Fractal Surface Model

  • Andreas Goedecke
Part of the Engineering Materials book series (ENG.MAT.)


The study of the fractal nature of surfaces appearing in engineering problems is a comparatively young field. It started in the 1980s and 1990s of the last century with phenomenological descriptions of fractal surface properties. While many ideas were presented before, Mandelbrot’s influence on the field, especially of his 1982 book The Fractal Geometry of Nature [162], can hardly be underestimated. This monograph collected many ideas from different fields and for the first time presented to a broad audience the baffling concept of a curve that is everywhere continuous, but nowhere differentiable.


Fractal Dimension Power Spectral Density Hurst Exponent Continuous Approximation Real Contact Area 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    ABAQUS Inc.: ABAQUS Analysis User’s Manual. ABAQUS Inc., Providence (2004)Google Scholar
  2. 2.
    Abuzeid, O.M.: A linear thermo-visco-elastic creep model for the contact of nominal flat surfaces based on fractal geometry: Kelvin-Voigt medium. J. Qual. Maint. Eng. 9, 202–216 (2003)CrossRefGoogle Scholar
  3. 3.
    Abuzeid, O.M.: A linear viscoelastic creep-contact model of a flat fractal surface: Kelvin-Voigt medium. Ind. Lubr. Tribol. 56, 334–340 (2004)CrossRefGoogle Scholar
  4. 4.
    Abuzeid, O.M., Alabed, T.A.: Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium. Tribol. Int. 42, 206–212 (2009)CrossRefGoogle Scholar
  5. 5.
    Abuzeid, O.M., Eberhard, P.: Linear viscoelastic creep model for the contact of nominal flat surfaces based on fractal geometry: standard linear solid (SLS) material. J. Tribol. 129, 461–466 (2007)CrossRefGoogle Scholar
  6. 6.
    Akay, A.: Acoustics of friction. J. Acoust. Soc. Am. 111, 1525–1548 (2002)CrossRefGoogle Scholar
  7. 7.
    Alabed, T.A., Abuzeid, O.M., Barghash, M.: A linear viscoelastic relaxation-contact model of a flat fractal surface: a Maxwell type medium. Int. J. Adv. Manuf. Technol. 39, 423–430 (2008)CrossRefGoogle Scholar
  8. 8.
    Ameida, L., Ramadoss, R., Jackson, R.L., Ishikawa, K., Yu, Q.: Study of the electrical contact resistance of multi-contact MEMS relays fabricated using the metalMUMPs process. J. Micromech. Microeng. 16, 1189–1194 (2006)CrossRefGoogle Scholar
  9. 9.
    ANSYS Inc.: ANSYS Theory Manual, Release 11. ANSYS USA, Canonsburg (2007)Google Scholar
  10. 10.
    ANSYS Inc.: Programmer’s Manual for ANSYS, Release 11. ANSYS USA, Canonsburg (2007)Google Scholar
  11. 11.
    Archard, R.F.: Elastic deformation and the laws of friction. Proc. R. Soc. Lond. A 243, 190–205 (1957)CrossRefGoogle Scholar
  12. 12.
    Armstrong-Hélouvry, B.: Control of machines with friction. Kluwer, Boston (1991)zbMATHCrossRefGoogle Scholar
  13. 13.
    Ashby, M.F., Jones, D.R.H.: Engineering Materials, vol. 1, 3rd edn. Butterworth-Heinemann, Oxford (2005)Google Scholar
  14. 14.
    Balluffi, R.W., Allen, S.M., Carter, W.C.: Kinetics of Materials. Wiley, Hoboken (2005)CrossRefGoogle Scholar
  15. 15.
    Baltazar, A., Rokhlin, S.I., Percorari, C.: On the relationship between ultrasonic and micro-structural properties of imperfect interfaces in layered solids. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 18B, pp. 1463–1470. American Institute of Physics, New York (1999)CrossRefGoogle Scholar
  16. 16.
    Barabási, A.L., Stanley, H.E.: Fractal Concepts in Surface Growth. Cambridge University Press, Cambridge (1995)zbMATHCrossRefGoogle Scholar
  17. 17.
    Baumberger, T., Berthoud, P.: Sliding dynamics at a multicontact interface. In: Wolf, D.E., Grassberger, P. (eds.) Workshop on Friction, Arching, Contact Dynamics, Forschungszentrum Jülich, pp. 3–12. World Scientific, Singapore (1996)Google Scholar
  18. 18.
    Baumberger, T., Berthoud, P., Caroli, C.: Physical analysis of the state- and rate-dependent friction law: II. Dynamic friction. Phys. Rev. B 60, 3928–3939 (1999)CrossRefGoogle Scholar
  19. 19.
    Baumberger, T., Caroli, C.: Solid friction from stick-slip down to pinning and aging. Adv. Phys. 55, 279–348 (2006)CrossRefGoogle Scholar
  20. 20.
    Belotserkovets, A., Dubois, A., Dubar, M., Dubar, L., Deltombe, R., Vandekinderen, H., Damasse, J.: 2D asperity deformation of stainless steel strip in cold rolling. Int. J. Mater. Form. 1, 351–354 (2008)CrossRefGoogle Scholar
  21. 21.
    Bengisu, M.T., Akay, A.: Stability of friction-induced vibrations in multi-degree-of-freedom systems. J. Sound Vib. 171, 557–570 (1994)zbMATHCrossRefGoogle Scholar
  22. 22.
    Berger, E.J.: Friction modeling for dynamic system simulation. Appl. Mech. Rev. 55, 535–577 (2002)CrossRefGoogle Scholar
  23. 23.
    Berry, M.V., Lewis, Z.V.: On the Weierstrass-Mandelbrot fractal function. Proc. R. Soc. Lond. A 370, 459–484 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Berthoud, P., Baumberger, T., G’Sell, C., Hiver, J.M.: Physical analysis of the state- and rate-dependent friction law: I. Static friction. Phys. Rev. B 59, 14313–14327 (1999)CrossRefGoogle Scholar
  25. 25.
    Bhushan, B. (ed.): Handbook of Micro/Nano Tribology. CRC Press, Boca Raton (1995)Google Scholar
  26. 26.
    Bhushan, B., Majumdar, A.: Elastic-plastic contact model for bifractal surfaces. Wear 153, 53–64 (1992)CrossRefGoogle Scholar
  27. 27.
    Blau, P.J.: Friction Science and Technology. Marcel Dekker, New York (1996)Google Scholar
  28. 28.
    Bliman, P.A., Bonald, T., Sorine, M.: Hysteresis operators and tyre friction models: application to vehicle dynamic simulation. In: Proceedings of ICIAM/GAMM 95, Hamburg, Germany, 1996, pp. 309–312Google Scholar
  29. 29.
    Bliman, P.A., Sorine, M.: Friction modelling by hysteresis operators: application to Dahl, stiction and Stribeck effects. In: Proceedings of Conference Models of Hysteresis, Trento, Italy, 1991Google Scholar
  30. 30.
