A Survey of Current Models for Simulating the Contact between Rough Surfaces

REFERENCES

• Johnson , K. L. , Contact Mechanics , Cambridge University Press , ( 1985 ).
   Google Scholar
• Greenwood , J. A. and Williamson , J. B. P. , “Contact of Nominally Flat Surface,” in Proc. Roy. Soc., A295 , pp 300 – 319 ( 1966 ).
   Google Scholar
• Greenwood , J. A. and Tripp , J. H. , “ The Contact of Two Nominally Flat Rough Surfaces,” in Proc. Instn. Mech. Engrs. , 185 , pp 48 – 71 ( 1971 ).
   Google Scholar
• Whitehouse , D. J. and Archard , J. F. , “The Properties of Random Surfaces of Significance in Their Contact,” in Proc. Roy. Soc. Lond, A316 , pp 97 – 121 ( 1970 ).
   Google Scholar
• Onions , R. A. and Archard , J. F. , “ The Contact of Surfaces Having a Random Structure,” Jour. of Phys. D, Appl. Phys. , 6 , pp 289 – 304 ( 1973 ).
   Web of Science ®Google Scholar
• Bush , A. W. , Gibson , R. D. and Thomas , T. R. , “ The Elastic Contact of a Rough Surface,” Wear , 35 , pp 87 – 111 ( 1975 ).
   Web of Science ®Google Scholar
• Bush , A. W. , Gibson , R. D. and Keogh , G. P. , “ Strongly Anisotropic Rough Surfaces,” ASME Jour. of Lubr. Tech. , 101 , pp 15 – 20 ( 1979 ).
   Google Scholar
• Thomas , T. R. , Rough Surfaces , Longman , London , ( 1982 ).
   Google Scholar
• McCool , J. I. , “ Comparison of Models for the Contact of Rough Surfaces,” Wear , 107 , pp 37 – 60 ( 1986 ).
   Web of Science ®Google Scholar
• Komvopoulos , K. and Choi , D. H. , “ Elastic Finite Element Analysis of Multi-Asperity Contacts,” ASME Jour. of Trib. , 114 , pp 823 – 831 ( 1992 ).
   Web of Science ®Google Scholar
• Goryacheva , I. , Sadeghi , F. and Nickel , D. A. , “ Internal Stresses in Contact of a Rough Body and a Viscoelastic Layered Semi-Infinite Plane,” ASME Jour. of Trib. , 118 , pp 131 – 136 ( 1996 ).
   Google Scholar
• Patir , N. , “ A Numerical Procedure for Random Generation of Rough Surfaces,” Wear , 47 , pp 263 – 277 ( 1978 ).
   Web of Science ®Google Scholar
• Lai , W. T. and Cheng , H. S. , “ Computer Simulation of Elastic Rough Contacts,” Trib. Trans. , 28 , pp 172 – 180 ( 1985 ).
   Google Scholar
• Ren , N. and Lee , S. C. , “ The Effects of Surface Roughness and Topography on the Contact Behavior of Elastic Bodies,” ASME Jour. of Trib. , 116 , pp 804 – 811 ( 1994 ).
   Web of Science ®Google Scholar
• Hu , Y. Z. and Tonder , K. , “ Simulation of 3-D Random Surface by 2-D Digital Filter and Fourier Analysis,” Int'l. Jour. of Mach. Tool Manufact. , 32 , pp 82 – 90 ( 1992 ).
   Google Scholar
• Tian , X. F. and Bhushan , B. , “ A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle,” ASME Jour. of Trib. , 118 , pp 33 – 42 ( 1996 ).
   Web of Science ®Google Scholar
• Yu , M. M. H. and Bhushan , B. , “ Contact Analysis of Three-Dimensional Rough Surfaces under Frictionless and Frictional Contact,” Wear , 200 , pp 265 – 280 ( 1996 ).
   Google Scholar
• Myshkin , N. K. , Petrokovets , M. I. and Chizhik , S. A. , “ Simulation of Real Contact in Tribology,” Trib. Int'l. , 31 , pp 79 – 86 ( 1998 ).
   Web of Science ®Google Scholar
• Williamson , J. B. P. , “ The Microtopography of Surfaces,” in Proc. Inst. Mech. Engrs. , 182 , 3k , pp 21 – 30 ( 1967/1968 ).
