L. Afferrante, F. Bottiglione, C. Putignano, B. Persson, and G. Carbone, Elastic contact mechanics of randomly rough surfaces: An assessment of advanced asperity models and persson's theory, Tribology Letters, vol.66, issue.2, p.75, 2018.

L. Afferrante, G. Carbone, and G. Demelio, Interacting and coalescing hertzian asperities: A new multiasperity contact model, Wear, vol.278, pp.28-33, 2012.

L. Afferrante, G. Carbone, and G. Demelio, Interacting and coalescing hertzian asperities: a new multiasperity contact model, Wear, vol.278, pp.28-33, 2012.

R. Aghababaei, D. H. Warner, and J. Molinari, Critical length scale controls adhesive wear mechanisms, Nature communications, vol.7, 2016.

S. Akarapu, T. Sharp, and M. O. Robbins, Stiffness of contacts between rough surfaces, Physical Review Letters, vol.106, issue.20, p.204301, 2011.

G. Anciaux and J. F. Molinari, Contact mechanics at the nanoscale, a 3d multiscale approach, Int J Numer Meth Eng, vol.79, issue.9, pp.1041-1067, 2009.

J. Archard and W. Hirst, The wear of metals under unlubricated conditions, Proc. R. Soc. Lond. A, vol.236, pp.397-410, 1206.

J. Barber, Bounds on the electrical resistance between contacting elastic rough bodies, In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.459, pp.53-66, 2003.

S. Basseville, E. Héripré, and G. Cailletaud, Numerical simulation of the third body in fretting problems, Wear, vol.270, pp.876-887, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00569974

A. Bemporad and M. Paggi, Optimization algorithms for the solution of the frictionless normal contact between rough surfaces, International Journal of Solids and Structures, vol.69, pp.94-105, 2015.

O. Ben-david, G. Cohen, and J. Fineberg, The dynamics of the onset of frictional slip, Science, vol.330, issue.6001, pp.211-214, 2010.

F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, 2001.

A. W. Bush, R. D. Gibson, and T. R. Thomas, The elastic contact of a rough surface, Wear, vol.35, issue.1, pp.87-111, 1975.

C. Campaná and M. H. Müser, Practical green's function approach to the simulation of elastic semi-infinite solids, Physical Review B, vol.74, issue.7, p.75420, 2006.

G. Carbone and F. Bottiglione, Asperity contact theories: Do they predict linearity between contact area and load?, J Mech Phys Solids, vol.56, pp.2555-2572, 2008.

M. Ciavarella, On the significance of asperity models predictions of rough contact with respect to recent alternative theories, Journal of Tribology, vol.139, issue.2, p.21402, 2017.

W. B. Dapp, A. Lücke, B. N. Persson, and M. H. Müser, Self-affine elastic contacts: percolation and leakage, Physical review letters, vol.108, issue.24, p.244301, 2012.

W. B. Dapp and M. H. Müser, Contact mechanics of and reynolds flow through saddle points: On the coalescence of contact patches and the leakage rate through near-critical constrictions, Europhysics Letters), vol.109, issue.4, p.44001, 2015.

W. B. Dapp and M. H. Müser, Fluid leakage near the percolation threshold, Scientific reports, vol.6, 2016.

B. V. Derjaguin, V. M. Muller, and Y. P. Toporov, Effect of contact deformations on the adhesion of particles, Journal of Colloid and interface science, vol.53, issue.2, pp.314-326, 1975.

T. Dick and G. Cailletaud, Fretting modelling with a crystal plasticity model of ti6al4v, Computational Materials Science, vol.38, issue.1, pp.113-125, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00133520

J. H. Dieterich and B. D. Kilgore, Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic, Tectonophysics, vol.256, issue.1-4, pp.219-239, 1996.

S. Fouvry, P. Kapsa, H. Zahouani, and L. Vincent, Wear analysis in fretting of hard coatings through a dissipated energy concept, Wear, vol.203, pp.393-403, 1997.