    Bliman, P.A., Sorine, M.: A system-theoretic approach of systems with hysteresis: application to friction modelling and compensation. In: Proceedings of the 2nd European Control Conference, pp. 1844–1849. Groningen, The Netherlands (1993)Google Scholar
  31. 31.
    Bo, L.C., Pavelescu, D.: The friction-speed relation and its influence on the critical velocity of stick-slip motion. Wear 82, 277–289 (1982)CrossRefGoogle Scholar
  32. 32.
    Boettcher, M.S., Marone, C.: Effects of normal stress variation on the strength and stability of creeping faults. J. Geophys. Res. 109, B03406 (2004)CrossRefGoogle Scholar
  33. 33.
    Bora, C.K., Flater, E.E., Street, M.D., Redmond, J.M., Starr, M.J., Carpick, R.W., Plesha, M.E.: Multiscale roughness and modeling of MEMS interfaces. Tribol. Lett. 19, 37–48 (2005)CrossRefGoogle Scholar
  34. 34.
    Borodich, F.M.: Comment on “Elastoplastic contact between randomly rough surfaces”. Phys. Rev. Lett. 88, 069601(1) (2002)CrossRefGoogle Scholar
  35. 35.
    Borri-Brunetto, M., Carpinteri, A., Chiaia, B.: Scaling phenomena due to fractal contact in concrete and rock fractures. Int. J. Fract. 95, 221–238 (1999)CrossRefGoogle Scholar
  36. 36.
    Borri-Brunetto, M., Chiaia, B., Ciavarella, M.: Incipient sliding of rough surfaces in contact: a multiscale numerical analysis. Comput. Methods Appl. Mech. Eng. 190, 6053–6073 (2001)zbMATHCrossRefGoogle Scholar
  37. 37.
    Boucly, V., Nélias, D., Green, I.: Modeling of the rolling and sliding contact between two asperities. J. Tribol. 129, 235–245 (2007)CrossRefGoogle Scholar
  38. 38.
    Bowden, F.P., Tabor, D.: The Friction and Lubrication of Solids. Clarendon Press, Oxford (1950)Google Scholar
  39. 39.
    Bowden, F.P., Tabor, D.: Friction: An Introduction to Tribology. Anchor Press, Garden City (1973)zbMATHGoogle Scholar
  40. 40.
    Bowden, F.P., Tabor, D.: The Friction and Lubrication of Solids (Oxford Classic Texts in the Physical Sciences). Oxford University, Oxford (2001)Google Scholar
  41. 41.
    Bower, A.F., Fleck, N.A., Needleman, A., Ogbonna, N.: Indentation of a power law creeping solid. Proc. R. Soc. Lond. A 441, 97–124 (1993)zbMATHCrossRefGoogle Scholar
  42. 42.
    Braunovic, M., Konchits, V.V., Myshkin, N.K.: Electrical Contacts: Fundamentals, Applications and Technology. CRC Press, Boca Raton (2007)Google Scholar
  43. 43.
    Brechet, Y., Estrin, Y.: The effect of strain rate sensitivity on dynamic friction of metals. Scr. Metall. Mater. 30, 1449–1454 (1994)CrossRefGoogle Scholar
  44. 44.
    Brizmer, V.: Elastic-plastic contact of a sphere and a flat under combined normal and tangential loading. Ph.D. thesis, Technion, Israel (2006)Google Scholar
  45. 45.
    Brizmer, V., Kligerman, Y., Etsion, I.: A model for junction growth of a spherical contact under full stick condition. J. Tribol. 129, 783–790 (2007)CrossRefGoogle Scholar
  46. 46.
    Brockley, C.A., Davis, H.R.: The time-dependence of static friction. J. Lubr. Technol. 90, 35–41 (1968)CrossRefGoogle Scholar
  47. 47.
    Broniec, Z., Lenkiewicz, W.: Static friction processes under dynamic loads and vibration. Wear 80, 261–271 (1982)CrossRefGoogle Scholar
  48. 48.
    Bronstein, I.N., Semendjaev, K.A.: Taschenbuch der Mathematik. Teubner, Leipzig (2003)Google Scholar
  49. 49.
    Brot, C.C., Etsion, I., Kligerman, Y.: A contact model for a creeping sphere and a rigid flat. Wear 265, 598–605 (2008)CrossRefGoogle Scholar
  50. 50.
    Buckingman, E.: On physically similar systems; illustrations of the use of dimensional equations. Phys. Rev. 4, 345–376 (1914)CrossRefGoogle Scholar
  51. 51.
    Bureau, L., Baumberger, T., Caroli, C.: Shear response of a frictional interface to a normal load modulation. Phys. Rev. E 62, 6810–6820 (2000)CrossRefGoogle Scholar
  52. 52.
    Bush, A.W., Gibson, R.D., Thomas, T.R.: The elastic contact of a rough surface. Wear 35, 87–111 (1975)CrossRefGoogle Scholar
  53. 53.
    Canudas de Wit, C., Olsson, H., Åström, K.J., Lischinsky, P.: A new model for control of systems with friction. IEEE Trans. Automat. Contr. 40, 419–425 (1995)Google Scholar
  54. 54.
    Chang, L., Zhang, H.: A mathematical model for frictional elastic-plastic sphere-on-flat contacts at sliding incipient. J. Appl. Mech. 74, 100–106 (2007)zbMATHCrossRefGoogle Scholar
  55. 55.
    Chang, W.R., Etsion, I., Bogy, D.B.: An elastic-plastic model for the contact of rough surfaces. J. Tribol. 109, 257–263 (1987)CrossRefGoogle Scholar
  56. 56.
    Chung, J.C., Lin, J.F.: Fractal model developed for elliptic elastic-plastic asperity microcontacts of rough surfaces. J. Tribol. 126, 646–654 (2004)CrossRefGoogle Scholar
  57. 57.
    Church, E.L.: Fractal surface finish. Appl. Opt. 27, 1518–1526 (1988)CrossRefGoogle Scholar
  58. 58.
    Ciavarella, M., Demelio, G.: Elastic multiscale contact of rough surfaces: Archard’s model revisited and comparisons with modern fractal models. J. Appl. Mech. 68, 496–498 (2001)zbMATHCrossRefGoogle Scholar
  59. 59.
    Ciavarella, M., Demelio, G., Barber, J.R., Jang, Y.H.: Linear elastic contact of the Weierstrass profile. Proc. R. Soc. Lond. A 456, 387–405 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Cochard, A., Bureau, L., Baumberger, T.: Stabilization of frictional sliding by normal load modulation. J. Appl. Mech. 70, 220–226 (2003)zbMATHCrossRefGoogle Scholar
  61. 61.
    Coulomb, C.A.: Théorie des machines simples. Mém. Math. Phys. Acad. Sci. 10, 161–331 (1785)Google Scholar
  62. 62.