   Google Scholar
• Bhushan , B. and Cook , N. H. , “ On the Correlation between Friction Coefficients and Adhesion Stresses,” ASME Jour. of Eng. Materials and Tech. , 97 , pp 285 – 287 ( 1975 ).
   Google Scholar
• Sayles , R. S. and Thomas , T. R. , “ Computer Simulation of the Contacting Rough Surfaces,” Wear , 49 , pp 273 – 296 ( 1978 ).
   Web of Science ®Google Scholar
• Webster , M. N. and Sayles , R. S. , “ A Numerical Model for the Elastic Frictionless Contact of Real Rough Surfaces,” ASME Jour. of Trib. , 108 , pp 314 – 320 ( 1986 ).
   Web of Science ®Google Scholar
• Cole , S. J. and Sayles , R. S. , “ A Numerical Model for the Contact of Layered Elastic Bodies with Real Rough Surfaces,” ASME Jour. of Trib. , 114 , pp 334 – 340 ( 1992 ).
   Web of Science ®Google Scholar
• Lee , S. C. and Cheng , H. S. , “ On the Relation of Load to Average Gap in the Contact Between Surfaces with Longitudinal Roughness,” STLE Trib. Trans. , 35 , pp 523 – 529 ( 1992 ).
   Web of Science ®Google Scholar
• Mao , K. , Sun , Y. and Bell , T. , “ A Numerical Model for the Dry Sliding Contact of Layered Elastic Bodies with Rough Surfaces,” STLE Trib. Trans. , 39 , pp 416 – 424 ( 1996 ).
   Web of Science ®Google Scholar
• Sui , P. C. , “ An Efficient computation Model for Calculating Surface Contact Pressures Using Measured Surface Roughness,” STLE Trib. Trans. , 40 , pp 243 – 250 ( 1997 ).
   Web of Science ®Google Scholar
• Bhushan , B. Wyant , J. C. and Meiling , J. , “ A New Three-Dimensional Non-Contact Digital Optical Profiler,” Wear , 122 , pp 301 – 312 ( 1988 ).
   Web of Science ®Google Scholar
• Kohno , T. , Osawa , N. , Miyamoto , K. and Mushas , T. , “ Practical Non-Contact Surface Measuring Instrument with One Nanometric Resolution,” in Proc. Eng. , 7 , pp 231 – 232 ( 1985 ).
   Google Scholar
• Myshkin , N. K. , Grigoryev , A. Y. and Kholodilov , O. V. , “ Quantitative Analysis of Surface Topography using Scanning Electron Microscopy,” Wear , 153 , pp 119 – 133 ( 1992 ).
   Google Scholar
• Binning , G. and Rohrer , H. , “ Scanning Tunneling Microscopy,” Physica. Acta , 55 , pp 726 – 735 ( 1982 ).
   Google Scholar
• Sarid , D. , Scanning Force Microscopy , Oxford University Press , ( 1994 ).
   Google Scholar
• Atomic Force Microscopy/Scanning Tunneling Microscopy , Cohen , S. H. , Bray , M. T. and Lightbody , M. L. , ed., Plenum Publication Corp. , ( 1995 ).
   Google Scholar
• Mandelbrot , B. B. , The Fractal Geometry of Nature , Freeman , New York , ( 1983 ).
   Google Scholar
• Majumdar , A. and Bhushan , B. , “ Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces,” ASME Jour. of Trib. , 112 , pp 204 – 216 ( 1990 ).
   Google Scholar
• Ganti , S. and Bhushan , B. , “ Generalized Fractal Analysis and Its Applications to Engineering Surfaces,” Wear , 180 , pp 17 – 34 ( 1995 ).
   Web of Science ®Google Scholar
• Majumdar , A. and Bhushan , B. , “ Fractal Model of Elastic-Plastic Contact between Rough Surfaces,” ASME Jour. of Trib. , 113 , pp 1 – 11 ( 1991 ).
   Web of Science ®Google Scholar
• Bhushan , B. and Majumdar , A. , “ Elastic-Plastic Contact Model of Bi-fractal Surfaces,” Wear , 153 , pp 53 – 64 ( 1992 ).
