An elastic-plastic contact (EPC) solution and code is developed using a modified semi-analytical method. The indentation tests with different hardening behavior are simulated by using the developed EPC code. The distributions of contact pressure, residual stress and plastic strain are obtained and compared with the results of the finite element method models without hardening. Some techniques, such as fast Fourier transform and fast convergence method, are used to increase the computation speed.

1.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
, 1966, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
1364-5021,
295
, pp.
300
319
.
2.
Tsukizoe
,
T.
, and
Hisakado
,
T.
, 1965, “
On Mechanism of Contact between Metal Surfaces—Penetrating Depth and Average Clearance
,”
J. Basic Eng.
0021-9223,
87
(
3
), pp.
666
674
.
3.
Tsukizoe
,
T.
, and
Hisakado
,
T.
, 1968, “
On Mechanism of Contact between Metal Surfaces. 2. Real Area and Number of Contact Points
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501,
90
(
1
), p.
73
.
4.
Onions
,
R. A.
, and
Archard
,
J. F.
, 1973, “
Contact of Surfaces Having a Random Structure
,”
J. Phys. D
0022-3727,
6
(
3
), pp.
289
304
.
5.
Mikic
,
B. B.
, and
Roca
,
R. T.
, 1974, “
Solution to Contact of 2 Rough Spherical Surfaces
,”
J. Appl. Mech.
0021-8936,
41
(
3
), pp.
801
803
.
6.
Bush
,
A. W.
,
Gibson
,
R. D.
, and
Thomas
,
T. R.
, 1975, “
Elastic Contact of a Rough Surface
,”
Wear
0043-1648,
35
(
1
), pp.
87
111
.
7.
Bush
,
A. W.
,
Gibson
,
R. D.
, and
Keogh
,
G. P.
, 1976, “
Limit of Elastic Deformation in Contact of Rough Surfaces
,”
Mech. Res. Commun.
0093-6413,
3
(
3
), pp.
169
174
.
8.
Bush
,
A. W.
,
Gibson
,
R. D.
, and
Keogh
,
G. P.
, 1977, “
Strongly Anisotropic Rough Surfaces
,”
ASME J. Lubr. Technol.
0022-2305,
101
, pp.
15
20
.
9.
Suratkar
,
P. T.
,
Pandit
,
S. M.
, and
Wu
,
S. M.
, 1976, “
A Stochastic Approach to the Mode of Deformation and Contact Between Rough Surfaces
,”
Wear
0043-1648,
39
, pp.
239
250
.
10.
Zhao
,
Y. W.
,
Maietta
,
D. M.
, and
Chang
,
L.
, 2000, “
An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow
,”
J. Tribol.
0742-4787,
122
(
1
), pp.
86
93
.
11.
Liu
,
Z. Q.
,
Neville
,
A.
, and
Reuben
,
R. L.
, 2000, “
An Analytical Solution for Elastic and Elastic-Plastic Contact Models
,”
Tribol. Trans.
1040-2004,
43
(
4
), pp.
627
634
.
12.
Chang
,
W. R.
,
Etsion
,
I.
, and
Bogy
,
D. B.
, 1987, “
An Elastic-Plastic Model for the Contact of Rough Surfaces
,”
J. Tribol.
0742-4787,
109
(
2
), pp.
257
263
.
13.
Gupta
,
V.
,
Hahn
,
G. T.
,
Bastias
,
P. C.
, and
Rubin
,
C. A.
, 1995, “
Contribution of Surface Irregularities to Rolling Contact Plasticity in Bearing Steels
,”
ASME J. Tribol.
0742-4787,
117
, pp.
660
666
.
14.
Liu
,
G.
,
et al.
, 2001, “
Elasto-Plastic Contact of Rough Surfaces
,”
Tribol. Trans.
1040-2004,
44
(
3
), pp.
437
443
.
15.
Kogut
,
L.
, and
Etsion
,
I.
, 2002, “
Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat
,”
J. Clim.
0894-8755,
69
(
5
), pp.
657
662
.
16.
Mesarovic
,
S. D.
, and
Fleck
,
N. A.
, 1999, “
Spherical Indentation of Elastic-Plastic Solids
,”
Proc. R. Soc. London, Ser. A
1364-5021,
455
(
1987
), pp.
2707
2728
.
17.
Komvopoulos
,
K.
, and
Choi
,
D. H.
, 1992, “
Elastic Finite-Element Analysis of Multiasperity Contacts
,”
J. Tribol.
0742-4787,
114
(
4
), pp.
823
831
.
18.
Love
,
A. E. H.
, 1952,
A Treatise on the Mathematical Theory of Elasticity
,
Cambridge University Press
, Cambridge.
