. J. Mech. A/Solids, Volume 29 (2010), pp. 496-507

[2] M. Raous; L. Cangémi; M. Cocou Un modèle couplant adhérence et frottement pour le contact entre deux solides déformables, CRAS, Série II b, Volume 325 (1997) no. 9, pp. 503-509

[3] M. Raous; L. Cangémi; M. Cocou A consistent model coupling adhesion, friction and unilateral contact, Comput. Methods Appl. Mech. Engrg., Volume 177 (1999), pp. 383-399

[4] M. Raous; Y. Monerie Unilateral contact, friction and adhesion in composite materials (J.A.C. Martins; M.D.P. Monteiro Marques, eds.), Contact Mechanics, Kluwer, Dordrecht, 2002, pp. 333-346

[5] D.S. Dugdale Yielding of steel sheets containing slits, J. Mech. Phys. Solids, Volume 8 (1960), pp. 100-104

[6] G.I. Barenblatt The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., Volume 7 (1962), pp. 55-129

[7] A. Needleman A continuum model for void nucleation by inclusion debonding, J. Appl. Mech., Volume 54 (1987), pp. 525-531

[8] A. Needleman An analysis of tensile decohesion along an interface, J. Mech. Phys. Solids, Volume 38 (1990) no. 3, pp. 289-324

[9] A. Needleman Micromechanical modeling of interfacial decohesion, Ultramicroscopy, Volume 40 (1992), pp. 203-214

[10] A. Needleman; A.J. Rosakis The effect of bond strength and loading rate on the conditions governing the attainment of intersonic crack growth along interfaces, J. Mech. Phys. Solids, Volume 47 (1999), pp. 2411-2449

[11] V. Tvergaard Effect of fiber debonding in a whisker-reinforced metal, Math. Sci. Engrg. A, Volume 125 (1990), pp. 203-213

[12] V. Tvergaard; J.W. Hutchinson The relation between crack growth resistance and fracture process parameters in elastic–plastic solids, J. Mech. Phys. Solids, Volume 40 (1992), pp. 1377-1397

[13] V. Tvergaard; J.W. Hutchinson Effects of strain-dependent cohesive zone model on prediction of crack growth resistance, Int. J. Solids Struct., Volume 33 (1996), pp. 3297-3308

[14] X.-P. Xu; A. Needleman Numerical simulations of fast crack growth in brittle solids, J. Mech. Phys. Solids, Volume 42 (1994) no. 9, pp. 1397-1434

[15] S. Brinckmann; Th. Siegmund A cohesive zone model based on the micromechanics of dislocations, Model. Simul. Mater. Sci. Eng., Volume 16 (2008), p. 19 pp

[16] F. Costanzo; J.R. Walton A study of dynamic crack growth in elastic materials using a cohesive zone model, Internat. J. Engrg. Sci., Volume 35 (1997) no. 12–13, pp. 1085-1114

[17] Y. Monerie, Fissuration des matériaux composites : rôle de lʼinterface fibre/matrice, Thesis, M. Raous (Adv.), Univ. Provence, 2000.

[18] J.-L. Chaboche; F. Feyel; Y. Monerie Interface debonding model: a viscous regularization with a limited rate dependency, Int. J. Solids Struct., Volume 38 (2001) no. 18, pp. 3127-3160

[19] C. Talon; A. Curnier A model of adhesion coupled to contact and friction, Eur. J. Mech. A/Solids, Volume 22 (2003), pp. 545-565

[20] J.C. Michel; P. Suquet An analytical and numerical study of the overall behavior of metal-matrix composites, Model. Simul. Mater. Sci. Eng., Volume 2 (1994), pp. 637-658

[21] O. Allix; P. Ladevèze; A. Corigliano Damage analysis of interlaminar fracture specimens, Comp. Struct., Volume 31 (1995) no. 1, pp. 61-74

[22] F. Freddi; M. Frémond Damage in domains and interfaces: a coupled predictive theory, J. Mech. Mater. Struct., Volume 1 (2006) no. 7, pp. 1205-1234

[23] M. Samimi; J.A.W. van Dommelen; M.G.D. Geers An enriched cohesive zone model for delamination in brittle interface, Internat. J. Numer. Methods Engrg., Volume 80 (2009), pp. 609-630

[24] C. Nguyen; A.J. Levy An exact theory of interfacial debonding in layered elastic composites, Int. J. Solids Struct., Volume 46 (2009), pp. 2712-2723

[25] S. Stupkiewicz Fiber sliding model accounting for interfacial micro-dilatancy, Mech. Mater., Volume 22 (1996), pp. 65-84

[26] M.J. van der Bosch; P.J.G. Schreurs; M.G.D. Geers A cohesive zone model with a large displacement formulation accounting for interfacial fibrillation, Eur. J. Mech. A/Solids, Volume 26 (2007), pp. 1-19