   Web of Science ®Google Scholar
• Warren , T. L. and Krajcinovic , D. , “ Fractal Models of Elastic-Perfectly Plastic Contact of Rough Surfaces Based on the Cantor Set,” Int'l. Jour. Solids Struct. , 32 , pp 2907 – 2922 ( 1995 ).
   Google Scholar
• Warren , T. L. and Krajcinovic , D. , “ Random Cantor Set Models for the Elastic-Perfectly Plastic Contact of Rough Surfaces,” Wear , 196 , pp 1 – 15 ( 1996 ).
   Google Scholar
• Timoshenko , S. P. and Goodier , J. N. , Theory of Elasticity , 3rd ed. , McGraw-Hill , New York , ( 1970 ).
   Google Scholar
• Francis , H. A. , “ The Accuracy of Plane Strain Models for the Elastic Contact of Three-Dimensional Rough Surfaces,” Wear , 85 , pp 239 – 256 ( 1983 ).
   Web of Science ®Google Scholar
• Ren , N. and Lee , S. C. , “ Contact Simulation of Three-Dimensional Rough Surfaces Using Moving Grid Method,” ASME Jour. of Trib. , 115 , pp 597 – 601 ( 1993 ).
   Web of Science ®Google Scholar
• Lee , S. C. and Ren , N. , “ Behavior of Elastic-Plastic Rough Surface Contacts as Affected by Surface Topography, Load, and Material Hardness,” Trib. Trans. , 39 , pp 67 – 74 ( 1996 ).
   Web of Science ®Google Scholar
• Leng , Y. S. , Yang , G. P. , Huang , Y. and Zheng , L. Q. , “ The Characteristics of Elastically Contacting Ideal Rough Surfaces,” ASME Jour. of Trib. , 118 , pp 90 – 97 ( 1996 ).
   Google Scholar
• Love , A. E. H. , “ The Stress Produced in a Semi-Infinite Solid by Pressure on Part of the Boundary,” Phil. Trans. Roy. Soc. (London), Series A. , 228 , pp 377 – 420 ( 1929 ).
   Google Scholar
• Ju , Y and Farris , T. N. , “ Spectral Analysis of Two-Dimensional Contact Problems,” ASME Jour. of Trib. , 118 , pp 320 – 328 ( 1996 ).
   Web of Science ®Google Scholar
• Ju , Y. and Zheng , L. , “ A Full Numerical Solution for the Elastic Contact of Three-Dimensional Real Rough Surfaces,” Wear , 157 , pp 151 – 161 ( 1992 ).
   Web of Science ®Google Scholar
• Stanley , H. M. and Kato , T. , “ An FFT-Based Method for Rough Surface Contact,” ASME Jour. of Trib. , 119 , pp 481 – 485 ( 1997 ).
   Web of Science ®Google Scholar
• O'Sullivan , T. C. and King , R. B. , “ Sliding Contact Stress Field Due to a Spherical Indenter on a Layered Elastic Half-Space,” ASME Jour. of Trib. , 110 , pp 235 – 240 ( 1988 ).
   Web of Science ®Google Scholar
• Nogi , T. and Kato , T. , “ Influence of a Hard Surface Layer on the Limit of Elastic Contact—Part I: Analysis Using a Real Surface Model,” ASME Jour. of Trib. , 119 , pp 493 – 500 ( 1997 ).
   Web of Science ®Google Scholar
• Hu , Y. Z. , Barber , G. C. and Zhu , D. , “ Numerical Analysis for the Elastic Contact of Real Rough Surfaces ,” 1998 STLE Annual Meeting Preprint No. 98-NP-2D-1 , STLE, Park Ridge, IL, ( 1998 ).
   Google Scholar
• Sneddon , I. N. , Fourier Transforms , McGraw-Hill , New York , ( 1951 ).
   Google Scholar
• Gupta , P. K. and Walowit , J. A. , “ Contact Stress Between an Elastic Cylinder and a Layered Elastic Solid,” ASME Jour. of Lubr. Tech. , 96 , pp 250 – 257 ( 1974 ).
   Google Scholar
• Merriman , T. and Kannel , J. , “ Analyses of the Role of Surface Roughness on Contact Stresses Between Elastic Cylinders With and Without Soft Surface Coating,” ASME Jour. of Trib. , 111 , pp 87 – 94 ( 1989 ).