19.
Poon
,
C. Y.
, and
Sayles
,
R. S.
, 1994, “
Numerical Contact Model of a Smooth Ball on an Anisotropic Rough-Surface
,”
J. Tribol.
0742-4787,
116
(
2
), pp.
194
201
.
20.
Lubrecht
,
A. A. a. L. E.
, 1991, “
A Fast Solution of the Dry Contact Problem and the Associated Subsurface Stress Field, Using Multilevel Techniques
,”
J. Tribol.
0742-4787,
113
, pp.
128
132
.
21.
Polonsky
,
I. A.
, and
Keer
,
L. M.
, 1999, “
A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient Techniques
,”
Wear
0043-1648,
231
(
2
), pp.
206
219
.
22.
Ju
,
Y.
, and
Farris
,
T. N.
, 1996, “
Spectral Analysis of Two-Dimensional Contact Problems
,”
J. Tribol.
0742-4787,
118
, pp.
320
328
.
23.
Polonsky
,
I. A.
, and
Keer
,
L. M.
, 2000, “
A Fast and Accurate Method for Numerical Analysis of Elastic Layered Contacts
,”
J. Tribol.
0742-4787,
122
(
1
), pp.
30
35
.
24.
Liu
,
S. B.
,
Wang
,
Q.
, and
Liu
,
G.
, 2000, “
A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses
,”
Wear
0043-1648,
243
(
1–2
), pp.
101
111
.
25.
Nogi
,
T.
, and
Kato
,
T.
, 1997, “
Influence of a Hard Surface Layer on the Limit of Elastic Contact. 1. Analysis Using a Real Surface Model
,”
J. Tribol.
0742-4787,
119
(
3
), pp.
493
500
.
26.
Stanley
,
H. M.
, and
Kato
,
T.
, 1997, “
An FFT-Based Method for Rough Surface Contact
,”
J. Tribol.
0742-4787,
119
(
3
), pp.
481
485
.
27.
Jacq
,
C.
,
et al.
, 2002, “
Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code
,”
J. Tribol.
0742-4787,
124
(
4
), pp.
653
667
.
28.
Mayeur
,
C.
,
Sainsot
,
P.
, and
Flamand
,
L.
, 1995, “
A Numerical Elastoplastic Model for Rough Contact
,”
ASME J. Tribol.
0742-4787,
117
, pp.
422
429
.
29.
Boussinesq
,
J.
, 1885,
Application des Potentials a l’Etude de l’Equilibre et du Mouvement des Solids Elastique
,
Gauthier-Villars
, Paris.
30.
Cerruti
,
V.
, 1882,
Roma, Acc. Lincei
, Mem. fis. mat.
31.
Liu
,
G.
,
Wang
,
Q. J.
, and
Lin
,
C.
, 1999, “
A Survey Of Current Models for Simulating the Contact Between Rough Surfaces
,”
Tribol. Trans.
1040-2004,
42
(
3
), pp.
581
591
.
32.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
, Cambridge.
33.
McCormic
,
G. P.
, 1983,
Nonlinear Programming: Theory, Algorithms, and Applications
,
Wiley
, New York.
34.
Minoux
,
M.
, 1986,
Mathematical Programming: Theory and Algorithms
,
Wiley-Interscience series in discrete mathematics and optimization
,
Wiley
, Chichester.
35.
Pshenichny
,
B. N. a. Y. M. D.
, 1975,
Numerical Methods in Optimization Problem
,
Nauka
, Moscow.
36.
Kalker
,
J. J.
, 1986, “
Numerical Calculation of the Elastic Field in a Half-Space
,”
Comm. Appl. Numer. Methods
,
2
, pp.
401
410
.
37.
Stoer
,
J. a. R. B.
, 1980,
Introduction to Numerical Analysis
,
Springer
, New York.
38.
Liu
,
S. B.
, and
Wang
,
Q.
, 2002, “
Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm
,”
J. Tribol.
0742-4787,
124
(
1
), pp.
36
45
.
39.
Brebbia
,
L. C.
, 1980, “
The Boundary Element Method for Engineers
,”
Pentech
, London.
40.
Chiu
,
Y. P.
, 1977, “
Stress-Field Due to Initial Strains in a Cuboid Surrounded by an Infinite Elastic Space
,”
J. Appl. Mech.
0021-8936,
44
(
4
), pp.
587
590
.
41.
Chiu
,
Y. P.
, 1978, “
Stress-Field and Surface Deformation in a Half Space with a Cuboidal Zone in Which Initial Strains Are Uniform
,”
J. Appl. Mech.
0021-8936,
452
(
2
), pp.
302
306
.
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