[27] I. Ozemir; W.A.M. Brekelmans; M.G.D. Geers A thermo-mechanical cohesive zone model, Comput. Mech., Volume 46 (2010), pp. 735-745

[28] M. Raous; M.A. Karray Model coupling friction and adhesion for steel-concrete interfaces, Int. J. Comput. Appl. Technol., Volume 34 (2009) no. 1, pp. 42-51

[29] N. Terfaya, M. Raous, A. Berga, Cohesive zone model and bipotential formulation: application to a pile/soil interface, in: Proceedings of the 3rd Euro Mediterranean Symposium on Advances in Geomaterials and Structures, 2010, 6 pp.

[30] D. Sheng; P. Wriggers; S.W. Sloan Application of frictional contact in geotechnical engineering, Int. J. Geomech. ( May–June 2007 ), pp. 176-185

[31] R.H.J. Peerlings; R. de Borst; W.A.M. Brekelmans; M.G.D. Geers Gradient-enhanced damage modeling of concrete fracture, Mech. Cohes.-Frict. Mater., Volume 3 (1998), pp. 323-342

[32] F. Fouchal; F. Lebon; I. Titeux Contribution to the modeling of interfaces in masonry construction, Constr. Build. Mater., Volume 23 (2009) no. 6, pp. 2428-2441

[33] G. Alfano; E. Sacco Combining damage and friction in a cohesive-zone model, Internat. J. Numer. Methods Engrg., Volume 65 (2006), pp. 542-582

[34] V. Acary, Y. Monerie, Nonsmooth fracture dynamics using a cohesive zone model, INRIA report n6032, 2006, 56 pp. (ISSN 0249-6399).

[35] M. Jean; V. Acary; Y. Monerie Non-smooth contact dynamics approach of cohesive materials, Philosophical Transactions: Mathematical, Physical Engineering Sciences, Royal Society, London A, Volume 359 (2001) no. 1789, pp. 2497-2518

[36] A. Rekik; F. Lebon Identification of the representative crack length evolution in a multi-level interface model for quasi-brittle masonry, Int. J. Solids Struct., Volume 47 (2010), pp. 3011-3021

[37] M. Campillo; I.R. Ionescu Initiation of antiplane shear instability under slip dependent friction, J. Geophys. Res., Volume 102 (1997) no. B9, pp. 20363-20371

[38] J.R. Rice; A.L. Ruina Stability of steady frictional slipping, J. Appl. Mech., Volume 50 (1983), pp. 343-349

[39] K. Uenishi; J.R. Rice Universal nucleation length for slip-weakening rupture instability under non-uniform fault loading, J. Geophys. Res., Volume 108 (2003) no. B1, p. 2042 | DOI

[40] G. Festa; J.-P. Vilotte; M. Raous; C. Henninger Scale-dependent friction and damage interface law: implications for effective earthquake rupture dynamics and radiation, Geophysical Research Abstracts (EGU2010), Volume 12 (2010), p. 11647

[41] G. Festa, J.-P. Vilotte, M. Raous, Nucleation length in an adhesive-frictional interface under nonuniform fault loading condition, in preparation.

[42] M. Frémond Adhérence des solides, J. Méc. Théor. Appl., Volume 6 (1987) no. 3, pp. 383-407

[43] M. Frémond Contact with adhesion (J.-J. Moreau; P.D. Panagiotopoulos, eds.), Nonsmooth Mechanics and Applications, CISM Courses and Lectures, vol. 302, Springer, Wien, 1988, pp. 177-221

[44] M. Frémond; B. Nedjar Damage, gradient of damage and principle of virtual power, Int. J. Solids Struct., Volume 8 (1996), pp. 1083-1103

[45] J. Lemaitre Formulation de lʼendommagement des interfaces, CRAS, série II, Volume 315 (1992), pp. 1047-1050

[46] M. Raous Quasistatic Signorini problem with Coulomb friction and coupling to adhesion (P. Wriggers; P. Panagiotopoulos, eds.), New Developments in Contact Problems, CISM Courses & Lect., vol. 384, Springer-Verlag, Wien, 1999, pp. 101-178

[47] K.L. Johnson; K. Kendall; A.D. Roberts Surface energy and the contact of elastic solids, Proc. Roy. Soc. London A, Volume 324 (1971), pp. 301-313

[48] K.L. Jonhson Contact Mechanics, Cambridge University Press, 1985

[49] K.L. Jonhson; H.M. Pollock The role of adhesion in the impact of elastic spheres, J. Adhes. Sci. Technol., Volume 8 (1994), pp. 1323-1332

[50] G. Sperling, Eine Theorie der Haftung von Feststoffteilchen an festen Korpern, Dissertation von der Facultat fur Machinenwesen der Technischen Hochschule Karlsruhe, 1964.