    Dahl, P.R.: A solid friction model. Technical report, The Aerospace Corporation, El Segundo, CA for Space and Missile Systems Organization, Air Force Systems Command, Los Angeles, CA (1968)Google Scholar
  63. 63.
    Derjaguin, B.V., Push, V.E., Tolstoi, D.M.: A theory of stick-slip sliding of solids. Sov. J. Tech. Phys. (in Russian) 26, 1329–1342 (1955)Google Scholar
  64. 64.
    Derjaguin, B.V., Push, V.E., Tolstoi, D.M.: A theory of stick-slip sliding of solids. In: Proceedings of the Conference Lubrication and Wear, pp. 265–269. The Institution of Mechanical Engineers, London (1957)Google Scholar
  65. 65.
    Dieterich, J.H.: Time-dependent friction and the mechanics of stick-slip. Pure Appl. Geophys. 116, 790–806 (1978)CrossRefGoogle Scholar
  66. 66.
    Dieterich, J.H.: Modeling of rock friction, 1. Experimental results and constitutive equations. J. Geophys. Res. 84, 2161–2168 (1979)CrossRefGoogle Scholar
  67. 67.
    Dieterich, J.H.: Modeling of rock friction, 2. Simulation of preseismic slip. J. Geophys. Res. 84, 2169–2176 (1979)CrossRefGoogle Scholar
  68. 68.
    Dieterich, J.H.: Experimental and model study of fault constitutive properties. In: Nemet-Nasser, S. (ed.) Solid Earth Geophysics and Geotechnology, pp. 21–30. ASME, New York (1980)Google Scholar
  69. 69.
    Dieterich, J.H.: Constitutive properties of faults with simulated gouge. In: Carter, N.L., Friedman, M., Logan, J.M., Stearns, D.W. (eds.) Mechanical Behavior of Crustal Rocks. Geophysical Monograph Series, vol. 24, pp. 103–120. American Geophysical Union, Washington (1981)CrossRefGoogle Scholar
  70. 70.
    Dieterich, J.H.: A model for the nucleation of earthquake slip. In: Das, S., Boatwright, J., Scholz, C.H. (eds.) Earthquake Source Mechanics. Geophysical Monograph Series, vol. 37, pp. 37–47. American Geophysical Union, Washington (1986)CrossRefGoogle Scholar
  71. 71.
    Dieterich, J.H.: Nucleation and triggering of earthquake slip: effect of periodic stresses. Tectonophysics 144, 127–139 (1987)CrossRefGoogle Scholar
  72. 72.
    Dieterich, J.H., Kilgore, B.: Direct observation of frictional contacts: new insights for state-dependent properties. Pure Appl. Geophys. 143, 283–302 (1994)CrossRefGoogle Scholar
  73. 73.
    Dieterich, J.H., Linker, M.F.: Fault stability under conditions of variable normal stress. Geophys. Res. Lett. 19, 1691–1694 (1992)CrossRefGoogle Scholar
  74. 74.
    Duan, C., Singh, R.: Influence of harmonically varying normal load on steady-state behavior of a 2dof torsional system with dry friction. J. Sound Vib. 294, 503–528 (2006)CrossRefGoogle Scholar
  75. 75.
    Dupont, P.E.: Friction modeling in dynamic robot simulation. In: Proceedings of the 1990 IEEE International Conference on Robotics and Automation, Sacramento, CA, 1990, pp. 1370–1376Google Scholar
  76. 76.
    Dupont, P.E., Bapna, D.: Stability of sliding frictional surfaces with varying normal force. J. Vib. Acoust. 116, 237–242 (1994)CrossRefGoogle Scholar
  77. 77.
    Dupont, P.E., Dunlap, E.P.: Friction modeling and control in boundary lubrication. In: Proceedings of the American Control Conference, San Francisco, CA, 1993Google Scholar
  78. 78.
    Dupont, P.E., Dunlap, E.P.: Friction modeling and PD compensation at very low velocities. J. Dyn. Syst. Meas. Control 117, 8–14 (1995)CrossRefGoogle Scholar
  79. 79.
    Dutton, R.E., Rahaman, M.N.: Sintering, creep, and electrical conductivity of model glass-matrix composites. J. Am. Ceram. Soc. 75, 2146–2154 (2005)CrossRefGoogle Scholar
  80. 80.
    Dwyer-Joyce, R.S., Drinkwater, B.W., Quinn, A.M.: The use of ultrasound in the investigation of rough surface interfaces. J. Tribol. 123, 8–16 (2001)CrossRefGoogle Scholar
  81. 81.
    Edgar, G.: Measure, Topology, and Fractal Geometry. Springer, Berlin (2008)zbMATHCrossRefGoogle Scholar
  82. 82.
    Etsion, I., Kligermann, Y., Kadin, Y.: Unloading of an elastic-plastic loaded spherical contact. Int. J. Solids Struct. 42, 3716–3729 (2005)zbMATHCrossRefGoogle Scholar
  83. 83.
    Falconer, K.J.: The Geometry of Fractal Sets. Cambridge University Press, Cambrige (1986)Google Scholar
  84. 84.
    Falconer, K.J.: Fractal Geometry: Mathematical Foundations and Applications. Wiley, Hoboken (2003)zbMATHCrossRefGoogle Scholar
  85. 85.
    Falk, M.L., Langer, J.S.: Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E 57, 7192–7205 (1998)CrossRefGoogle Scholar
  86. 86.
    Feeny, B.F., Liang, J.W.: Phase-space reconstructions and stick-slip. Nonlinear Dyn. 13, 39–57 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  87. 87.
    Filippov, A.E., Popov, V.L.: Fractal Tomlinson model for mesoscopic friction: from microscopic velocity-dependent damping to macroscopic coulomb friction. Phys. Rev. E 75, 027,103(4) (2007)Google Scholar
  88. 88.
    Friedman, H.D., Levesque, P.: Reduction of static friction by sonic vibrations. J. Appl. Phys. 30, 1572–1575 (1959)CrossRefGoogle Scholar
  89. 89.
    Frost, H.J., Ashby, M.F.: Deformation-mechanism maps: the plasticity and creep of metals and ceramics. Pergamon Press, Oxford (1982)Google Scholar
  90. 90.
    Fujii, H., Asakura, T.: Roughness measurements of metal surfaces using laser speckle. J. Opt. Soc. Am. 67, 1171–1176 (1977)CrossRefGoogle Scholar
  91. 91.
    Fuller, D.D.: Theory and Practice of Lubrication for Engineers, pp. 336–338. Wiley, Hoboken (1956)Google Scholar
  92. 92.
    Gao, Y.F., Bower, A.F.: Elastic-plastic contact of a rough surface with Weierstrass profile. Proc. R. Soc. Lond. A 462, 319–348 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  93. 93.
    Garofalo, F.: Fundamentals of Creep and Creep-Rupture in Metals. Macmillan Publishers, New York (1965)Google Scholar
  94. 94.
