Material Multipole Mechanics of Elastic Dielectric Composites

Zhou Shu-ang

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(3): 208-223

Zhou Shu-ang. Material Multipole Mechanics of Elastic Dielectric Composites[J]. Applied Mathematics and Mechanics, 1990, 11(3): 208-223.

Citation:

Zhou Shu-ang. Material Multipole Mechanics of Elastic Dielectric Composites[J]. Applied Mathematics and Mechanics, 1990, 11(3): 208-223.

Citation:

Zhou Shu-ang. Material Multipole Mechanics of Elastic Dielectric Composites[J]. Applied Mathematics and Mechanics, 1990, 11(3): 208-223.

PDF( 1354 KB)

Material Multipole Mechanics of Elastic Dielectric Composites

Zhou Shu-ang

Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden

Received Date: 1988-04-19
Publish Date: 1990-03-15

Abstract

Abstract

The overall mechanical and electrical behaviors of elastic dielectric composites are investigated with the aid of the concept of material multipoles. In particular, by introducing a statistical continuum material multipole theory, the effects of the electric-elastic interaction and the microstructure (size, shape, orientation,...) of inhomogeneous particles on the overall behaviors of the composites can be obtained. A basic solution for an ellipsoidal elastic inhomogeneity with electric polarization in an infinite elastic dielectric medium is first given, which shows that classical Eshelby's elastic solution is modified by the presence of electric-elastic interaction. The overall macroscopic constitutive relations and their overall macroscopic material parameters accounting for electroelastic interaction effect are then derived for the elastic dielectric composites. Some quantitative calculations on the problems with statistical anisotropy, the shape effect and the electric-elastic interaction are finally given for dilute composites.

FullText(HTML)

References(29)

References

[1]	Böttcher,C.J.F.,Rec.Trav.Chim.Pays-Bas,64(1945),47.
[2]	Kröner,E.,Arch.Rational Mech.Anal.,4(1959),273.
[3]	Willis,J.R.,ASME J.Appl.Mech.,50,(1983),1202.
[4]	Hashin,Z and S.Shtrikman,J.Appl.Phys.,33,(1962),3215.
[5]	Beran,M.,Statistical Continuum Theory,Interscience Publ.,New York(1968).
[6]	Miller,M.N.,J.Math.Phys.,10,(1969),1988.
[7]	Jeffrey,D.J.,Proc.R.Soc.Lond.,A 335,(1973),355.
[8]	McCoy,J.J.and M.J.Beran,Int.Engng.Sci.,14,(1976),7.
[9]	van Beek,J.K.H.,Progress in Dielectrics,7,(1967),69.
[10]	Hale,D.K.,J.Materials Sci.,11,(1976),2105.
[11]	Christensen,R.M.,Mechanics of Composite Materials,John Wiley & Sons,New York(1979).
[12]	Zhou,S.A.and R.K.T.Hsieh,Int.J.Engng.Sci.,24,(1986),1195.
[13]	Nelson,D.F.,Electric Optic and Acoustic Interactions in Dielectrics.Wiley,New York(1979).
[14]	Maugin,G.A.,(ed)The mechanical behavior of electromagnetic solid continua,IUTAM Symp.,North-Holland,Amsterdam(1984).
[15]	Moon,F.C.,Magneto-Solid Mechanics.John Wiley & Sons,New York(1984).
[16]	Zhou.S.A.,R.K.T.Hsieh and G.A.Maugin,Int.J.Solids Structures,22,(1986),1411.
[17]	Zhou,S.A.and R.K.T.Hsieh,Int.J.Engng.Sci.,26,(1988),13.
[18]	Hsieh,R.K.T.,Int.J.Engng.Sci.,20,(1982),201.
[19]	Zhou,S.A.,Material multipole mechanics of electromagnetoelastic solids with defects.Ph.D.Thesis,Royal Institute of Technology,Stockholm(1987).[20] Eshelby,J.D.,Prog.Solid Mech.,2,(1961),89.
[20]	Mura,T.,Micromechanics of Defects in Solids.Martinus Nijhoff Publishers,Hague(1982).
[21]	Jeffrey,D.J.,Proc.R.Soc.Lond..A 338,(1974).503.
[22]	Hershey,A.V.,J.Appl.Mech.,21(1954),236.
[23]	Hashin,Z.,J.Comp.Mater.,2,(1968).284.
[24]	Hori,M.,J.Math.Phys..14,(1973).514.
[25]	Willis,J.R.,J.Mech.Phys.Solids.25.(1977).185.
[26]	Stratton,J.A.,Electromagnetic Theory,McGraw-Hill.New York(1941).
[27]	de Groot,S.R.and L.G.Suttorp,Foundations of Electrodynamics,North-Holland.Amsterdam(1972).
[28]	Rayleigh,J.W.,Phil.Mag.,34.(1892),481.
[29]	Kröner,H.,Modelling Small Deformations of Polycrystals(Ed by J Gittus and J.Zarka),Elsevider Appl.Sci Publ.London(1986),229-291.