[51] D. Maugis Adhesion of spheres: the JKR–DMT transition using a Dugdale model, J. Colloid Interface Sci., Volume 150 (1992), pp. 243-269

[52] D. Maugis; M. Barquins Fracture mechanics and adherence of viscoelastic solids (L.H. Lee, ed.), Adhesion, Adsorption of Polymers (part A), Plenum Press, New York, 1980, pp. 20-277

[53] M. Barquins Adherence, friction and wear of rubber-like materials (R. Denton; M.K. Keshavan, eds.), Wear and Friction of Elastomers, American Society for Testing and Materials, Philadelphia, 1992, pp. 82-113

[54] J.A. Greenwood Adhesion of elastic spheres, Proc. Roy. Soc. London A, Volume 453 (1997), pp. 1277-1297

[55] I. Goryacheva; Y. Makhovskaya Adhesion effects in contact interaction of solids, C. R. Mecanique, Volume 336 (2008), pp. 118-125

[56] F. Péralès, Fissuration des matériaux à gradient de propriétés, Application au Zircaloy hydruré, Thesis, A. Chrysochoos, Y. Monerie (Adv.), Univ. Montpellier II, 2005.

[57] M. Schryve, Modéle dʼadhésion cicatrisante et applications au contact verre/élastomére, Thesis, M. Raous, M. Cocou (Adv.), Univ. Provence, 2000.

[58] M. Raous; M. Schryve; M. Cocou Restorable adhesion and friction (C.C. Baniotopoulos, ed.), Nonsmooth/Nonconvex Mechanics with Applications in Engineering, Ziti Publisher, Thessaloniki, 2006, pp. 165-172

[59] M. Cocou; M. Schryve; M. Raous A dynamic unilateral contact problem with adhesion and friction in viscoelasticity, ZAMP, Volume 61 (2010), pp. 721-743

[60] Y. Monerie; M. Raous A model coupling adhesion to friction for the interaction between a crack and a fiber/matrix interface, Z. Angew. Mat. Mech., Volume 80 (2000) no. Special Issue, pp. 205-209

[61] N. Valoroso; L. Champaney A damage-mechanics-based approach for modeling decohesion in adhesively bonded assemblies, Engineering Fracture Mechanics, Volume 73 (2006) no. 18, pp. 2774-2801

[62] J.H. Dieterich Time dependant friction and the mechanics of stick-slip, Pure Appl. Geophys., Volume 116 (1978) no. 4–5, pp. 790-806

[63] A.C. Palmer; J.R. Rice The growth of slip surfaces in the progressive failure of over-consolidated clay, Proc. Roy. Soc. London A, Volume 332 (1973), pp. 527-548

[64] M. Cocou; L. Cangemi; M. Raous Approximation results for a class of quasistatic contact problems including adhesion and friction (P. Argoul; M. Frémond; Q.S. Nguyen, eds.), Proc. IUTAM Symposium on Variations de Domaines et Frontières Libres en Mécanique des Solides, Kluwer, 1999, pp. 211-218

[65] M. Cocou; M. Raous Adhesive contact and implicit evolution variational inequalities (C.C. Baniotopoulos, ed.), Nonsmooth/Nonconvex Mechanics with Applications in Engineering – In Memoriam of Prof. P.D. Panagiotopoulos, Ziti Publisher, 2002, pp. 167-174

[66] M. Raous; S. Barbarin Preconditioned conjugate gradient method for a unilateral problem with friction (A. Curnier, ed.), Contact Mechanics, Polytech. et Univ. Romandes Press, 1992, pp. 423-432

[67] L. Cangémi, Frottement et adhérence : modèle, traitement numérique et application à lʼinterface fibre/matrice, Thesis, M. Raous (Adv.), Univ. Provence, 1997.

[68] Y. Monerie; M. Raous; F.H. Leroy; O. Suder; F. Feyel; J.-L. Chaboche Comparaison de lois dʼinterface fibre/matrice sur la base dʼun modèle uniaxial dʼexpérience de micro-indentation (J. Lamon; D. Baptiste, eds.), Proceedings 11ième Journées Nationales sur les Composites, t. 2, AMAC Publish., 1998, pp. 565-574

[69] J.-J. Moreau Unilateral contact and dry friction in finite freedom dynamics (J.J. Moreau; P.D. Panagiotopoulos, eds.), Non-Smooth Mechanics and Applications, CISM Courses and Lectures, vol. 302, Springer, Wien, 1988, pp. 1-82

[70] M. Jean The non-smooth contact dynamics method, Comput. Methods Appl. Mech. Engrg., Volume 177 (1999) no. 3–4, pp. 235-257

