×

Piezoelectric properties of multiphase fibrous composites: Some theoretical results. (English) Zbl 0798.73045

The paper concerns the evaluation of effective electromechanical moduli in special classes of piezoelectric composites. A number of exact results are established for such moduli when the composites consist of many perfectly bonded transversely isotropic phases of cylindrical shape (fibers) and arbitrary transverse geometry. In the case of such three- phase media, three universal relationships that are independent of the geometry at fixed volume fractions, are shown to connect six of the effective moduli. When the phases have equal transverse rigidity in shear, then exact values of certain of the overall moduli can be derived for multiphase systems. It is proved that the explicit formulae depend then solely on the concentrations and phase moduli. More precisely, seven out of a total of ten overall moduli of a transversely isotropic composite can be found thus, while the remaining three are shown to obey an exact relationship. The latter would also apply in the analysis of other phenomena in composite materials, e.g., magnetoelectric and thermoelectric effects. This work follows and generalizes previous works by R. Hill [J. Mech. Phys. Solids 35, 565-576 (1987; Zbl 0616.73004)] in pure elasticity and by K. S. Mendelson in pure dielectric problems. It fits in the current research of materials science with application to new materials, in particular, artificially produced ones such as electromechanical composites.
Reviewer: G.A.Maugin (Paris)

MSC:

74F15 Electromagnetic effects in solid mechanics
74E30 Composite and mixture properties
74B05 Classical linear elasticity

Citations:

Zbl 0616.73004
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Benveniste, Y., Exact results in the micromechanics of fibrous piezoelectric composites exhibiting pyroelectricity, Proc. R. Soc. Land., A441, 59-81 (1993)
[2] Benveniste, Y., Universal relations in piezoelectric composites with eigenstress and polarization fields. I. Binary media : local fields and effective behavior, J. Appl. Mech., 60, 265-269 (1993) · Zbl 0774.73058
[3] Benveniste, Y., Universal relations in piezoelectric composites with eigenstress and polarization fields. II. Multiphase media : effective behavior, J. Appl. Mech., 60, 270-275 (1993) · Zbl 0774.73058
[4] Benveniste, Y.; Dvorak, G. J., Uniform fields and universal relations in piezoelectric composites, J. Mech. Phys. Solids, 40, 1295-1312 (1992) · Zbl 0763.73046
[5] Cherkaev, A. V.; Lurie, K. A.; Milton, G. W., Invariant properties of the stress in plane elasticity and equivalence classes of composites, Proc. R. Soc. Land., A438, 519-529 (1992) · Zbl 0791.73011
[6] Dunn, M. L.; Taya, M., Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites, Int. J. Solids Struct., 30, 161-175 (1993) · Zbl 0772.73068
[7] Dvorak, G. J., On uniform fields in heterogeneous media, Proc. R. Soc. Land., A431, 89-110 (1990) · Zbl 0726.73002
[8] Dykhne, A. M., Conductivity of a two-dimensional system, Sov. Phys. JETP, 32, 63-65 (1971)
[9] Hill, R., Discontinuity relations in mechanics of solids, (Sneddon, I. N.; Hill, R., Progress in Solid Mechanics, Vol. 2 (1961), North-Holland: North-Holland Amsterdam), 247-276
[10] Hill, R., Elastic properties of reinforced solids : some theoretical principles, J. Mech. Phys. Solids, 11, 351-372 (1963) · Zbl 0114.15804
[11] Hill, R., Theory of mechanical properties of fibre-strengthened materials-I. Elastic behaviour, J. Mech. Phys. Solids, 12, 199-212 (1964)
[12] Ikeda, T., (Fundamentals of Piezoelectricity (1990), Oxford University Press: Oxford University Press New York)
[13] Keller, J. B., A theorem on the conductivity of a composite medium, J. Math. Phys., 5, 548-549 (1964) · Zbl 0129.44001
[14] Khoroshun, L. P.; Dorodnykh, T. I., Piezoelectrics of polycrystalline structure, Sov. Appl. Mech., 27, 660-665 (1991)
[15] Mendelson, K. S., Effective conductivity of two-phase material with cylindrical phase boundaries, J. Appl. Phys., 46, 917-918 (1975)
[16] Milgrom, M.; Shtrikman, S., Linear response of two-phase composites with cross moduli: exact universal relations, Phys. Rev. A., 40, 1568-1575 (1989)
[17] Nye, J. F., Physical Properties of Crystals: Their Representation by Tensors and Matrices (1957), Clarendon Press: Clarendon Press Oxford · Zbl 0079.22601
[18] Olson, T.; Avellaneda, M., Effective dielectric and elastic constants of piezoelectric polycrystals, J. Appl. Phys., 71, 4455-4464 (1992)
[19] Schulgasser, K., On a phase interchange relationship for composite materials, J. Math. Phys., 17, 378-381 (1976)
[20] Schulgasser, K., Relationships between the effective properties of transversely isotropic piezoelectric composites, J. Mech. Phys. Solids, 40, 473-479 (1992) · Zbl 0825.73629
[21] Thorpe, M. F.; Jasiuk, I., New results in the theory for two-dimensional composites, Proc. R. Soc. Land., A438, 531-544 (1992) · Zbl 0806.73042
[22] Tiersten, H. F., Linear Piezoelectric Plate Vibrations (1969), Plenum Press: Plenum Press New York · Zbl 0534.73083
[23] Walpole, L. J., The analysis of the overall elastic properties of composite materials, (Bilby, B. A.; Miller, K. J.; Willis, J. R., Fundamentals of Deformation and Fracture (1984), Cambridge University Press: Cambridge University Press Cambridge), 91-107 · Zbl 0561.73008
[24] Wang, B., Three-dimensional analysis of an ellipsoidal inclusion in a piezoelectric material, Int. J. Solids Struct., 29, 293-308 (1992) · Zbl 0753.73071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.