    Gitis, N.V., Volpe, L.: Nature of static friction time dependence. J. Phys. D Appl. Phys. 25, 605–612 (1992)CrossRefGoogle Scholar
  95. 95.
    Glocker, C.: Set-valued force laws: dynamics of non-smooth systems. Springer, Berlin (2001)zbMATHCrossRefGoogle Scholar
  96. 96.
    Godfrey, D.: Vibration reduces metal to metal contact and causes an apparent reduction in friction. ASLE Trans. 10, 183–192 (1967)CrossRefGoogle Scholar
  97. 97.
    Goedecke, A.: Kinetische Monte Carlo Simulationen zum Wachstum zweidimensionaler Kristalle. Master’s thesis, RWTH Aachen (2003)Google Scholar
  98. 98.
    Goedecke, A., Mock, R.: A new fractal model for dynamic contact phenomena including friction. In: Proceedings of the European COMSOL Conference 2008, Hannover, 2008, p. 6Google Scholar
  99. 99.
    Goedecke, A., Mock, R.: A novel dynamic friction model based on asperity creep. In: Proceedings of the 9th Biennial ASME Conference on Engineering Systems Design and Analysis (ESDA2008) Haifa Israel, 2008, p. 59366(10)Google Scholar
  100. 100.
    Goedecke, A., Mock, R.: Creep relaxation of an elastic-perfectly plastic hemisphere in fully plastic contact. J. Tribol. 131, 021407(10) (2009)CrossRefGoogle Scholar
  101. 101.
    Goedecke, A., Mock, R.: Transient friction effects due to variable normal load in a multi-scale asperity-creep friction model. In: Proceedings of the ASME/STLE International Joint Tribology Conference IJTC 2010 (IJTC2010), San Francisco, California, 2010, p. 41190(3)Google Scholar
  102. 102.
    Greenwod, J.A., Rowe, G.W.: Deformation of surface asperities during bulk plastic flow. J. Appl. Phys. 36, 667–668 (1965)CrossRefGoogle Scholar
  103. 103.
    Greenwood, J.A.: A simplified elliptic model of rough surface contact. Wear 261, 191–200 (2006)CrossRefGoogle Scholar
  104. 104.
    Greenwood, J.A., Tripp, J.H.: The elastic contact of rough spheres. J. Appl. Mech. 34, 153–159 (1967)CrossRefGoogle Scholar
  105. 105.
    Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. R. Soc. Lond. A 295, 300–319 (1966)CrossRefGoogle Scholar
  106. 106.
    Greenwood, J.A., Wu, J.J.: Surface roughness and contact: an apology. Meccanica 36, 617–630 (2001)zbMATHCrossRefGoogle Scholar
  107. 107.
    Guinea, F., Louis, E., Katz, J.: Fractures, fractals and foreign physics. Phys. Today 44, 13 (1991)CrossRefGoogle Scholar
  108. 108.
    Haessig, D.A., Friedland, B.: On the modelling and simulation of friction. J. Dyn. Syst. Meas. Control 113, 354–362 (1992)CrossRefGoogle Scholar
  109. 109.
    Hegazy, A.A.H.: Thermal joint conductance of comforming rough surfaces: effect of surface micro-hardness variation. Ph.D. thesis, University of Waterloo, UK (1985)Google Scholar
  110. 110.
    Hertz, H.: Über die Berührung fester elastischer Körper. J. Reine Angew. Math. 92, 156–171 (1881)Google Scholar
  111. 111.
    Heslot, F., Baumberger, T., Perrin, B., Caroli, B., Caroli, C.: Creep, stick-slip, and dry-friction dynamics: experiments and a heuristic model. Phys. Rev. E 49, 4973–4988 (1994)CrossRefGoogle Scholar
  112. 112.
    Hess, D.P., Soom, A.: Friction at a lubricated line contact operating at oscillating sliding velocities. J. Tribol. 112, 147–152 (1990)CrossRefGoogle Scholar
  113. 113.
    Hess, D.P., Soom, A., Kim, C.H.: Normal vibrations and friction at a Hertzian contact under random excitation: Theory and experiment. J. Sound Vib. 153, 491–508 (1991)CrossRefGoogle Scholar
  114. 114.
    Hinrichs, N.: Reibungsschwingungen mit Selbst- und Fremderregung: Experiment, Modellierung und Berechnung. In: Fortschr.-Ber. VDI, Reihe 11, vol. 240. VDI-Verlag, Dsseldorf (1997)Google Scholar
  115. 115.
    Hobbs, B.E., Brady, B.H.G.: Normal stress changes and the constitutive law for rock friction (abstract). EOS Trans. Am. Geophys. Union 66, 382 (1985)Google Scholar
  116. 116.
    Höge, M.: Sensorische rückwirkung von piezoelektrischen aktoren und ihre anwendung im kraftfahrzeug. Ph.D. thesis, Johannes Kepler University, Linz, Austria (2007)Google Scholar
  117. 117.
    Howe, P.G., Benton, D.P., Puddington, I.E.: London - Van der Waals attractive forces between glass surfaces. Can. J. Chem. 33, 1375–1383 (1955)CrossRefGoogle Scholar
  118. 118.
    Huber, C.: Modellbasierte regelkonzepte auf der basis sensorischer rückwirkung von schnell schaltenden aktoren. Ph.D. thesis, Johannes Kepler University (2011)Google Scholar
  119. 119.
    Hui, C.Y., Lin, Y.Y., Baney, J.M.: The mechanics of tack: viscoelastic contact on a rough surface. J. Polym. Sci. B Polym. Phys. 38, 1485–1495 (2000)CrossRefGoogle Scholar
  120. 120.
    Hurd, A.J., Weitz, D.A., Mandelbrot, B.B. (eds.): Fractal Aspects of Materials: Disordered Systems. Materials Research Society, Pittsburgh (1987)Google Scholar
  121. 121.
    Hyun, S., Pei, L., Molinari, J.F., Robbins, M.O.: Finite-element analysis of contact between elastic self-affine surfaces. Phys. Rev. E 70, 026117(12) (2004)CrossRefGoogle Scholar
  122. 122.
    Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaos. Part I: Mechanics of contact and friction. Appl. Mech. Rev. 47, 209–226 (1994)CrossRefGoogle Scholar
  123. 123.
    Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaos. Part II: Dynamics and modeling. Appl. Mech. Rev. 47, 227–253 (1994)CrossRefGoogle Scholar
  124. 124.
    Irfan, M.A., Prakash, V.: Time resolved friction during dry sliding of metal on metal. Int. J. Solids Struct. 37, 2859–2882 (2000)zbMATHCrossRefGoogle Scholar
  125. 125.
    Ishlinsky, A.Y., Kragelsky, I.Y.: On stick-slip in sliding (in Russian). J. Tech. Phys. 14, 276–282 (1944)Google Scholar
  126. 126.
    Jackson, R.L., Chusoipin, I., Green, I.: A finite element study of the residual stress and deformation in hemispherical contacts. J. Tribol. 127, 484–493 (2005)CrossRefGoogle Scholar
  127. 127.