[71] F. Dubois; M. Jean Une plateforme de développement dédiée la modélisation des problèmes dʼinteraction (M. Potier-Ferry; M. Bonnet; A. Bignonnet, eds.), Proc. VI Coll. Nat. Calcul de Struct. V1, Giens, 2003, pp. 111-118

[72] Y. Monerie; V. Acary Formulation dynamique dʼun modèle de zone cohésive tridimensionnelle couplant endommagement et frottement, Revue Européenne des Eléments Finis, Volume 10 (2001), pp. 489-504

[73] J.-J. Marigo; L. Truskinovsky Initiation and propagation of fracture in the models of Griffith and Barenblatt, Contin. Mech. Thermodyn., Volume 16 (2004), pp. 391-409

[74] M. Charlotte; J. Laverne; J.-J. Marigo Initiation of cracks with cohesive force models: a variational approach, Eur. J. Mech. A/Solids, Volume 25 (2006), pp. 649-669

[75] M. Cocou; R. Rocca Existence results for unilateral quasistatic contact problems with friction and adhesion, Math. Model. Num. Anal., Volume 34 (2000) no. 5, pp. 981-1001

[76] R.H.J. Peerlings; R. de Borst; W.A.M. Brekelmans; J.H.P. de Vree Gradient enhanced damage for quasi-brittle materials, Internat. J. Numer. Methods Engrg., Volume 39 (1996), pp. 3391-3403

[77] M.G.D. Geers; R. de Borst; W.A.M. Brekelmans; R.H.L. Peerlings Validation and internal length scale determination for a gradient damage model: application to short glass-fiber-reinforced polypropylene, Int. J. Solids Struct., Volume 36 (1999), pp. 2557-2583

[78] E. Lorentz A mixed interface finite element for cohesive zone models, Comput. Methods Appl. Mech. Engrg., Volume 198 (2008), pp. 317-320

[79] E. Lorentz; S. Cuvilliez; K. Kazymyrenko Convergence of a gradient damage model toward a cohesive zone model, C. R. Mécanique, Volume 339 (2011), pp. 20-26

[80] F. Cazes; M. Coret; A. Combescure; A. Gravouil A thermodynamic method for the construction of a cohesive law from a non-local damage model, Int. J. Solids Struct., Volume 46 (2009) no. 6, pp. 1476-1490

[81] F. Cazes; A. Simatos; M. Coret; A. Combescure A cohesive zone model which bis energetically equivalent to a gradient-enhanced coupled damage-plasticity model, Eur. J. Mech. A/Solids, Volume 29 (2010), pp. 976-989

[82] A. Jaubert; J.-J. Marigo Justification of Paris-type fatigue laws from cohesive forces model via a variational approach, Contin. Mech. Thermodyn., Volume 18 (2006), pp. 23-45

[83] R. Abdelmoula; J.-J. Marigo; Th. Weller Contruction dʼune loi de fatigue à partir dʼun modèle de forces coh ésives : cas des fissures en mode I, C. R. Mecanique, Volume 337 (2009), pp. 166-172

[84] R. Abdelmoula; J.-J. Marigo; Th. Weller Contruction dʼune loi de fatigue à partir dʼun modèle de forces coh ésives : cas des fissures en mode III, C. R. Mecanique, Volume 337 (2009), pp. 53-59

[85] H.D. Espinosa; P.D. Zavattieri A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials, Part 1: Theory and numerical implementation, Mech. Mater., Volume 35 (2003), pp. 333-364

[86] M.G.A. Tijssens; L.J. Sluys; E. van der Giessen Numerical simulation of quasi-brittle fracture using damaging cohesive surface, Eur. J. Mech. A/Solids, Volume 19 (2000), pp. 761-779

[87] N. Moës; C. Stolz; P.-E. Bernard; N. Chevaugeon A level set based model for damage growth: the thick level set approach, Internat. J. Numer. Methods Engrg., Volume 86 (2011) no. 3, pp. 358-380

[88] Ch. Licht; G. Miraille A modeling of elastic adhesive bonded joints, Adv. Math. Sci. Appl., Volume 7 (1997), pp. 711-740

[89] F. Lebon; R. Rizzoni; S. Ronel-Idrissi Asymptotic analysis of some non-linear soft thin layers, Comp. Struct., Volume 82 (2004), pp. 1929-1938

[90] F. Lebon; A. Ould Khaoua; C. Licht Numerical study of soft adhesive bounded joints in finite elasticity, Comput. Mech., Volume 21 (1998), pp. 134-140

[91] R. De Boorst; J.J.C. Remmers; A. Needleman Mesh-independent discrete numerical representation of cohesive-zone models, Engineering Fracture Mechanics, Volume 73 (2006), pp. 160-177

[92] M. Frémond Non-Smooth Thermo-Mechanics, Springer-Verlag, Heidelberg, 2002

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