A Monte Carlo method for simulating fractal surfaces

Physica A: Statistical Mechanics and its Applications

Volumn 386, Issue 1, 2007, Pages 176-186

  Zou, Mingqing ^a   Yu, Boming ^a   Feng, Yongjin ^a   Xu, Peng ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Asperity; Fractal; Monte Carlo simulation; Rough surface; Self affine

Indexed keywords

COMPUTER SIMULATION; FRACTAL DIMENSION; PROBABILITY; SURFACE ROUGHNESS; TOPOGRAPHY;

ASPERITY DIAMETER; FRACTAL SURFACES; SELF-AFFINE PROPERTY;

MONTE CARLO METHODS;

EID: 35148840609     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.07.058     Document Type: Article

References (47)

1. W. Peng, Contact mechanics of multilayered rough surfaces in tribology, Ph.D. Thesis, The Ohio State University, Columbus, 2001.
2. Lévy P. Processus Stochastiques et Mouvement Brownien (1948), Gauthier-Villars, Paris
3. Jang Y.H., and Barber J.R. Effect of contact statistics on electrical contact resistance. J. Appl. Phys. 94 (2003) 7215-7221
4. R.F. Voss, Random fractal forgeries, in: R.A. Earnshaw (Ed.), Fundamental Algorithms for Computer Graphics, 1986, pp. 805-835.
5. Patir N. A numerical procedure for random generation of rough surfaces. Wear 47 (1978) 263-277
6. Watson W., and Spedding T.A. The time series modeling of non-Gaussian engineering processes. Wear 83 (1982) 215-231
7. Whitehouse D.J. The generation of two-dimensional random surfaces having a specified function. Ann. CIRP (1983) 495-498
8. Newland D.E. An Introduction to Random Vibration and Spectral Analysis. second ed. (1984), Longman, London
9. Hu H.Z., and Tonder K. Simulation of 3-D random rough surface by 2-D digital filter and Fourier analysis. Int. J. Mach. Tools Manuf. 32 (1992) 83-90
10. Mihailidis A., and Bakolas V. Numerical simulation of real 3-D rough surfaces. J. Balk. Tribol. Assoc. 5 (1999) 247-255
11. Wu J.J. Simulation of rough surfaces with FFT. Tribol. Int. 33 (2000) 47-58
12. Bakolas V. Numerical generation of arbitrarily oriented non-Gaussian three-dimensional rough surfaces. Wear 254 (2003) 546-554
13. Mantoglou A., and Wilson J.L. The Turning Bands Method for the simulation of random fields using line generation by a spectral method. Water Resour. Res. 18 (1982) 1379-1394
14. Tompson A.F.B., Ababou R., and Gelhar L.W. Implementation of the three-dimensional turning bands random field generator. Water Resour. Res. 25 (1989) 2227-2243
15. Zhang X., Cong P.Z., Fujiwara S.J., and Fujii M.T. A new method for numerical simulation of thermal contact resistance in cylindrical coordinates. Int. J. Heat Mass Transfer 47 (2004) 1091-1098
16. Majumdar A., and Tien C.L. Fractal characterization and simulation of rough surfaces. Wear 136 (1990) 313-327
17. Patrikar R.M. Modeling and simulation of surface roughness. Appl. Surf. Sci. 228 (2004) 213-220
18. Cai Z.J., Chen D.Q., and Lu S. Reconstruction of a fractal rough surface. Physica D 213 (2006) 25-30
19. Greenwood J.A., and Williamson J.B.P. Contact of nominally flat surfaces. Proc. R. Soc. London Ser. A 295 (1966) 300-319
20. Berry M.V., and Lewis Z.V. On the Weierstrass-Mandelbrot fractal function. Proc. R. Soc. A 370 (1980) 459-484
21. Mandelbrot B.B. The Fractal Geometry of Nature (1983), Freeman, New York
22. Voss R.F. Fractals in nature: from characterization to simulation. In: Peitgen H.O., and Saupe D. (Eds). The Science of Fractal Images (1988), Springer, New York 21-70
