An exact analysis on frictional contact between a rigid punch and anisotropic magneto-electro-elastic materials is performed, within the framework of the fully coupled theory. The indenter moves relative to magneto-electro-elastic materials, and Coulomb friction law is used. The mixed boundary value problem is reduced to singular integral equations of the second kind with analytical solution presented. For a triangular or semiparabolic indenter, explicit expression for surface physical in-plane stress, electrical displacement and magnetic induction are obtained. Influences of the friction coefficient and the volume fraction on contact behaviors are detailed under the prescribed contact loading conditions. Under either a triangular or semiparabolic indenter, the surface in-plane stress, electric displacement and magnetic induction are discontinuous and unbounded around the leading edge, and such a serious near-edge response can be relieved through adjusting the values of the friction coefficient or the volume fraction.
References
1.
Ahn
, Y. J.
, 2009
, “Response of Coupled Frictional Contacts to Cyclic Loading
,” Ph.D. thesis, The University of Michigan, Ann Arbor, MI.2.
Walsh
, J. B.
, 2003
, “A Theoretical Analysis of Sliding of Rough Surfaces
,” J. Geophys. Res.
, 108
(B8
), pp. ESE 6-1
–ESE 6-15
10.1029/2002JB002127.3.
Murthy
, H.
, Harish
, G.
, and Farris
, T. N.
, 2004
, “Efficient Modeling of Fretting of Blade/Disk Contacts Including Load History Effects
,” ASME J. Tribol.
126
(1
), pp. 56
–64
.10.1115/1.15401254.
Law
, S. S.
, Wu
, Z. M.
, and Chan
, S. L.
, 2006
, “Analytical Model of a Slotted Bolted Connection Element and Its Behaviour Under Dynamic Load
,” J. Sound Vib.
, 292
(3–5
), pp. 777
–787
.10.1016/j.jsv.2005.09.0285.
Antoni
, N.
, Nguyen
, Q. S.
, Ligier
, J. L.
, Saffre
, P.
, and Pastor
, J.
, 2007
, “On the Cumulative Microslip Phenomenon
,” Eur. J. Mech. A—Solids
, 26
(4
), pp. 626
–646
.10.1016/j.euromechsol.2006.09.0046.
Holt
, R. M.
, Kjolaas
, J.
, Larsen
, I.
, Li
, L.
, Gotusso Pillitteri
, A.
, and Sonstebo
, E. F.
, 2005
, “Comparison Between Controlled Laboratory Experiments and Discrete Particle Simulations of the Mechanical Behaviour of Rock
,” Int. J. Rock Mech. Min.
, 42
(7–8
), pp. 985
–995
.10.1016/j.ijrmms.2005.05.0067.
Leurer
, K. C.
, and Dvorkin
, J.
, 2006
, “Viscoelasticity of Precompacted Unconsolidated Sand With Viscous Cement
,” Geophys.
, 71
(2
), pp. 31
–40
.10.1190/1.21877958.
Zhang
, H. P.
, and Makse
, H. A.
, 2005
, “Jamming Transition in Emulsions and Granular Materials
,” Phys. Rev. E
, 72
, p. 011301
.10.1103/PhysRevE.72.0113019.
Galin
, L. A.
, 1953
, Contact Problems of the Theory of Elasticity
, Gostehizdat
, Moscow
.10.
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
(5
), pp. 975
–999
.10.1016/j.jmps.2005.01.00211.
Gladwell
, G. M. L.
, 1980
, Contact Problems in the Classical Theory of Elasticity
, Sijthoff and Noorthoff
, Amsterdam
.12.
Johnson
, K. L.
, 1985
, Contact Mechanics
, Cambridge University
, Cambridge, UK
.13.
Fabrikant
, V. I.
, 1989
, Application of Potential Theory in Mechanics, A Selection of New Results
, Kluwer, Amsterdam.14.
Fabrikant
, V. I.
, 1991
, Mixed Boundary Value Problems of Potential Theory and Their Application in Mechanics
, Kluwer, Dordrecht, Netherlands.15.
Hills
, D. A.
, Nowell
, D.
, and Sackfield
, A.
, 1993
, Mechanics of Elastic Contacts
, Butterworth-Heinemann
, Oxford, UK
.16.
Raous
, M.
, Jean
, M.
, and Moreau
J. J.
, 1995
, Contact Mechanics
, Plenum
, New York
.17.
Afferrante
, L.
, Ciaarella
, M.
, and Barber
, J. R.
, 2006
, “Sliding Thermoelastodynamic Instability
,” Proc. R. Soc. A
, 462
(2071
), pp. 2161
–2176
.10.1098/rspa.2006.167618.
