In this paper, a solution to the quasi-static adhesive contact problem between a rigid cylinder and a transversely isotropic substrate is extended to the most general case by taking adhesion hysteresis into account. An analytical solution to the contact stress is obtained by solving the integral equations established on the basis of the Green's function for the two-dimensional transversely isotropic half-space problem. By using equilibrium conditions and Griffith's criterion, the adhesion force and resistant moment to rolling are determined as functions of contact geometries and material properties of the contacting solids. Detailed discussions on the adhesion force and resistant moment are presented for some specific cases, revealing adhesion behaviors that have not been predicted by previous models. As the most generalized solution to the discussed problem, our results would have extensive applications in predicting the adhesion behavior between solids undergoing sophisticated mechanical loadings.

References

References
1.
Hertz
,
H.
,
1882
, “
Ueber Die Berührung Fester Elastischer Körper (on the Contact of Elastic Solids)
,”
J. Reine Angew. Math.
,
92
, pp.
156
171
.
2.
Johnson
,
K. L.
,
Kendall
,
K.
, and
Roberts
,
A. D.
,
1971
, “
Surface Energy and Contact of Elastic Solids
,”
Proc. R. Soc. London, Ser. A
,
324
, pp.
301
313
.10.1098/rspa.1971.0141
3.
Griffith
,
A. A.
,
1921
, “
The Phenomena of Rupture and Flow in Solids
,”
Philos. Trans. R. Soc. London, Ser. A
,
221
, pp.
163
198
.10.1098/rsta.1921.0006
4.
Chaudhury
,
M. K.
, and
Whitesides
,
G. M.
,
1991
, “
Direct Measurement of Interfacial Interactions Between Semispherical Lenses and Flat Sheets of Poly(Dimethylsiloxane) and Their Chemical Derivatives
,”
Langmuir
,
7
, pp.
1013
1025
.10.1021/la00053a033
5.
Dutrowski
,
R. C.
,
1969
, “
Hertzian Contact and Adhesion of Elastomers
,”
ASME J. Lubr. Technol.
,
91F
, pp.
732
737
.10.1115/1.3555031
6.
Horn
,
R. G.
,
Israelachvili
,
J. N.
, and
Pribac
,
F.
,
1987
, “
Measurement of the Deformation and Adhesion of Solids in Contact
,”
J. Colloid Interface Sci.
,
115
, pp.
480
492
.10.1016/0021-9797(87)90065-8
7.
Chaudhury
,
M. K.
, and
Owen
,
M. J.
,
1993
, “
Correlation Between Adhesion Hysteresis and Phase State of Monolayer Films
,”
J. Phys. Chem.
,
97
, pp.
5722
5726
.10.1021/j100123a043
8.
Shanahana
,
M. E. R.
, and
Michelb
,
F.
,
1991
, “
Physical Adhesion of Rubber to Glass: Cross–Link Density Effects Near Equilibrium
,”
Int. J. Adhes. Adhes.
,
11
, pp.
170
176
.10.1016/0143-7496(91)90019-E
9.
Chen
,
Y. L.
,
Helm
,
C. A.
, and
Israelachvili
,
J. N.
,
1991
, “
Molecular Mechanisms Associated With Adhesion and Contact Angle Hysteresis of Monolayer Surfaces
,”
J. Phys. Chem.
,
95
, pp.
10,736
10,747
.10.1021/j100179a041
10.
Dominik
,
C.
, and
Tielens
,
A. G. G. M.
,
1995
, “
Resistance to Rolling in the Adhesive Contact of Two Spheres
,”
Philos. Mag. A
,
72
, pp.
783
803
.10.1080/01418619508243800
11.
Heim
,
L. O.
,
Blum
,
J.
,
Preuss
,
M.
, and
Butt
,
H. J.
,
1999
, “
Adhesion and Friction Forces Between Spherical Micrometer-Sized Particles
,”
Phys. Rev. Lett.
,
83
, pp.
3328
3331
.10.1103/PhysRevLett.83.3328
12.
Baney
,
J. M.
, and
Hui
,
C. Y.
,
1997
, “
A Cohesive Zone Model for the Adhesion of Cylinders
,”
J. Adhes. Sci. Technol.
,
11
, pp.
393
406
.10.1163/156856197X00778
13.
Chaudhury
,
M. K.
,
Weaver
,
T.
,
Hui
,
C. Y.
, and
Kramer
,
E. J.
,
1996
, “
Adhesive Contact of Cylindrical Lens and a Flat Sheet
,”
J. Appl. Phys.
,
80
, pp.
30
37
.10.1063/1.362819
14.
