The contact of coated systems under sliding conditions is considered within the framework of elasticity theory with the assumption of perfect bond between coating and substrate. Formulation is introduced in the form of a system of coupled singular integral equations of the second kind with Cauchy kernels that describe contact problems for coated bodies under complete, semi-complete and incomplete contact conditions. Accurate and efficient numerical method for the solution of sliding contact problems is described. Explicit results are presented for the interpolative Gauss-Jacobi numerical integration scheme for singular integral equations of the second kind with Cauchy kernels. The method captures correctly both regular and singular behavior of the traction distribution near the edges of contact. Several cases of sliding contact are considered to demonstrate the validity of the method.

1.
Ihara
,
T.
,
Shaw
,
M. C.
, and
Bhushan
,
B.
, 1986, “
A Finite Element Analysis of Contact Stress and Strain in an Elastic Film on a Rigid Substrate-Part II: With Friction
,”
ASME J. Tribol.
0742-4787,
108
, pp.
534
539
.
2.
Komovopoulus
,
K.
, 1988, “
Finite Element Analysis of a Layered Elastic Solid in Normal Contact With a Rigid Substrate
,”
ASME J. Tribol.
0742-4787,
110
, pp.
477
485
.
3.
Cormier
,
N. G.
,
Smallwood
,
B. S.
,
Sinclair
,
G. B.
, and
Meda
,
G.
, 1999, “
Aggressive Submodeling of Stress Concentrations
,”
Int. J. Numer. Methods Eng.
0029-5981,
46
, pp.
889
909
.
4.
Aleksandrov
,
V. M.
, 1968, “
Asymptotic Methods in Contact Problems of Elasticity Theory
,”
J. Appl. Math. Mech.
0021-8928,
32
, pp.
691
.
5.
Wu
,
T.-S.
, and
Chiu
,
Y. P.
, 1967, “
On the Contact Problem of Layered Elastic Bodies
,”
Q. Appl. Math.
0033-569X,
25
, pp.
233
242
.
6.
Nowell
,
D.
, and
Hills
,
D. A.
, 1988, “
Contact Problems Incorporating Elastics Layers
,”
Int. J. Solids Struct.
0020-7683,
24
, pp.
105
115
.
7.
Jaffar
,
M. J.
, 1991, “
Elastic Strips in Sliding Contact
,”
J. Strain Anal. Eng. Des.
0309-3247,
26
, pp.
193
199
.
8.
Ma
,
L. F.
, and
Korsunsky
,
A. M.
, 2004, “
Fundamental Formation for Contact Problems of Coated Systems
,”
Int. J. Solids Struct.
0020-7683,
41
, pp.
2837
2854
.
9.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
, Cambridge, pp.
119
124
.
10.
Hills
,
D. A.
,
Nowell
,
D.
, and
Sackfield
,
A.
, 1993,
Mechanics of Elastic Contacts
,
Butterworth-Heinemann Ltd.
, Oxford, pp.
107
157
.
11.
Muskhelishvili
,
N. I.
, 1953,
Some Problems of Mathematical Theory of Elasticity
,
Noordhoff
, Groningen, pp.
341
440
.
12.
Erdogan
,
F.
,
Gupta
,
G. D.
, and
Cook
,
T. S.
, 1973, “
Numerical Solution of Singular Integral Equation
,” In
Methods of Analysis and Solutions of Crack Problems
,
G. C.
Sih
ed.
,
Noordhoff
, Groningen, pp.
368
425
.
13.
Ma
,
L. F.
, and
Korsunsky
,
A. M.
, 2005, “
An Efficient Numerical Method for the Solution of the Sliding Contact Problems
,”
Int. J. Numer. Methods Eng.
0029-5981,
64
, pp.
1236
1255
.
14.
Yakimiw
,
E.
, 1996, “
Accurate Computation of Weights in Classical Gauss-Christoffel Quadrature Rules
,”
J. Comput. Phys.
0021-9991,
129
, pp.
406
430
.
15.
Stroud
,
A. H.
, and
Secrest
,
D.
, 1966,
Gaussian Quadrature Formulas
,
Macmillan
, New York, pp.
17
36
.
16.
Monegato
,
G.
, 1987, “
On the Weights of Certain Quadratures for the Numerical Evaluation of Cauchy Principal Value Integrals and Their Derivatives
,”
Numer. Math.
0029-599X,
50
, pp.
273
281
.
17.
Ma
,
L. F.
, and
Korsunsky
,
A. M.
, 2003, “
Effect of Friction on Edge Singularities in Slip Bands
,”
Int. J. Fract.
0376-9429,
123
, pp.
L143
L150
.
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