New exact results for the effective electric, elastic, piezoelectric and other properties of composite ellipsoid assemblages

Journal of the Mechanics and Physics of Solids

Volumn 51, Issue 10, 2003, Pages 1773-1813

  Benveniste, Y ^a   Milton, G W ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

A. Microstructures; A. Voids and inclusions; B. Coupled field exact solutions; B. Fibre reinforced composite material; B. Particulate reinforced material

Indexed keywords

ELASTICITY; ELECTRIC CONDUCTIVITY; MOLECULAR ORIENTATION; PIEZOELECTRIC DEVICES; SEGREGATION (METALLOGRAPHY); TENSORS;

COMPOSITE ELLIPSOID ASSEMBLAGES;

COMPOSITE MATERIALS;

EID: 0043130433     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(03)00074-7     Document Type: Article

References (43)

1. Albers, W., 1973. Physical properties of composite materials. In: Proceedings of the Conference on in situ Composites, 5-8 September 1972, Lakeville, Connecticut, Publication NMAB-308-III, National Academy of Sciences, Washington, DC, pp. 1-19.
2. Alshits V.I., Darinskii A.N., Lothe J. On the existence of surface waves in half-infinite anisotropic media with piezoelectric and piezomagnetic properties. Wave Motion. 16:1992;265-283.
3. Avellaneda M., Harshe G. Magnetoelectric effect in piezoelectric/magnetostrictive multilayer (2-2) composites. J. Intell. Mater. Syst. Struct. 5:1994;501-513.
4. Barnett D.M., Lothe J. Dislocations and line charges in anisotropic piezoelectric insulators. Phys. Stat. Sol. B. 67:1975;105-111.
5. Benveniste Y. Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Phys. Rev. B. 51:1995;16424-16427.
6. Benveniste Y., Miloh T. An exact solution for the effective thermal conductivity of cracked bodies with oriented elliptical cracks. J. Appl. Phys. 66:1989;176-180.
7. Benveniste Y., Miloh T. On the effective thermal conductivity of coated short fiber composites. J. Appl. Phys. 69:1991;1337-1344.
8. Bergman D.J. The dielectric constant of a composite material - A problem in classical physics. Phys. Rep. 43:1978;377-407.
9. Bergman D.J. Rigorous bounds for the complex dielectric constant of a two-component composite. Ann. Phys. 138:1982;78-114.
10. Bhagavantam S. Crystal Symmetry and Physical Properties. 1966;Academic Press, New York.
11. Dvorak, G.J., Benveniste, Y., 1997. On micromechanics of inelastic and piezoelectric composites. In: Tatsumi, T., Watanabe, E., Kambe, T. (Eds.), Theoretical and Applied Mechanics 1996, Proceedings of the XIXth International Congress of Theoretical and Applied Mechanics, Kyoto, Japan, 25-31 August 1996, pp. 217-237.
12. Grabovsky Y. Bounds and extremal microstructures for two-component composites. a unified treatment based on the translation method Proc. Roy. Soc. London A. 452:1996;919-944.
13. Grabovsky Y., Kohn R.V. Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. I. The confocal ellipse construction. J. Mech. Phys. Solids. 43:1995;933-947.
14. Grabovsky Y., Milton G.W., Sage D.S. Exact relations for the effective tensors of composites. necessary conditions and sufficient conditions Comm. Pure Appl. Math. 53:2000;330-353.
15. Harshe G., Dougherty J.P., Newnham R.E. Theoretical modelling of multilayer magnetoelectric composites. Int. J. Appl. Electromagn. Mater. 4:1993;145-159.
16. Harshe G., Dougherty J.P., Newnham R.E. Theoretical modelling of 3-0/0-3 magnetoelectric composites. Int. J. Appl. Electromagn. Mater. 4:1993;161-171.
17. Hashin Z. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29:1962;143-150.
