A new numerical method for the analysis of elastic and elastic-plastic contacts of two rough surfaces has been developed. The method is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. The present variational approach guarantees the uniqueness of the solution of the contact problem and significantly reduces the computation time as compared with the conventional matrix inversion method, and thus, makes it feasible to solve 3-D contact problem with large number of contact points. The model is extended to elastic-perfectly plastic contacts. The model is used to predict contact statistics for computer generated surfaces.

1.
Akyuz
F. A.
, and
Merwin
M.
,
1968
, “
Solution of Nonlinear Problems of Elastoplasticity by Finite Element Method
,”
AIAA J.
, Vol.
6
, pp.
1825
1831
.
2.
Bhushan, B., 1990, Tribology and Mechanics of Magnetic Storage Devices, Springer-Verlag, NY.
3.
Bhushan
B.
, and
Cook
N. H.
,
1975
, “
On the Correlation between Friction Coefficients and Adhesion Stresses
,”
ASME Journal of Engineering Materials and Technology
, Vol.
97
, pp.
285
287
.
4.
Bhushan
B.
, and
Majumdar
A.
,
1992
, “
Elastic-Plastic Contact Model of Bifractal Surfaces
,”
Wear
, Vol.
153
, pp.
53
64
.
5.
Bush
A. W.
,
Gibson
R. D.
, and
Thomas
T. R.
,
1975
, “
The Elastic Contact of a Rough Surface
,”
Wear
, Vol.
35
, pp.
87
111
.
6.
Bush
A. W.
,
Gibson
R. D.
, and
Keogh
G. P.
,
1979
, “
Strongly Anisotropic Rough Surfaces
,”
ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol.
101
, pp.
15
20
.
7.
Conry
T. F.
, and
Seireg
A.
,
1971
, “
A Mathematical Programming Method for Design of Elastic Bodies in Contact
,”
ASME Journal of Applied Mechanics
, Vol.
38
, pp.
387
392
.
8.
Francis
H. A.
,
1983
, “
The Accuracy of Plane-Strain Models for the Elastic Contact of Three-Dimensional Rough Surfaces
,”
Wear
, Vol.
85
, pp.
239
256
.
9.
Ganti
S.
, and
Bhushan
B.
,
1995
, “
Generalized Fractal Analysis and its Applications to Engineering Surfaces
,”
Wear
, Vol.
180
, pp.
17
34
.
10.
Greenwood
J. A.
, and
Williamson
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. Roy. Soc.
(London), Series A., Vol.
295
, pp.
300
319
.
11.
Hu
Y. Z.
, and
Tonder
K.
,
1992
, “
Simulation of 3-D Random Surface by 2-D Digital Filter and Fourier Analysis
,”
Int. Journal of Mach. Tool Manufact.
, Vol.
32
, pp.
82
90
.
12.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press.
13.
Kalker
J. J.
, and
van Randen
Y.
,
1972
, “
A Minimum Principle for Frictionless Elastic Contact with Application to Non-Hertzian Half-Space Contact Problems
,”
Journal of Eng. Math.
, Vol.
6
, pp.
193
206
.
14.
Komvopoulos
K.
, and
Choi
D. H.
,
1992
, “
Elastic Finite Element Analysis of Multi-asperity Contact
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
114
, pp.
823
831
.
15.
Lai
W. T.
, and
Cheng
H. S.
,
1985
, “
Computer Simulation of Elastic Rough Contacts
,”
ASLE Trans.
, Vol.
28
, pp.
172
180
.
16.
Love
A. E. H.
,
1929
, “
The Stress Produced in a Semi-infinite Solid by Pressure on Part of the Boundary
,”
Phil. Trans. Roy. Soc.
(London) Series A., Vol.
228
, pp.
377
420
.
17.
Majumdar
A.
, and
Bhushan
B.
,
1990
, “
Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
112
, pp.
204
216
.
18.
Majumdar
A.
, and
Bhushan
B.
,
1991
, “
Fractal Model of Elastic-Plastic Contact Between Rough Surfaces
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
113
, pp.
1
11
.
19.
McCool
J. I.
,
1986
, “
Comparison of Models for the Contact of Rough Surfaces
,”
Wear
, Vol.
107
, pp.
37
60
.
20.
Onions
R. A.
, and
Archard
J. F.
,
1973
, “
The Contact of Surfaces Having a Random Structure
,”
J. Phys., D.: Appl. Phys.
, Vol.
6
, pp.
289
304
.
21.
Poon
C. Y.
, and
Sayles
R. S.
,
1994
, “
Numerical Contact Model of a Smooth Ball on an Anisotropic Rough Surface
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
116
, pp.
194
201
.
22.
Ren
N.
, and
Lee
S. C.
,
1993
, “
Contact Simulation of Three-Dimensional Rough Surfaces Using Moving Grid Method
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
115
, pp.
597
601
.
23.
Richards, T. H., 1977, Energy Methods in Stress Analysis, Ellis Horwood.
24.
Sayles
R. S.
, and
Thomas
T. R.
,
1978
, “
Computer Simulation of the Contacting Rough Surfaces
,”
Wear
, Vol.
49
, pp.
273
296
.
25.
Thomas, T. R., 1982, Rough Surfaces, Longman, London.
26.
Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, 3rd edition, McGraw-Hill, N.Y.
27.
Varga, R. S., 1962, Matrix Iterative Analysis, Prentice-Hall, N.J.
28.
Webster
M. N.
, and
Sayles
R. S.
,
1986
, “
A Numerical Model for the Elastic Frictionless Contact of Real Rough Surfaces
,”
ASME JOURNAL OF TRIBOLOGY
, Vol.
108
, pp.
314
320
.
29.
West, M. A., and Sayles, R. S., 1987, “A 3-Dimensional Method of Studying 3-Body Contact Geometry and Stress on Real Rough Surfaces,” Proc. 14th Leeds-Lyon Symposium on Tribology, Vol. 12, pp. 195–200.
30.
Whitehouse
D. J.
, and
Archard
J. F.
,
1970
, “
The Properties of Random Surface of Significance in Their Contact
,”
Proc. Roy. Soc.
(London), Series A., Vol.
316
, pp.
97
121
.
31.
Williamson
J. B. P.
,
1967
/68
, “
The Microtopography of Surfaces
,”
Proc. Inst. Mech. Engrs.
, Vol.
182
, Part 3k, pp.
21
30
.
32.
Wolfe
P.
,
1959
, “
The Simplex Method for Quadratic Programming
,”
Econometrica
, Vol.
27
, pp.
382
395
.
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