Jang
, Y. H.
, and Ahn
, S. H.
, 2007
, “Frictionally-Excited Thermoelastic Instability in Functionally Graded Material
,” Wear
, 262
(9–10
), pp. 1102
–1112
.10.1016/j.wear.2006.11.01119.
Lee
, S. W.
, and Jang
, Y. H.
, 2009
, “Frictionally Excited Thermoelastic Instability in a Thin Layer of Functionally Graded Material Sliding Between Two Half-Planes
,” Wear
, 267
(9–10
), pp. 1715
–1722
.10.1016/j.wear.2009.06.03720.
Raúl
, G. D.
, Reinaldo
, R. R.
, Julián
, B. C.
, Federico
, J. S.
, Guillermo
, M. G.
, and Wang
Y. S.
, 2013
, “Plane Magneto-Electro-Elastic Moduli of Fiber Composites With Interphase
,” Mech. Adv. Mater. Struct.
, 20
(7)
, pp. 552
–563
10.1080/15376494.2011.643276.21.
Li
, L.
, Lee
, M. G.
, and Aderson
, P. M.
, 2012
, “Probing the Relation Between Dislocation Substructure and Indentation Characteristics Using Quantized Crystal Plasticity
,” ASME J. Appl. Mech.
, 79
(3
), p. 031009
.10.1115/1.400589422.
Jin
, F.
, Guo
, X.
, and Zhang
, W.
, 2013
, “A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space
,” ASME J. Appl Mech.,
80
(6
), p. 061024
.10.1115/1.402398023.
Chen
, W.
, Pan
, E.
, Wang
, H.
, and Zhang
, Ch. Z.
, 2010
, “Theory of Indentation on Multiferroic Composite Materials
,” J. Mech. Phys. Solids
58
(10
), pp. 1524
–1551
.10.1016/j.jmps.2010.07.01224.
Rogowski
, B.
, 2012
, “A Concave Indenter on a Piezoelectromagneto-Elastic Substrate or a Layer Elastically Supported
,” J. Strain Anal. Eng.
, 47
(6
), pp. 362
–378
.10.1177/030932471244789925.
Zhou
, Y. T.
, and Lee
, K. Y.
, 2012
, “Contact Problem for Magneto-Electro-Elastic Half-Plane Materials Indented by a Moving Punch. Part I: Closed-Form Solutions
,” Int. J. Solids Struct.
, 49
(26
), pp. 3853
–3865
.10.1016/j.ijsolstr.2012.08.01726.
Zhou
, Y. T.
, and Lee
, K. Y.
, 2013
, “Theory of Sliding Contact for Multiferroic Materials Indented by a Rigid Punch
,” Int. J. Mech. Sci.
, 66
, pp. 156
–167
.10.1016/j.ijmecsci.2012.11.00427.
Li
, J. Y.
, and Dunn
, M. L.
, 1998
, “Anisotropic Coupled-Field Inclusion and Inhomogeneity Problems
,” Philos. Mag. A
, 77
(5
), pp. 1341
–1350
.10.1080/0141861980821425628.
Zhang
, Ch. L.
, Chen
, W. Q.
, Li
, J. Y.
, and Yang
, J. Sh.
, 2009
, “Two-Dimensional Analysis of Magnetoelectric Effects in Multiferroic Laminated Plates
,” IEEE. Trans. Ultrason. Ferroelectr. Freq. Control.
, 56
(5
), pp. 1046
–1053
.10.1109/TUFFC.2009.113729.
Guler
, M. A.
, and Erdogan
, F.
, 2007
, “The Frictional Sliding Contact Problems of Rigid Parabolic and Cylindrical Stamps on Graded Coatings
,” Int. J. Mech. Sci.
49
(2
), 161
–182
.10.1016/j.ijmecsci.2006.08.00630.
Sturla
, F. A.
, and Baber
, J. R.
, 1988
, “Thermal Stresses Due to a Plane Crack in General Anisotropic Material
,” ASME J. Appl. Mech.
, 55
(2
), pp. 372
–376
.10.1115/1.317368531.
Erdogan
, F.
, 1975
, Complex Function Technique
, Academic
, New York
.32.
Gradshteyn
, I. S.
, and Ryzhik
, I. M.
, 1980
, Tables of Integrals, Series, and Products
, 4th ed., Academic
, New York
.33.
Pan
, E.
, and Wang
, R.
, 2009
, “Effects of Geometric Size and Mechanical Boundary Conditions on Magnetoelectric Coupling in Multiferroic Composites
,” J. Phys. D: Appl. Phys.
, 42
(24
), p. 245503
.10.1088/0022-3727/42/24/245503Copyright © 2014 by ASME
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