L. Frérot, R. Aghababaei, and J. Molinari, A mechanistic understanding of the wear coefficient: From single to multiple asperities contact, Journal of the Mechanics and Physics of Solids, vol.114, pp.172-184, 2018.

K. Fuller and D. Tabor, The effect of surface roughness on the adhesion of elastic solids, Proc. R. Soc. Lond. A, vol.345, pp.327-342, 1642.

I. Goryacheva, Mechanics of discrete contact, Tribology international, vol.39, issue.5, pp.381-386, 2006.

I. G. Goryacheva, Contact mechanics in tribology, vol.61, 2013.

J. Greenwood and J. Tripp, The contact of two nominally flat rough surfaces. Proceedings of the institution of mechanical engineers, vol.185, pp.625-633, 1970.

J. A. Greenwood, Constriction resistance and the real area of contact, British Journal of Applied Physics, vol.17, issue.12, p.1621, 1966.

J. A. Greenwood, Formulas for moderately elliptical hertzian contacts, J. Tribol. (ASME), vol.107, pp.501-504, 1985.

J. A. Greenwood, A simplified elliptic model of rough surface contact, Wear, vol.261, 2006.

J. A. Greenwood, A note on Nayak's third paper, Wear, vol.262, pp.225-227, 2007.

J. A. Greenwood and J. H. Tripp, The elastic contact of rough spheres, Journal of Applied Mechanics, vol.34, issue.1, pp.153-159, 1967.

J. A. Greenwood and J. B. Williamson, Contact of nominally flat surfaces, P Roy Soc Lond A Mat, vol.295, pp.300-319, 1966.

R. Hill, B. Storåkers, and A. Zdunek, A theoretical study of the brinell hardness test, Proc. R. Soc. Lond. A, vol.423, pp.301-330, 1865.

D. A. Hills, Mechanics of fretting fatigue, Wear, vol.175, issue.1-2, pp.107-113, 1994.

K. Hokkirigawa and K. Kato, An experimental and theoretical investigation of ploughing, cutting and wedge formation during abrasive wear, Tribology International, vol.21, issue.1, pp.51-57, 1988.

Y. Z. Hu and K. Tonder, Simulation of 3-D random rough surface by 2-D digital filter and fourier analysis, Int J Mach Tool Manu, vol.32, pp.83-90, 1992.

G. Huber, S. N. Gorb, N. Hosoda, R. Spolenak, and E. Arzt, Influence of surface roughness on gecko adhesion, Acta biomaterialia, vol.3, issue.4, pp.607-610, 2007.

S. Hyun, L. Pei, J. F. Molinari, and M. O. Robbins, Finite-element analysis of contact between elastic self-affine surfaces, Phys Rev E, vol.70, issue.2, p.26117, 2004.

S. Hyun and M. O. Robbins, Elastic contact between rough surfaces: Effect of roughness at large and small wavelengths, Tribology International, vol.40, pp.1413-1422, 2007.

K. Johnson and J. Greenwood, An adhesion map for the contact of elastic spheres, Journal of colloid and interface science, vol.192, issue.2, pp.326-333, 1997.

K. L. Johnson, Contact mechanics, 1985.

K. L. Johnson, K. Kendall, and A. Roberts, Surface energy and the contact of elastic solids, Proc. R. Soc. Lond. A, vol.324, pp.301-313, 1558.

Y. Kim, E. Gwak, S. Ahn, N. Kang, H. N. Han et al., Indentation size effect for spherical nanoindentation on nanoporous gold, Scripta Materialia, vol.143, pp.10-14, 2018.

L. Kogut and I. Etsion, Elastic-plastic contact analysis of a sphere and a rigid flat, Journal of applied Mechanics, vol.69, issue.5, pp.657-662, 2002.

K. Kubiak, T. Liskiewicz, and T. Mathia, Surface morphology in engineering applications: Influence of roughness on sliding and wear in dry fretting, Tribology International, vol.44, issue.11, pp.1427-1432, 2011.