23. A. Majumdar, Fractal surfaces and their applications to surface phenomena, Ph.D. Thesis, University of California, Berkley, 1989.
24. Majumdar A., and Bhushan B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces. J. Tribol. 112 (1990) 205-216
25. Majumdar A., and Bhushan B. Fractal model of elastic-plastic contact between rough surfaces. ASME J. Tribol. 113 (1991) 1-11
26. Majumdar A., and Tien C.L. Fractal network model for contact conductance. Trans. ASME, J. Heat Transfer 113 (1991) 516-525
27. Russ J.C. Fractal Surfaces. first ed. (1994), Springer 320pp
28. Warren T.L., and Krajcinovic D. Fractal models of elastic-perfectly plastic contact of rough surfaces based on the Cantor set. Int. J. Solids Struct. 32 (1995) 2907-2922
29. Warren T.L., and Krajcinovic D. Random Cantor set models for the elastic-perfectly plastic contact of rough surfaces. Wear 196 (1996) 1-15
30. Sahimi M., and Mukhopadhyay S. Scaling properties of a percolation model with long-range correlations. Phys. Rev. E 54 (1996) 3870-3880
31. Turcotte D.L. Fractals and Chaos in Geology and Geophysics. second ed. (1997), Cambridge University Press 398pp
32. Yan W., and Komvopoulos K. Contact analysis of elastic-plastic fractal surfaces. J. Appl. Phys. 84 (1998) 3617-3624
33. Mourzenko V.V., Thovert J.-F., and Adler P.M. Percolation and conductivity of self-affine fractures. Phys. Rev. E 54 (1999) 4265-4284
34. Komvopoulos K., and Ye N. Three-dimensional contact analysis of elastic-plastic layered media with fractal surface topographies. J. Tribol. 123 (2001) 632-640
35. Yang Z.Y., and Di C.C. A directional method for directly calculating the fractal parameters of joint surface roughness. Int. J. Rock Mech. Min. Sci. 38 (2001) 1201-1210
36. Drazer G., and Koplik J. Transport in rough self-affine fractures. Phys. Rev. E 66 (2002) 026303
37. Kogut L., and Komvopoulos K. Electrical contact resistance theory for conductive rough surfaces. J. Appl. Phys. 94 (2003) 3153-3162
38. C.A. Morrow, Adhesive rough surface contact, Ph.D. Thesis, University of Pittsburgh, Pittsburgh, 2003.
39. Zhou H.W., and Xie H. Direct estimation of the fractal dimensions of a fracture surface of rock. Surf. Rev. Lett. 10 (2003) 751-762
40. Jafari G.R., Fazeli S.M., Ghasemi F., Vaez Allaei S.M., Reza Rahimi Tabar M., Iraji zad A., and Kavei G. Stochastic analysis and regeneration of rough surfaces. Phys. Rev. Lett. 91 (2003) 226101
41. Poon C.Y., and Bhushan B. Numerical contact and stiction analyses of Gaussian isotropic surfaces for magnetic head slider disk contact. Wear 202 (1996) 83-98
42. Develi K., and Babadagli T. Quantification of natural fracture surfaces using fractal geometry. Math. Geol. 30 (1998) 971-998
43. Ponson L., Bonamy D., and Bouchaud E. Two-dimensional scaling properties of experimental fracture surfaces. Phys. Rev. Lett. 96 (2006) 035506
44. Yu B.M., and Li J.H. Some fractal characters of porous media. Fractals 9 (2001) 365-372
45. Yu B.M., and Cheng P. A fractal permeability model for bidispersed porous media. Int. J. Heat Mass Transfer 45 (2002) 2983-2993
46. Yu B.M., Lee L.J., and Cao H.Q. A fractal in-plane permeability model for fabrics. Polym. Compos. 23 (2002) 201-221
47. Yu B.M., Zou M.Q., and Feng Y.J. Permeability of fractal porous media by Monte Carlo simulations. Int. J. Heat Mass Transfer 48 (2005) 2787-2794