   Web of Science ®Google Scholar
• Elsharkawy , A. A. and Hamrock , B. J. , “ A Numerical Solution for Dry Sliding Line Contact of Multilayered Elastic Bodies,” ASME Jour. of Trib. , 115 , pp 237 – 245 ( 1993 ).
   Web of Science ®Google Scholar
• Kucharski , S. , Klimczak , T. , Polijaniuk , A. and Kaczmarek , J. , “ Finite-Element Model for the Contact of Rough Surfaces,” Wear , 177 , pp 1 – 13 ( 1994 ).
   Web of Science ®Google Scholar
• Kral , E. R. , Komvopoulos , K. and Ogy , D. B. , “ Elastic-Plastic Finite Element Analysis of Repeated Indentation of a Half-Space by a Rigid Sphere,” ASME Jour. Appl. Mech. , 60 , pp 829 – 841 ( 1993 ).
   Web of Science ®Google Scholar
• Kral , E. R. , Komvopoulos , K. and Ogy , D. B. , “ Finite Element Analysis of Repeated Indentation of an Elastic-Plastic Layered Medium by a Rigid Sphere,” ASME Jour. Appl. Mech. , 62 , pp 20 – 42 ( 1995 ).
   Google Scholar
• West , M. A. and Sayles , R. S. , “ A 3-Dimensional Method for Studying 3-Body Contact Geometry and Stress on Real Rough Surfaces,” in Proc. 14th Leeds Lyon Symp. on Trib. , 12 , pp 195 – 200 ( 1987 ).
   Google Scholar
• Poon , C. Y. and Sayles , R. S. , “ Numerical Contact Model of a Smooth Ball on Anisotropic Rough Surfaces,” ASME Jour. of Trib. , 116 , pp 194 – 201 ( 1994 ).
   Web of Science ®Google Scholar
• Sayles , R. S. , “ Basic Principles of Rough Surface Contact Analysis Using Numerical Methods,” Trib. Int'l. , 29 , pp 639 – 650 ( 1996 ).
   Google Scholar
• Conry , T. F. and Seireg , A. , “ A Mathematical Programming Method for Design of Elastic Bodies in Contact,” ASME Jour. of Applied Mechanics , 38 , pp 387 – 392 ( 1971 ).
   Google Scholar
• Kalker , J. J. and van Randen , Y. , “ A Minimum Principle for Frictionless Elastic Contact with Application to Non-Hertzian Half-Space Contact Problems,” Jour. of Eng. Math. , 6 , pp 193 – 200 ( 1972 ).
   Google Scholar
• Kalker , J. J. , “ Variational Principles in Contact Elastostatics,” Jour. Inst. Math. Appl. , 20 , p 199 , ( 1977 ).
   Web of Science ®Google Scholar
• Wolfe , P. , “ The Simplex Method for Quadratic Programming,” Econometrica , 27 , pp 382 – 395 ( 1959 ).
   Web of Science ®Google Scholar
• Varga , R. S. , Matrix Iterative Analysis , Prentice-Hill , New York , ( 1962 ).
   Google Scholar
• Bhushan , B. , “ Contact Mechanics of Rough Surfaces in Tribology: Multiple Asperity Contact,” Trib. Letters , 4 , pp 1 – 35 ( 1998 ).
   Web of Science ®Google Scholar
• Klarbring , A. , “ A Mathematical Programming Approach to Three-Dimensional Contact Problems with Friction,” Comp. Meth. Appl. Mech. Eng. , 58 , pp 175 – 200 ( 1986 ).
   Web of Science ®Google Scholar
• Klarbring , A. and Bjorkman , G. , “ The Treatment of Problems in Contact Mechanics by Mathematical Programming,” Jour. of Theoretical and Applied Mechanics , 7 , pp 83 – 96 ( 1988 ).
   Google Scholar
• Klarbring , A. and Bjorkman , G. , “ A Mathematical Programming Approach to Contact Problems with Friction and Varying Contact Surfaces,” Comp. and Struct. , 30 , pp 1185 – 1198 ( 1988 ).