    Jackson, R.L., Duvvuru, R.S., Meghani, H., Mahajan, M.: An analysis of elasto-plastic sliding spherical asperity interaction. Wear 262, 210–219 (2006)CrossRefGoogle Scholar
  128. 128.
    Jackson, R.L., Green, I.: A finite element study of elasto-plastic hemispherical contact against a rigid flat. J. Tribol. 127, 343–354 (2005)CrossRefGoogle Scholar
  129. 129.
    Jackson, R.L., Green, I., Marghitu, D.B.: Predicting the coefficient of restitution of impacting elastic-perfectly plastic spheres. Nonlinear Dyn. 60, 217–229 (2009)CrossRefGoogle Scholar
  130. 130.
    Jackson, R.L., Streator, J.L.: A multi-scale model for contact between rough surfaces. Wear 261, 1337–1347 (2006)CrossRefGoogle Scholar
  131. 131.
    Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)zbMATHCrossRefGoogle Scholar
  132. 132.
    Johnson, T.: Time-dependent friction of granite: implications for precursory slip on faults. J. Geophys. Res. 86, 6017–6028 (1981)CrossRefGoogle Scholar
  133. 133.
    Ju, Y., Farris, T.N.: Spectral analysis of two-dimensional contact problems. J. Tribol. 118, 320–328 (1996)CrossRefGoogle Scholar
  134. 134.
    Jung, C.M., Feeny, B.F.: Friction-induced vibration in periodic linear elastic media. J. Sound Vib. 252, 945–954 (2002)CrossRefGoogle Scholar
  135. 135.
    Kadin, Y., Kligerman, Y., Etsion, I.: Unloading an elastic-plastic contact of rough surfaces. J. Mech. Phys. Solids 54, 2652–2674 (2006)CrossRefGoogle Scholar
  136. 136.
    Kadin, Y., Kligerman, Y., Etsion, I.: Jump-in induced plastic yield onset of approaching microcontacts in the presence of adhesion. J. Appl. Phys. 103, 013513 (2008)CrossRefGoogle Scholar
  137. 137.
    Kadin, Y., Kligerman, Y., Etsion, I.: Loading-unloading of an elastic-plastic adhesive spherical microcontact. J. Colloid Interface Sci. 321, 242–250 (2008)CrossRefGoogle Scholar
  138. 138.
    Kadin, Y., Kligermann, Y., Etsion, I.: Multiple loading-unloading of an elastic-plastic spherical contact. Int. J. Solids Struct. 43, 7119–7127 (2006)zbMATHCrossRefGoogle Scholar
  139. 139.
    Karnopp, D.: Computer simulation of stick-slip friction in mechanical dynamic systems. J. Dyn. Syst. Meas. Control 107, 100–103 (1985)CrossRefGoogle Scholar
  140. 140.
    Kato, S., Matsubayashi, T.: On the dynamic behavior of machine tool slideway. Bull. JSME 13, 170–179 (1970)CrossRefGoogle Scholar
  141. 141.
    Kato, S., Sato, N., Matsubayashi, T.: Some considerations on characteristics of static friction in machine tool slideway. J. Lubr. Technol. 94, 234–247 (1972)CrossRefGoogle Scholar
  142. 142.
    Kim, J.Y., Baltazar, A., Rokhlin, S.I.: Ultrasonic assessment of rough surface contact between solids from elastoplastic loading-unloading hysteresis cycle. J. Mech. Phys. Solids 52, 1911–1934 (2004)CrossRefGoogle Scholar
  143. 143.
    Kligerman, Y., Etsion, I., Brizmer, V., Kadin, Y.: Friction and contact between rough surfaces based on elastic-plastic sphere and rigid flat interaction. In: Wiggers, P., Nackenhorst, U. (eds.) Analysis and Simulation of Contact Problems, pp. 223–229. Springer, Berlin (2006)CrossRefGoogle Scholar
  144. 144.
    Kogut, L., Etsion, I.: Elastic-plastic contact analysis of a sphere and a rigid flat. J. Appl. Mech. 69, 657–662 (2002)zbMATHCrossRefGoogle Scholar
  145. 145.
    Kogut, L., Etsion, I.: A semi-analytical solution for the sliding inception of a spherical contact. J. Tribol. 125, 499–506 (2003)CrossRefGoogle Scholar
  146. 146.
    Kragelsky, I.V., Alisin, V.V., Palkin, F., Palkin, V.: Tribology: lubrication, friction and wear. Wiley, Hoboken (2005)Google Scholar
  147. 147.
    Krallis, M., Hess, D.P.: Stick-slip in the presence of a normal vibration. Tribotest J. 8–3, 205–219 (2002)CrossRefGoogle Scholar
  148. 148.
    Krithivasan, V., Jackson, R.L.: An analysis of three-dimensional elasto-plastic sinusoidal contact. Tribol. Lett. 27, 31–43 (2007)CrossRefGoogle Scholar
  149. 149.
    Kucharski, S., Klimczak, T., Polijaniuk, A., Kaczmarek, J.: Finite-elements model for the contact of rough surfaces. Wear 177, 1–13 (1994)CrossRefGoogle Scholar
  150. 150.
    Lau, J.H. (ed.): Ball Grid Array Technology. McGraw-Hill, New York (1995)Google Scholar
  151. 151.
    Laursen, T.A.: Computational Contact and Impact Mechanics. Springer, Berlin (2002)zbMATHGoogle Scholar
  152. 152.
    Lin, L.P., Lin, J.F.: An elastoplastic microasperity contact model for metallic materials. J. Tribol. 127, 666–672 (2005)CrossRefGoogle Scholar
  153. 153.
    Linker, M.F., Dieterich, J.H.: Effects of variable normal stress on rock friction: observations and constitutive equations. J. Geophys. Res. 95, 4923–4940 (1992)CrossRefGoogle Scholar
  154. 154.
    Lockner, D.A., Summers, R., Byerlee, J.D.: Effects of temperature and sliding rate on frictional strength of granite. Pure Appl. Geophys. 124, 445–469 (1986)CrossRefGoogle Scholar
  155. 155.
    Longuet-Higgins, M.S.: Statistical properties of an isotropic random surface. Proc. R. Soc. Lond. A 250, 157–174 (1957)MathSciNetzbMATHGoogle Scholar
  156. 156.
    Lu, C.J., Kuo, M.C.: Coefficients of restitution based on a fractal surface model. J. Appl. Mech. 70, 339–345 (2003)zbMATHCrossRefGoogle Scholar
  157. 157.
    Luo, J., Liu, S., Wen, S.: Contact ratio and deformation of asperity in nano-partial lubrication. Sci. China A 44, 78–85 (2001)CrossRefGoogle Scholar
  158. 158.
    Majumdar, A., Bhushan, B.: Role of fractal geometry in roughness characterization and contact mechanics of surfaces. J. Tribol. 112, 205–216 (1990)CrossRefGoogle Scholar
  159. 159.