C. V. Madhusudana, Thermal contact conductance, 1996.

D. Maugis, Adhesion of spheres: the jkr-dmt transition using a dugdale model, Journal of colloid and interface science, vol.150, issue.1, pp.243-269, 1992.

P. Meakin, Fractals, scaling and growth far from equilibrium, vol.5, 1998.

S. D. Mesarovic and N. A. Fleck, Spherical indentation of elastic-plastic solids, In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.455, pp.2707-2728, 1999.

Y. Mo, K. T. Turner, and I. Szlufarska, Friction laws at the nanoscale, Nature, vol.457, issue.7233, p.1116, 2009.

M. H. Müser, W. B. Dapp, R. Bugnicourt, P. Sainsot, N. Lesaffre et al., Meeting the contact-mechanics challenge, Tribology Letters, vol.65, issue.4, p.118, 2017.

P. R. Nayak, Random process model of rough surfaces, J Lubr Technol (ASME), vol.93, pp.398-407, 1971.

M. Paggi and M. Ciavarella, The coefficient of proportionality ? between real contact area and load, with new asperity models, Wear, vol.268, issue.7-8, pp.1020-1029, 2010.

L. Pastewka, S. Moser, P. Gumbsch, and M. Moseler, Anisotropic mechanical amorphization drives wear in diamond, Nature materials, vol.10, issue.1, p.34, 2011.

L. Pastewka, N. Prodanov, B. Lorenz, M. H. Müser, M. O. Robbins et al., Finite-size scaling in the interfacial stiffness of rough elastic contacts, Phys Rev E, vol.87, p.62809, 2013.

L. Pastewka and M. O. Robbins, Contact between rough surfaces and a criterion for macroscopic adhesion, Proceedings of the National Academy of Sciences, p.201320846, 2014.

L. Pastewka and M. O. Robbins, Contact area of rough spheres: large scale simulations and simple scaling laws, Applied Physics Letters, vol.108, issue.22, p.221601, 2016.

N. Patir and H. Cheng, An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication, Journal of lubrication Technology, vol.100, issue.1, pp.12-17, 1978.

L. Pei, S. Hyun, J. Molinari, and M. O. Robbins, Finite element modeling of elasto-plastic contact between rough surfaces, Journal of the Mechanics and Physics of Solids, vol.53, issue.11, pp.2385-2409, 2005.

L. Pei, S. Hyun, J. F. Molinari, and M. O. Robbins, Finite element modeling of elasto-plastic contact between rough surfaces, J Mech Phys Solids, vol.53, pp.2385-2409, 2005.

B. N. Persson, Theory of rubber friction and contact mechanics, J Chem Phys, vol.115, pp.3840-3861, 2001.

I. Polonsky and L. Keer, A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques, Wear, vol.231, issue.2, pp.206-219, 1999.

H. Proudhon, S. Fouvry, and J. Buffière, A fretting crack initiation prediction taking into account the surface roughness and the crack nucleation process volume, International Journal of Fatigue, vol.27, issue.5, pp.569-579, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00180854

C. Putignano, L. Afferrante, G. Carbone, and G. Demelio, The influence of the statistical properties of self-affine surfaces in elastic contacts: A numerical investigation, J Mech Phys Solids, vol.60, pp.973-982, 2012.

C. Putignano, L. Afferrante, G. Carbone, and G. Demelio, A new efficient numerical method for contact mechanics of rough surfaces, Int J Solids Struct, vol.49, issue.2, pp.338-343, 2012.

A. Ramesh and S. N. Melkote, Modeling of white layer formation under thermally dominant conditions in orthogonal machining of hardened aisi 52100 steel, International Journal of Machine Tools and Manufacture, vol.48, issue.3-4, pp.402-414, 2008.