18. Hashin, Z., 1972. Theory of fiber reinforced materials, NASA Contractor Report CR-1974, NASA, Washington, DC.
19. Hashin Z., Rosen B.W. The elastic moduli of fiber-reinforced materials. J. Appl. Mech. 46:1964;543-550.
20. Hashin Z., Shtrikman S. A variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys. 33:1962;3125-3131.
21. Hatta H., Taya M. Thermal conductivity of coated fiber composites. J. Appl. Phys. 59:1986;1851-1860.
22. Hill R. The elastic behaviour of a crystalline aggregate. Phys. Soc. A. 65:1952;349-354.
23. Hill R. Theory of mechanical properties of fiber-strengthened materials - I. Elastic behaviour. J. Mech. Phys. Solids. 12:1964;199-212.
24. Huang Y., Hu K.X. A generalized self-consistent mechanics method for solids containing elliptical inclusions. J. Appl. Mech. 62:1995;566-572.
25. Kellogg O.D. Foundations of Potential Theory. 1929;The Murray Printing Company, Frederick Ungar Publishing Company, New York.
26. Li J.Y., Dunn M.L. Anisotropic coupled-field inclusion and inhomogeneity problems. Philos. Mag. A. 77:1998;1341-1350.
27. Lurie K.A., Cherkaev A.V. The problem of formation of an optimal isotropic multicomponent composite. J. Opt. Theor. Appl. 46:1985;571-589.
28. Milgrom M., Shtrikman S. A layered-shell model of isotropic composites and exact expressions for the effective properties. J. Appl. Phys. 66:1989;3429-3436.
29. Miloh T., Benveniste Y. A generalized self-consistent method for the effective conductivity of composites with ellipsoidal inclusions and cracked bodies. J. Appl. Phys. 63:1988;789-796.
30. Milton G.W. Bounds on the complex permitivity of a two-component composite material. J. Appl. Phys. 52:1981;5286-5293.
31. Milton G.W. Concerning bounds on the transport and mechanical properties of multicomponent composite materials. Appl. Phys. A. 26:1981;125-130.
32. Milton G.W. The Theory of Composites. 2002;Cambridge University Press, Cambridge.
33. Milton G.W., Serkov S.K. Neutral coated inclusions in conductivity and anti-plane elasticity. Proc. Roy. Soc. London A. 457:2001;1973-1997.
34. Mikata Y., Taya M. Stress field in and around a coated short fiber in an infinite matrix subjected to uniaxial and biaxial loading. J. Appl. Mech. 52:1985;19-24.
35. Mikata Y., Taya M. Thermal stress in a coated short fiber composite. J. Appl. Mech. 53:1986;681-689.
36. Nan C.W. Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B. 50:1994;6082-6088.
37. Nye J.F. Physical Properties of Crystals. 1957;Clarendon Press, Oxford.
38. Riccardi A., Montheillet F. A generalized self-consistent method for solids containing randomly oriented spheroidal inclusions. Acta Mech. 133:1999;39-56.
39. Ru C.Q. Three-phase elliptical inclusions with internal uniform hydrostatic stresses. J. Mech. Phys. Solids. 47:1999;259-273.
40. Ru C.Q., Schiavone P., Mioduchowski A. Uniformity of stresses within a three-phase elliptic inclusion in anti-plane shear. J. Elasticity. 52:1999;121-128.
41. Schulgasser K. Concerning the effective transverse conductivity of a two-dimensional, two-phase material. Int. J. Heat Mass Transfer. 20:1977;1226-1230.
42. Stroud D., Bergman D.J. New exact results for the Hall coefficient and magnetoresistance of inhomogeneous two-dimensional metals. Phys. Rev. B. 30:1984;447-449.
43. Tartar, L., 1985. Estimations fines des coefficients homogénéisés. (French) [Fine estimations of homogenized coefficients] In: P. Krée (Ed.), Ennio de Giorgi Colloquium: Papers Presented at a Colloquium Held in the H. Poincaré Institute, Pitman Publishing Ltd, London, November 1983, pp. 168-187, ISBN 0-273-08680-4.