    Majumdar, A., Bhushan, B.: Fractal model of elastic-plastic contact between rough surfaces. J. Tribol. 113, 1–11 (1991)CrossRefGoogle Scholar
  160. 160.
    Majumdar, A., Tien, C.L.: Fractal characterization and simulation of rough surfaces. Wear 136, 313–327 (1990)CrossRefGoogle Scholar
  161. 161.
    Majumdar, A., Tien, C.L.: Fractal network model for contact conductance. J. Heat Transfer 113, 516–525 (1991)CrossRefGoogle Scholar
  162. 162.
    Mandelbrot, B.B.: The Fractal Geometry of Nature. W.H. Freeman and Co., New York (1982)zbMATHGoogle Scholar
  163. 163.
    Manners, W., Greenwood, J.A.: Some observations on Persson’s diffusion theory of elastic contact. Wear 261, 600–610 (2006)CrossRefzbMATHGoogle Scholar
  164. 164.
    Marone, C.: Laboratory-derived friction laws and their application to seismic faulting. Annu. Rev. Earth Planet. Sci. 26, 643–696 (1998)CrossRefGoogle Scholar
  165. 165.
    McCool, J.I.: Comparison of models for the contact of rough surfaces. Wear 107, 37–60 (1986)CrossRefGoogle Scholar
  166. 166.
    Michaelis, S.: Entwicklung von mikromechanischen schaltern für neuartige mems-produkte unter aspekten industrieller fertigungsprozesse. Ph.D. thesis, University Bremen (2001)Google Scholar
  167. 167.
    Michely, T., Krug, J.: Islands, Mounds, and Atoms: Patterns and Processes in Crystal Growth Far from Equilibrium. Springer, Berlin (2004)CrossRefGoogle Scholar
  168. 168.
    Mikic, B.B.: Thermal contact conductance: theoretical considerations. Int. J. Heat Mass Transf. 17, 205–214 (1974)CrossRefGoogle Scholar
  169. 169.
    Moore, A.C., Tabor, D.: Some mechanical and adhesive properties of indium. Br. J. Appl. Phys. 3, 299–301 (1952)CrossRefGoogle Scholar
  170. 170.
    Moore, A.J.W.: Deformation of metals in static and in sliding contact. Proc. R. Soc. Lond. A 195, 231–244 (1948)CrossRefGoogle Scholar
  171. 171.
    Morag, Y., Etsion, I.: Resolving the contradiction of asperities plastic to elastic mode transition in current contact models of fractal rough surfaces. Wear 262, 624–629 (2007)CrossRefGoogle Scholar
  172. 172.
    Mulhearn, T.O., Tabor, D.: Creep and hardness of metals: a physical study. J. Inst. Met. 89, 7–12 (1960)Google Scholar
  173. 173.
    Müser, M.H.: Rigorous field-theoretical approach to the contact mechanics of rough elastic solids. Phys. Rev. Lett. 100, 055,504(4) (2008)Google Scholar
  174. 174.
    Nayak, P.R.: Random process model of rough surfaces. J. Lubr. Technol. 93, 398–407 (1971)CrossRefGoogle Scholar
  175. 175.
    Nayak, P.R.: Random process model of rough surfaces in plastic contact. Wear 26, 305–333 (1973)CrossRefGoogle Scholar
  176. 176.
    Nayak, P.R.: Some aspects of surface roughness measurement. Wear 26, 165–174 (1973)CrossRefGoogle Scholar
  177. 177.
    Nix, W.D., Gao, H.J.: Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411–425 (1998)zbMATHCrossRefGoogle Scholar
  178. 178.
    Oden, J.T., Martins, J.A.C.: Models and computational methods for dynamic friction phenomena. Comput. Methods Appl. Mech. Eng. 52, 527–634 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  179. 179.
    Ogbonna, N., Fleck, N.A., Cocks, C.F.: Transient creep analysis of ball indentation. Int. J. Mech. Sci. 37, 1179–1202 (1995)zbMATHCrossRefGoogle Scholar
  180. 180.
    Okamura, K., Matsubara, T., Noro, S., Yamane, T.: Study of frictional vibration (theoretical analysis). J. Jpn. Soc. Precis. Eng. 34, 31–36 (1968)Google Scholar
  181. 181.
    Olsson, H.: Control systems with friction. Ph.D. thesis, Lund Institute of Technology, Lund, Sweden (1996)Google Scholar
  182. 182.
    Olsson, W.A.: Normal stress history effects on friction in tuff. EOS Trans. Am. Geophys. Union 66, 1101 (1985)Google Scholar
  183. 183.
    Olsson, W.A.: The effects of changes in normal stress on rock friction. In: Desai, C.S., Krempl, E., Kiousis, P.D., Kundu, T. (eds.) Constitutive Laws for Engineering Materials – Theory and Applications, pp. 1059–1066. Elsevier, New York (1987)Google Scholar
  184. 184.
    Olsson, W.A.: Rock joint compliance studies. Technical Report, SAND86–0177, Sandia National Laboratories Report, Abuquerque (1987)Google Scholar
  185. 185.
    Olsson, W.A.: The effects of normal stress history on rock friction. In: Cundall, P.A., Starfield, A.M., Sterling, R.L. (eds.) Key Questions in Rock Mechanics: Proceedings of the 29th US Symposium on Rock Mechanics, pp. 111–117 (1988)Google Scholar
  186. 186.
    Olsson, W.A.: The effects of shear and normal stress paths on rock friction. In: Barton, N., Stephansson, O. (eds.) Rock Joints: Proceedings of the International Symposium on Rock Joints, pp. 475–479 (1990)Google Scholar
  187. 187.
    Ossa, E.A., Deshpande, V.S., Cebon, D.: Spherical indentation behaviour of bitumen. Acta Mater. 53, 3103–3113 (2005)CrossRefGoogle Scholar
  188. 188.
    Panagiotopoulos, P.D.: Fractals and fractal approximation in structural mechanics. Meccanica 27, 25–33 (1992)zbMATHCrossRefGoogle Scholar
  189. 189.
    Perfettini, H., Schmittbuhl, J., Rice, J.R., Cocco, M.: Frictional response induced by time-dependent fluctuations of the normal loading. J. Geophys. Res. 106, 13455–13472 (2001)CrossRefGoogle Scholar
  190. 190.
    Persson, B.N.J.: Theory of friction: Stress domains, relaxation, and creep. Phys. Rev. E 51, 13568–13585 (1995)Google Scholar
  191. 191.
    Persson, B.N.J.: Sliding Friction: Physical Principles and Applications, 2nd edn. Springer, Berlin (2000)zbMATHCrossRefGoogle Scholar
  192. 192.
    Persson, B.N.J.: Theory of time-dependent plastic deformation in disordered solids. Phys. Rev. B 61, 5949–5966 (2000)CrossRefGoogle Scholar
  193. 193.