Zhupanska
,
O. I.
, and
Ulitko
,
A. F.
,
2005
, “
Contact With Friction of a Rigid Cylinder With an Elastic Half-Space
,”
J. Mech. Phys. Solids
,
53
, pp.
975
999
.10.1016/j.jmps.2005.01.002
15.
Kendall
,
K.
,
1975
, “
Rolling Friction and Adhesion Between Smooth Solids
,”
Wear
,
33
, pp.
351
358
.10.1016/0043-1648(75)90288-4
16.
She
,
H.
,
Malotky
,
D.
, and
Chaudhury
,
M. K.
,
1998
, “
Estimation of Adhesion Hysteresis at Polymer/Oxide Interfaces Using Rolling Contact Mechanics
,”
Langmuir
,
14
, pp.
3090
3100
.10.1021/la971061m
17.
She
,
H.
, and
Chaudhury
,
M. K.
,
2000
, “
Estimation of Adhesion Hysteresis Using Rolling Contact Mechanics
,”
Langmuir
,
16
, pp.
622
625
.10.1021/la9907984
18.
Chen
,
S.
, and
Gao
,
H.
,
2007
, “
Bio-Inspired Mechanics of Reversible Adhesion: Orientation-Dependent Adhesion Strength for Non-Slipping Adhesive Contact With Transversely Isotropic Elastic Materials
,”
J. Mech. Phys. Solids
,
55
, pp.
1001
1015
.10.1016/j.jmps.2006.10.008
19.
Yao
,
H.
,
Chen
,
S.
,
Guduru
,
P. R.
, and
Gao
,
H.
,
2009
, “
Orientation-Dependent Adhesion Strength of a Rigid Cylinder in Non-Slipping Contact With a Transversely Isotropic Half-Space
,”
Int. J. Solids Struct.
,
46
, pp.
1167
1175
.10.1016/j.ijsolstr.2008.10.011
20.
Barnett
,
D. M.
, and
Lothe
,
J.
,
1973
, “
Synthesis of the Sextic and the Integral Formalism for Dislocations, Greens Function and Surface Waves in Anisotropic Elastic Solids
,”
Phys. Norv.
,
7
, pp.
13
19
.
21.
Ting
,
T. C. T.
,
1996
,
Anisotropic Elasticity
,
Oxford University Press
,
New York
.
22.
Chen
,
S. H.
, and
Gao
,
H. J.
,
2006
, “
Non-Slipping Adhesive Contact of an Elastic Cylinder on Stretched Substrates
,”
Proc. R. Soc. London, Ser. A
,
462
, pp.
211
228
.10.1098/rspa.2005.1553
23.
Anderson
,
T. L.
,
2005
,
Fracture Mechanics: Fundamentals and Applications
,
Taylor & Francis
,
Boca Raton, FL
.
24.
Hwu
,
C.
,
1993
, “
Fracture Parameters for Orthotropic Biomaterial Interface Cracks
,”
Eng. Fract. Mech.
,
45
, pp.
89
97
.10.1016/0013-7944(93)90010-P
25.
Rice
,
J. R.
,
1988
, “
Elastic Fracture Mechanics Concepts for Interfacial Cracks
,”
J. Appl. Mech.
,
55
, pp.
98
103
.10.1115/1.3173668
26.
Kendall
,
K.
,
1975
, “
Kinetics of Contact Between Smooth Solids
,”
J. Adhes.
,
7
, pp.
55
72
.10.1080/00218467508078897
27.
Barquins
,
M.
,
1988
, “
Adherence and Rolling Kinetics of a Rigid Cylinder in Contact With a Natural Rubber Surface
,”
J. Adhes.
,
26
, pp.
1
12
.10.1080/00218468808071271
28.
Fischer
,
K. E.
,
Aleman
,
B. J.
,
Tao
,
S. L.
,
Daniels
,
R. H.
,
Li
,
M. E.
,
Buenger
,
M. D.
,
Nagaraj
,
G.
,
Singh
,
P.
,
Zettl
,
A.
, and
Desai
,
T.
,
2009
, “
Biomimetic Nanowire Coatings for Next Generation Adhesive Drug Delivery Systems
,”
Nano Lett.
,
9
, pp.
716
720
.10.1021/nl803219f
29.
Alon
,
R.
,
Hammer
,
D. A.
, and
Springer
,
T. A.
,
1995
, “
Lifetime of the P-Selectin-Carbohydrate Bond and its Response to Tensile Force in Hydrodynamic Flow
,”
Nature
,
374
, pp.
539
542
.10.1038/374539a0
30.
Dongye
,
C.
, and
Ting
,
T. C. T.
,
1989
, “
Explicit Expressions of Barnett-Lothe Tensors and Their Associated Tensors for Orthotropic Materials
,”
Q. Appl. Math.
,
47
, pp.
723
734
.
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