   Web of Science ®Google Scholar
• Sviridenok , A. I. , Chizhik , S. A. and Petrokovets , M. I. , Mechanics of Discrete Friction Contact (in Russian), Nauka I technika , Minsk , ( 1990 ).
   Google Scholar
• Zhu , D. , Cheng , H. S. , Arai , T. and Hamai , K. , “ A Numerical Analysis for Piston Skirts in Mixed Lubrication—Part I: Basic Modeling,” ASME Jour. of Trib. , 114 , pp 553 – 562 ( 1992 ).
   Web of Science ®Google Scholar
• Ai , X. , Cheng , H. S. , Hua , D. , Moteki , K. and Aoyama , S. , “ A Finite Element Analysis of Dynamically Loaded Journal Bearings in Mixed Lubrication,” Trib. Trans. , 41 , pp 273 – 281 ( 1998 ).
   Web of Science ®Google Scholar
• Chang , W. R. , Bogy , D. B. and Etsion , I. , “ Elastic-Plastic Model for the Contact of Rough Surface,” ASME Jour. of Trib. , 109 , pp 15 – 20 ( 1987 ).
   Web of Science ®Google Scholar
• Polonsky , I. A. and Keer , L. M. , “ Scale Effects of Elastic-Plastic Behavior of Microscopic Asperity Contacts ,” ASME 95-TRIB-27 , ASME , New York , p 6 , ( 1995 ).
   Google Scholar
• Ling , F. F. and Kennedy , F. E. , Jr. , “Contact and Surface Mechanics,” 1990 ASME/STLE Trib. Conf., Achievements in Tribology , ASME , New York , pp 129 – 149 ( 1990 ).
   Google Scholar
• Bhushan , B. , “ Contact Mechanics of Rough Surfaces in Tribology: Single Asperity Contact,” Appl. Mech. Rev. , 49 , pp 275 – 298 ( 1996 ).
   Google Scholar
• Holmberg , K. and Mathews , A. , “ Coatings Tribology: a Concept, Critical Aspects and Future Directions,” Thin Solid Films , 253 , pp 173 – 178 ( 1994 ).
   Web of Science ®Google Scholar
• Kuo , C. H. and Keer , L. M. , “ Contact Stress Analysis of a Layered Transversely Isotropic Half-Space,” ASME Jour. of Trib. , 114 , pp 252 – 261 ( 1992 ).
   Google Scholar
• Goryacheva , I. and Torskaya , E. , “ Stress Field Analysis in Multiple Loaded Coated Bodies,” Friction and Wear , 15 , pp 349 – 357 ( 1994 ).
   Google Scholar
• Kennedy , F. E. , Cullen , S. C. and Leroy , J. M. , “ Contact Temperature and Its Effects in an Oscillatory Contact,” ASME Jour. of Trib. , 111 , pp 63 – 69 ( 1989 ).
   Web of Science ®Google Scholar
• Tian , X. and Kennedy , F. E. , “ Temperature Rise at the Sliding Contact Interface for a Coated Semi-Infinite Body,” ASME Jour. of Trib. , 115 , pp 1 – 9 ( 1993 ).
   Google Scholar
• Varadi , K. , Neder , Z. and Friedrich , K. , “ Evaluation of the Real Contact Area, Pressure Distributions and Contact Temperatures during Sliding Contact Between Real Metal Surface,” Wear , 200 , pp 55 – 62 ( 1996 ).
   Web of Science ®Google Scholar
• Ting , B. Y. and Winer , W. O. , “ Frictional-Induced Thermal Influences in Elastic Contact Between Spherical Asperities,” ASME Jour. of Trib. , 111 , pp 315 – 322 ( 1989 ).
   Web of Science ®Google Scholar
• Wang , S. and Komvopoulos , K. , “ A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part 1—Elastic Contact and Heat Transfer Analysis,” ASME Jour. of Trib. , 116 , pp 812 – 823 ( 1994 ).
   Web of Science ®Google Scholar
• Wang , S. and Komvopoulos , K. , “ A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part 2—Multiple Domains, Elastoplastic Contacts and Applications,” ASME Jour. of Trib. , 116 , pp 824 – 832 ( 1994 ).
