A micromechanics approach is developed to analyze the average fields and effective moduli of heterogeneous media that exhibit full coupling between stationary elastic, electric, and magnetic fields. Exact relations regarding the internal field distribution inside a heterogeneous magnetoelectroelastic solid are first established, followed by exact connections between the effective magnetoelectroelastic and thermal moduli of two-phase composites. The Mori-Tanaka mean field approach is then applied to obtain closed form expressions for the effective moduli of fibrous and laminated composites. Finally, numerical results for BaTiO3-CoFe2O4 composites are presented and discussed.
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References
1.
Aboudi, J.1991. Mechanics of Composite Materials, Elsevier.
2.
Alshits, V. I. , A. N. Darinskii and J. Lothe. 1992. "On the Existence of Surface Waves in Half-Infinite Anisotropic Elastic Media with Piezoelectric and Piezomagnetic Properties,"Wave Motion, Vol. 16, 265-284.
3.
Avellaneda, M. and G. Harshe. 1994. "Magnetoelectric Effect in Piezoelectric/Magnetostrictive Multilayer (2-2) Composites,"Journal of Intelligent Material Systems and Structures, Vol. 5, pp. 501-513.
4.
Barnett, D. M. and J. Lothe. 1975. "Dislocations and Line Charges in Anisotropic Piezoelectric Insulators,"Phys. Stat. Sol. (b), Vol. 67, pp. 105-111.
5.
Benveniste, Y.1993a. "Universal Relations in Piezoelectric Composites with Eigenstress and Polarization Fields. I Binary Media: Local Fields and Effective Behavior,"Journal of Applied Mechanics, Vol. 60, pp. 265-269.
6.
Benveniste, Y.1993b. "Universal Relations in Piezoelectric Composites with Eigenstress and Polarization Fields. II Multiphase Media: Effective Behavior,"Journal of Applied Mechanics, Vol. 60, pp. 270-275.
7.
Benveniste, Y.1993c. "Exact Results in the Micromechanics of Fibrous Piezoelectric Composites Exhibiting Pyroelectricity,"Proceedings of the Royal Society of London A, Vol. 441, pp. 59-81.
8.
Benveniste, Y.1994. "Exact Results Concerning the Local Fields and Effective Properties in Piezoelectric Composites,"ASME Journal of Engineering Materials and Technology, Vol. 260, pp. 260-267.
9.
Benveniste, Y.1995. "Magnetoelectric Effect in Fibrous Composites with Piezoelectric and Piezomagnetic Phases,"Physical Review B, Vol. 51, No. 9, pp. 16424-16427.
10.
Benveniste, Y. and G. J. Dvorak. 1992. "Uniform Fields and Universal Relations in Piezoelectric Composites,"Journal of the Mechanics and Physics of Solids, Vol. 40, No. 6, pp. 1295-1312.
11.
Bracke, L. P. M. and R. G. Van Vliet. 1981. "A Broadband Magneto-Electric Transducer Using a Composite Materials,"Int. J. Electronics, Vol. 51, pp. 255-262.
12.
Cao, H. , Q. M. Zhang and L. E. Cross. 1992a. "Theoretical Study on the Static Performance of Piezoelectric Ceramic-Polymer Composites with 1-3 Connectivity,"Journal of Applied Physics, Vol. 72, pp. 5814-5821.
13.
Cao, H. , Q. M. Zhang and L. E. Cross. 1992b. "Theoretical Study on the Static Performance of Piezoelectric Ceramic-Polymer Composites with 2-2 Connectivity,"IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, Vol. 40, pp. 103-109.
14.
Chen, T.1993. "Piezoelectric Properties of Multiphase Fibrous Composites: Some Theoretical Results,"J. Mech. Phys. Solids, Vol. 41, pp. 1781-1794.
15.
Chen, T.1994. "Micromechanical Estimates of the Overall Thermoelectroelastic Moduli of Multiphase Fibrous Composites,"Int. J Solids Structures, Vol. 31, pp. 3099-3111.
16.
Chen, T.1996. "Effective Properties of Platelet Reinforced Piezocomposites,"Composites, Vol. 27B, pp. 467-474.
17.
Dunn, M. L.1993a. "Exact Relations between the Thermoelectroelastic Moduli of Heterogeneous Media,"Proceedings of the Royal Society of London A, Vol. 441, pp. 549-557.