    Persson, B.N.J.: Elastoplastic contact between randomly rough surfaces. Phys. Rev. Lett. 87, 116101(4) (2001)CrossRefGoogle Scholar
  194. 194.
    Persson, B.N.J.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115, 3840–3861 (2001)CrossRefGoogle Scholar
  195. 195.
    Persson, B.N.J.: Reply to Borodich’s comment on “Elastoplastic contact between randomly rough surfaces”. Phys. Rev. Lett. 88, 069602(1) (2002)Google Scholar
  196. 196.
    Persson, B.N.J.: Contact mechanics for randomly rough surfaces. Surf. Sci. Rep. 61, 201–227 (2006)MathSciNetCrossRefGoogle Scholar
  197. 197.
    Persson, B.N.J.: Relation between interfacial separation and load: a general theory of contact mechanics. Phys. Rev. Lett. 99, 125502(4) (2007)CrossRefGoogle Scholar
  198. 198.
    Persson, B.N.J., Albohr, O., Tartaglino, U., Volokitin, A.I., Tosatti, E.: On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J. Phys. Condens. Matter 17, R1–R62 (2005)CrossRefGoogle Scholar
  199. 199.
    Persson, B.N.J., Bucher, F., Chiaia, B.: Elastic contact between randomly rough surfaces: comparison of theory with numerical results. Phys. Rev. B 65, 184106(7) (2002)Google Scholar
  200. 200.
    Persson, B.N.J., Tosatti, E. (eds.): Physics of Sliding Friction. In: NATO ASI Series, Series E: Applied Sciences, vol. 311. Kluwer, Dordrecht (1996)Google Scholar
  201. 201.
    Pilipchuk, V.N., Tan, C.A.: Creep-slip capture as a possible source of squeal during decelerated sliding. Nonlinear Dyn. 35, 259–285 (2004)zbMATHCrossRefGoogle Scholar
  202. 202.
    Pinto da Costa, A., Martins, J.A.C., Figueiredo, I.N., Júdice, J.J.: The directional instability problem in systems with frictional contacts. Comput. Methods Appl. Mech. Eng. 193, 357–384 (2004)Google Scholar
  203. 203.
    Prakash, V.: Frictional response of sliding interfaces subjected to time varying normal pressures. J. Tribol. 120, 97–102 (1998)CrossRefGoogle Scholar
  204. 204.
    Quicksall, J.J., Jackson, R.L., Green, I.: Elasto-plastic hemispherical contact models for various mechanical properties. Proc. Inst. Mech. Eng. J Eng. Tribol. 218, 313–322 (2004)CrossRefGoogle Scholar
  205. 205.
    Rabinowicz, E.: The instrinsic variables affecting the stick-slip process. Proc. Phys. Soc. 71, 668–675 (1958)CrossRefGoogle Scholar
  206. 206.
    Rabinowicz, E.: Friction and Wear of Materials. Wiley, Hoboken (1965)Google Scholar
  207. 207.
    Ramesh Kumar, M.V., Narasimhan, R.: Analysis of spherical indentation of linear viscoelastic materials. Curr. Sci. 87, 1088–1095 (2004)Google Scholar
  208. 208.
    Rice, J.R., Lapusta, N., Ranjith, K.: Rate and state dependent friction and the stability of sliding between elastically deformable solids. J. Mech. Phys. Solids 49, 1865–1898 (2001)zbMATHCrossRefGoogle Scholar
  209. 209.
    Rice, J.R., Ruina, A.L.: Stability of steady frictional slipping. J. Appl. Mech. 50, 343–349 (1983)zbMATHCrossRefGoogle Scholar
  210. 210.
    Richardson, E., Marone, C.: Effects of normal stress vibrations on frictional healing. J. Geophys. Res. 104, 28859–28878 (1999)CrossRefGoogle Scholar
  211. 211.
    Ruina, A.L.: Friction laws and instabilities: A quasistatic analysis of some dry frictional behavior. Ph.D. thesis, Brown University, Providence, USA (1980)Google Scholar
  212. 212.
    Ruina, A.L.: Slip instability and state variable friction laws. J. Geophys. Res. 88, 10359–10370 (1983)CrossRefGoogle Scholar
  213. 213.
    Russ, J.C.: Fractal Surfaces. Plenum Press, New York (1994)Google Scholar
  214. 214.
    Ryabov, V.B., Ito, H.M.: Multistability and chaos in a spring-block model. Phys. Rev. E 52, 6101–6112 (1995)CrossRefzbMATHGoogle Scholar
  215. 215.
    Sahoo, P., Banerjee, A.: Asperity interaction in elastic-plastic contact of rough surfaces in presence of adhesion. J. Phys. D Appl. Phys. 38, 2841–2847 (2005)CrossRefGoogle Scholar
  216. 216.
    Scholz, C.H.: Earthquakes and friction laws. Nature 391, 37–42 (1998)CrossRefGoogle Scholar
  217. 217.
    Scholz, C.H.: The Mechanics of Earthquakes and Faulting, 2nd edn. Cambridge University Press, Cambridge (2002)CrossRefGoogle Scholar
  218. 218.
    Sellgren, U., Olofsson, U.: Application of a constitutive model for micro-slip in finite element analysis. Comput. Methods Appl. Mech. Eng. 170, 65–77 (1999)zbMATHCrossRefGoogle Scholar
  219. 219.
    Sextro, W.: Dynamical Contact Problems with Friction: Models, Methods, Experiments and Applications, 2nd edn. Springer, Berlin (2007)zbMATHCrossRefGoogle Scholar
  220. 220.
    Sheng, G.: Friction-Induced Vibrations and Sound: Principles and Applications. CRC Press, Boca Raton (2007)Google Scholar
  221. 221.
    Singer, I.L., Pollock, H.M. (eds.): Fundamentals of Friction: Macroscopic and Microscopic Processes. NATO ASI Series, Series E: Applied Sciences, vol. 220. Kluwer, Dordrecht (1992)Google Scholar
  222. 222.
    Soom, A., Kim, C.: Interactions between dynamic normal and frictional forces during unlubricated sliding. J. Lubr. Technol. 105, 221–229 (1983)CrossRefGoogle Scholar
  223. 223.
    Spurr, R.T.: Creep and static friction. Br. J. Appl. Phys. 6, 402–403 (1955)CrossRefGoogle Scholar
  224. 224.
    Spurr, R.T., Newcomb, T.P.: The adhesion theory of friction. Proc. Phys. Soc. B 70, 98–101 (1957)CrossRefGoogle Scholar
  225. 225.
    Spurr, R.T., Newcomb, T.P.: The variation of friction with velocity. Proc. Phys. Soc. B 70, 198–200 (1957)CrossRefGoogle Scholar
  226. 226.
    Srinivasan, S., Russ, J.C., Scattergood, R.O.: Fractal analysis of erosion surfaces. J. Mater. Res. 5, 2616–2619 (1990)CrossRefGoogle Scholar
  227. 227.