   Web of Science ®Google Scholar
• Guha , D. and Chowdhuri , R. S.K. , “ The Effect of Surface Roughness on the Temperature at the Contact Between Sliding Bodies,” Wear , 197 , pp 63 – 73 ( 1996 ).
   Web of Science ®Google Scholar
• Du , S. Q. , Zagrodzki , P. , Barber , J. R. and Hulbert , G. M. , “ Finite Element Analysis of Frictionally Excited Thermoelastic Instability,” Jour. of Thermal Stresses , 20 , pp 185 – 201 ( 1997 ).
   Web of Science ®Google Scholar
• Burton , R. A. , “ Thermal Deformation in Frictionally Heated Contact,” Wear , 59 , pp 1 – 20 ( 1980 ).
   Web of Science ®Google Scholar
• Barber , J. R. , “ Thermoelastic Distortion of the Half-Space,” Jour. of Thermal Stresses , 10 , pp 21 – 228 ( 1987 ).
   Google Scholar
• Yeo , T. and Barber , J. R. , “ Finite Element Analysis of Thermoelastic Contact Stability,” ASME Jour. of Applied Mechanics , 61 , pp 919 – 922 ( 1994 ).
   Google Scholar
• Azarkhin , A. , Barber , J. R. and Rolf , R. L. , “ Combined Thermal-Mechanical Effects in Frictional Sliding,” Key Engineering Materials , 33 , pp 135 – 160 ( 1989 ).
   Google Scholar
• Stromberg , N. , Johansson , L. and Klarbring , A. , “ Derivation and Analysis of Generalized Standard Model for Contact, Friction and Wear,” Int'l. Jour. Solids Structures , 33 , pp 1817 – 1836 ( 1996 ).
   Web of Science ®Google Scholar
• Andrews , K. T. , Shillor , M. , Wright , S. and Klarbring , A. , “ A Dynamic Thermoviscoelastic Contact Problem with Friction and Wear,” Int'l. Jour. Eng. Sci. , 35 , pp 1291 – 1309 ( 1997 ).
   Web of Science ®Google Scholar
• Johansson , L. and Klarbring , A. , “ Thermoelastic Frictional Contact Problems: Modelling, Finite Element Approximation and Numerical Realization,” Comp. Meth. Appl. Mech. Eng. , 105 , pp 181 – 210 ( 1993 ).
   Web of Science ®Google Scholar
• Ferrante , J. and Bozzolo , G. , “ Fundamentals of Tribology at the Atomic Level,” Mat. Res. Soc. Symp. Proc. , 140 , pp 37 – 50 ( 1989 ).
   Google Scholar
• Ferrante , J. and Bozzolo , G. , “ Fundamentals of Tribology at the Atomic Level,” Mat. Res. Soc. Symp. Proc. , 140 , pp 37 – 50 ( 1989 ).
   Google Scholar
• Belak , J. and Stowers , I. F. , “ Molecular Dynamics Studies of Surface Indentation in Two Dimensions,” Mat. Res. Soc. Symp. Proc. , 193 , pp 259 – 264 ( 1990 ).
   Google Scholar
• Belak , J. and Stowers , I. F. , “ The Indentation and Scraping of a Metal Surface: A Molecular Dynamics Study ,” Fundamentals of Friction: Macroscopic and Microscopic Process , Singer , I. L. and Pollock , H. M. , eds., Kluwer Academic Publishers , Netherlands , pp 511 – 520 ( 1992 ).
   Google Scholar
• Harrison , J. A. , White , C. T. , Colton , R. J. and Brenner , D. W. , “ Nanoscale Investigation of Indentation, Adhesion and Fracture of Diamond (III) Surfaces,” Surface Science , 271 , pp 57 – 67 ( 1992 ).
   Web of Science ®Google Scholar
• Harrison , J. A. and Brenner , D. W. , “ Atomic-Scale Simulation of Tribological and Related Phenomena ,” Handbook of Micro/Nanotribology , Bhushan , B. , ed., CRC Press , New York , NY , pp 397 – 439 ( 1995 ).
   Google Scholar
• Yan , W. and Komvopoulos , K. , “ Three-Dimensional Molecular Dynamics Analysis of Atomic-Scale Indentation ,” ASME 97-TRIB-35 , ASME , New York , p 9 , ( 1997 ).
   Google Scholar