18.
Dunn, M. L.1993b. "Micromechanics of Coupled Electroelastic Composites: Effective Thermal Expansion and Pyroelectric Coefficients,"Jour-nal of Applied Physics, Vol. 73, No. 10, pp. 5131-5140.
19.
Dunn, M. L. and M. Taya. 1993a. "An Analysis of Composite Materials Containing Ellipsoidal Piezoelectric Inhomogeneities,"Proceedings of the Royal Society of London A, Vol. 443, pp. 265-287.
20.
Dunn, M. L. and M. Taya. 1993b. "Micromechanics Predictions of the Effective Electro-Elastic Moduli of Piezoelectric Composites,"International Journal of Solids and Structures, Vol. 30, No. 2, pp. 161-175.
21.
Harshe, G. , J. P. Dougherty and R. E. Newnham. 1993a. "Theoretical Modelling of Multilayer Magnetoelectric Composites,"International Journal of Applied Electromagnetics in Materials, Vol.4, pp. 145-159.
22.
Harshe, G. , J. P. Dougherty and R. E. Newnham. 1993b. "Theoretical Modelling of 3-0/0-3 Magnetoelectric Composites,"International Journal of AppliedElectromagnetics in Materials, Vol. 4, pp. 161-171.
23.
Hill, R.1963. "Elastic Properties of Reinforced Solids: Some Theoretical Principles,"J. Mech. Phys. Solids, Vol. 11, pp. 357-372.
24.
Kreher, W.1988. "Internal Stresses and Relations between Effective Thermoelastic Properties of Stochastic Solids-Some Exact Solutions,"ZAMMZ. Angelv. Math. Mech., Vol. 68, pp. 147-154.
25.
Levin, V. M.1967. "On the Coefficients of Thermal Expansion of Heterogeneous Materials,"Mekhanika Tverdogo Tela, pp. 88-94.
26.
Li, J. Y. and M. L. Dunn. 1998a. "Anisotropic Coupled-Field Inclusion and Inhomogeneity Problems,"Philosophical Magazine A, Vol. 77, pp. 1341-1350.
27.
Li, J. Y. and M. L. Dunn. 1998b. "Analysis of Random Microstructural Fields in Heterogeneous Peizoelectric Solids,"International Journal of Engineering Science, accepted for publication.
28.
Mori, T. and K. Tanaka. 1973. "Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions,"Acta Metallurgica, Vol. 21, pp. 571-574.
29.
Nan, C. W.1994. "Magnetoelectric Effect in Composites of Piezoelectric and Piezomagnetic Phases,"Physical Review B, Vol. 50, No. 22, pp. 6082-6088.
30.
Nye, J. F.1985. Physical Properties of Crystals, Oxford University Press.
31.
Rosen, B. W. and Z. Hashin. 1970. "Effective Thermal Expansion Coefficients and Specific Heats of Composite Materials,"International Journal of Engineering Science, Vol. 8, pp. 157-173.
32.
Schulgasser, K.1992. "Relationships between the Effective Properties of Transversely Isotropic Piezoelectric Composites,"Journal of the Mechanics and Physics of Solids, Vol. 40, No. 2, pp. 473-479.
33.
Sottos, N. R. , L. Li, W. R. Scott and M. J. Ryan. 1993. "Micromechanical Behavior of 1-3 Piezocomposites," in Smart Materials, SPIE Vol. 1916, V. K. Varadan, ed., pp. 275-285.
34.
Wang, B.1992. "Three-Dimensional Analysis of an Ellipsoidal Inclusion in a Piezoelectric Material,"Int. J. Solids Structures, Vol. 29, No. 3, pp. 293-308.
35.
Van Run , A. M. J. G., D. R. Terrell and J. H. Scholing. 1974. 'An in situ Grown Eutectic Magnetoelectric Composite Material,"Journal of Materials Science, Vol. 9, pp. 1710-1714.
36.
Voigt, W. 1889. "Ueber die Beziehung zwischen den beiden Elastizita tskonstanten isotroper Korper," Annalen der Physik, Vol. 38, 573-587.
37.
Zhang, Q. M. , H. Cao, H. Wang and L. E. Cross. 1993. "Characterization of the Performance of 1-3 Type Piezocomposites for Low-Frequency Applications,"Journal of Applied Physics, Vol. 73, pp. 1403-1410.