    Stanley, H.M., Kato, T.: An FFT-based method for rough surface contact. J. Tribol. 119, 481–485 (1997)CrossRefGoogle Scholar
  228. 228.
    Stribeck, R.: Die wesentlichen Eigenschaften der Gleit-und Rollenlager. Z. Verein. Deut. Ing. 46, 1341–1348 (1902)Google Scholar
  229. 229.
    Tabor, D.: The Hardness of Metals. Clarendon Press, Oxford (1951)Google Scholar
  230. 230.
    Tabor, D.: Friction – the present state of our understanding. J. Lubr. Technol. 103, 169–179 (1981)Google Scholar
  231. 231.
    Tariku, F.A.: Simulation of dynamic mechanical systems with stick-slip friction (master’s thesis). Master’s thesis, University of New Brunswick, Canada (1998)Google Scholar
  232. 232.
    Tariku, F.A., Rogers, R.J.: Improved dynamic friction models for simulation of one-dimensional and two-dimensional stick-slip motion. J. Tribol. 123, 661–669 (2001)CrossRefGoogle Scholar
  233. 233.
    Taylor, J.H., Kebede, D.: Modeling and simulation of hybrid systems. In: 34th Proceedings of the IEEE Conference on Decision and Control, pp. 2685–2687 (1995)Google Scholar
  234. 234.
    Taylor, J.H., Kebede, D.: Rigorous hybrid systems simulation of an electro-mechanical pointing system with discrete-time control. In: Proceedings of the 1997 American Control Conference, pp. 2786–2789 (1997)Google Scholar
  235. 235.
    Thomas, K.: Cold welding. In: ASM Handbook, vol. 6. Welding, Brazing, and Soldering, pp. 307–310. ASM International, Russell Township (1993)Google Scholar
  236. 236.
    Thompson, M.K., Thompson, J.M.: Considerations for the incorporation of measured surfaces in finite element models. Scanning 32, 183–198 (2010)CrossRefGoogle Scholar
  237. 237.
    Tolstoi, D.M.: Significance of the normal degree of freedom and natural normal vibrations in contact friction. Wear 10, 199–213 (1967)CrossRefGoogle Scholar
  238. 238.
    Tucker, K., Green, I.: Finite element analysis of electromagnetic effects on hemispherical contacts. In: Proceedings of the 9th Biennial ASME Conference on Engineering Systems Design and Analysis (ESDA2008), Haifa Israel, 2008, p. 59040(6)Google Scholar
  239. 239.
    Tworzydlo, W.W., Becker, E.: Influence of forced vibrations on the static coefficient of friction – numerical modeling. Wear 143, 175–196 (1991)CrossRefGoogle Scholar
  240. 240.
    Tworzydlo, W.W., Hamzeh, O.N.: On the importance of normal vibrations in modeling of stick slip in rock sliding. J. Geophys. Res. 102, 15091–15103 (1997)CrossRefGoogle Scholar
  241. 241.
    Ullah, H., Irfan, M.A., Prakash, V.: State and rate dependent friction laws for modeling high-speed frictional slip at metal-on-metal interfaces. J. Tribol. 129, 17–22 (2007)CrossRefGoogle Scholar
  242. 242.
    Wang, W., Scholz, C.H.: Micromechanics of the velocity and normal stress dependence of rock friction. Pure Appl. Geophys. 143, 303–315 (1994)CrossRefGoogle Scholar
  243. 243.
    Wang, Z., Dohda, K., Haruyama, Y.: Effects of entraining velocity of lubricant and sliding velocity on friction behavior in stainless steel sheet rolling. Wear 260, 249–257 (2006)CrossRefGoogle Scholar
  244. 244.
    Warren, T.L., Krajcinovic, D.: Random cantor set models for the elastic-perfectly plastic contact of rough surfaces. Wear 196, 1–15 (1996)CrossRefGoogle Scholar
  245. 245.
    Westergaard, H.M.: Bearing pressures and cracks. J. Appl. Mech. 6, 49–53 (1939)Google Scholar
  246. 246.
    Williamson, J.B.P., Hunt, R.T.: Asperity persistence and the real area of contact between rough surfaces. Proc. R. Soc. Lond. A 327, 147–157 (1972)CrossRefGoogle Scholar
  247. 247.
    Willner, K.: Elasto-plastic normal contact of three-dimensional fractal surfaces using halfspace theory. J. Tribol. 126, 28–33 (2004)CrossRefGoogle Scholar
  248. 248.
    Wolf, D.E., Grassberger, P. (eds.): HLRZ Workshop on Friction, Arching, Contact Dynamics. World Scientific, Singapore (1997)Google Scholar
  249. 249.
    Wong, P.Z., Bray, A.J.: Small-angle scattering by rough and fractal surfaces. J. Appl. Crystallogr. 21, 786–794 (1988)CrossRefGoogle Scholar
  250. 250.
    Yan, W., Komvopoulos, K.: Contact analysis of elastic-plastic fractal surfaces. J. Appl. Phys. 84, 3617–3624 (1998)CrossRefGoogle Scholar
  251. 251.
    Yang, C., Persson, B.N.J.: Contact mechanics: Contact area and interfacial separation from small contact to full contact. J. Phys. Condens. Matter 20, 215214(13) (2008)Google Scholar
  252. 252.
    Yang, C., Persson, B.N.J., Israelachvili, J., Rosenberg, K.: Contact mechanics with adhesion: interfacial separation and contact area. Europhys. Lett. 84, 46004(5) (2008)Google Scholar
  253. 253.
    Yang, C., Tartaglino, U., Persson, B.N.J.: A multiscale molecular dynamics approach to contact mechanics. Eur. Phys. J. E 19, 47–58 (2006)CrossRefGoogle Scholar
  254. 254.
    Yang, J., Komvopoulos, K.: A mechanics approach to static friction of elastic-plastic fractal surfaces. J. Tribol. 127, 315–324 (2005)CrossRefGoogle Scholar
  255. 255.
    Yashioka, N.: A review of the micromechanical approach to the physics of contacting surfaces. Tectonophysics 277, 29–40 (1997)CrossRefGoogle Scholar
  256. 256.
    Zavarise, G., Borri-Brunetto, M., Paggi, M.: On the resolution dependence of micromechanical contact models. Wear 262, 42–54 (2007)CrossRefGoogle Scholar
  257. 257.
    Zhao, Y., Chang, L.: A model of asperity interactions in elastic-plastic contact of rough surfaces. J. Tribol. 123, 857–864 (2001)CrossRefGoogle Scholar
  258. 258.
    Zhuang, W.D., Chang, P.C., Chou, F.Y., Shiue, R.K.: Effect of solder creep on the reliability of large area die attachment. Microelectron. Reliab. 41, 2011–2021 (2001)CrossRefGoogle Scholar

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Authors and Affiliations

  • Andreas Goedecke
    • 1
  1. 1.Siemens Corporate Technology Siemens AGMunichGermany

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