V. Rey, S. Krumscheid, and F. Nobile, Quantifying uncertainties in contact mechanics of rough surfaces using the multilevel monte carlo method. Hal, 2017. available online on hal
URL : https://hal.archives-ouvertes.fr/hal-02059926

J. R. Rice, Heating and weakening of faults during earthquake slip, Journal of Geophysical Research: Solid Earth, vol.111, issue.B5, 2006.

A. Ruina, Slip instability and state variable friction laws, Journal of Geophysical Research: Solid Earth, vol.88, issue.B12, pp.10359-10370, 1983.

T. Sasada, M. Oike, and N. Emori, The effect of abrasive grain size on the transition between abrasive and adhesive wear, Wear, vol.97, issue.3, pp.291-302, 1984.

R. Sayles and P. Macpherson, Influence of wear debris on rolling contact fatigue, Rolling contact fatigue testing of bearing steels, 1982.

M. Scherge, S. Gorb, and S. N. Gorb, Biological micro-and nanotribology, 2001.

A. G. Shvarts and V. A. Yastrebov, Trapped fluid in contact interface, Journal of the Mechanics and Physics of Solids, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01853388

P. G. Slade, Electrical contacts: principles and applications, 2017.

H. M. Stanley and T. Kato, An FFT-based method for rough surface contact, J Tribol-T ASME, vol.119, pp.481-485, 1997.

J. Swadener, E. George, and G. Pharr, The correlation of the indentation size effect measured with indenters of various shapes, Journal of the Mechanics and Physics of Solids, vol.50, issue.4, pp.681-694, 2002.

D. Tabor, The hardness of metals, 2000.

A. Vakis, V. Yastrebov, J. Scheibert, L. Nicola, D. Dini et al., Modeling and simulation in tribology across scales: An overview, Tribology International, vol.125, pp.169-199, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01802145

A. Wang and M. H. Müser, Gauging persson theory on adhesion, Tribology Letters, vol.65, issue.3, p.103, 2017.

P. Wriggers and G. Zavarise, Application of augmented lagrangian techniques for non-linear constitutive laws in contact interfaces, Communications in Numerical Methods in Engineering, vol.9, issue.10, pp.815-824, 1993.

V. Yastrebov, G. Anciaux, and J. Molinari, The contact of elastic regular wavy surfaces revisited, Tribology Letters, vol.56, issue.1, pp.171-183, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01083586

V. A. Yastrebov, G. Anciaux, and J. Molinari, Contact between representative rough surfaces, Physical Review E, vol.86, issue.3, p.35601, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00750394

V. A. Yastrebov, G. Anciaux, and J. Molinari, From infinitesimal to full contact between rough surfaces: evolution of the contact area, International Journal of Solids and Structures, vol.52, pp.83-102, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01113725

V. A. Yastrebov, G. Anciaux, and J. Molinari, The role of the roughness spectral breadth in elastic contact of rough surfaces, Journal of the Mechanics and Physics of Solids, vol.107, pp.469-493, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01599693

V. A. Yastrebov, G. Cailletaud, H. Proudhon, F. S. Mballa, S. Noël et al., Threelevel multi-scale modeling of electrical contacts sensitivity study and experimental validation, Electrical Contacts (Holm), 2015 IEEE 61st Holm Conference on, pp.414-422, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01218663

V. A. Yastrebov, J. Durand, H. Proudhon, and G. Cailletaud, Rough surface contact analysis by means of the finite element method and of a new reduced model, Comptes Rendus Mécanique, vol.339, issue.7-8, pp.473-490, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00624090

V. A. Yastrebov, J. Durand, H. Proudhon, and G. Cailletaud, Rough surface contact analysis by means of the finite element method and of a new reduced model, Comptes Rendus Mécanique, vol.339, pp.473-490, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00624090

X. Yin and K. Komvopoulos, An adhesive wear model of fractal surfaces in normal contact, International Journal of Solids and Structures, vol.47, issue.7-8, pp.912-921, 2010.