×

Closed-form expressions for the effective coefficients of a fibre-reinforced composite with transversely isotropic constituents. II: Piezoelectric and hexagonal symmetry. (English) Zbl 1017.74056

Summary: The purpose is to determine effective elastic, piezoelectric and dielectric properties of reinforced piezoelectric composite materials with unidirectional cylindrical fibres periodically distributed in two directions at an angle \(\pi/3\) by means of asymptotic homogenization method. Each periodic cell of the medium is a binary piezoelectric composite, wherein both constituents are homogeneous piezoelectric materials with transversely isotropic properties. This paper makes use of some results obtained in part I [see the foregoing entry]. Simple closed-form expressions for overall properties are obtained by means of potential method of complex variable and Weierstrass elliptic and related functions. Schulgasser-type universal relations are derived in a new way by means of homogenized asymptotic method.

MSC:

74Q15 Effective constitutive equations in solid mechanics
74E30 Composite and mixture properties
74F15 Electromagnetic effects in solid mechanics
74E10 Anisotropy in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Avellaneda, M.; Swart, P.J., Calculating the performance of 1-3 piezoelectric composites for hydrophone applications: an effective medium approach, J. acoust. soc. am., 103, 1449-1467, (1998)
[2] Banno, H., Effects of shape and volume fraction of closed pores on dielectric, elastic and electromechanical properties of dielectric and piezoelectric ceramic — a theoretical approach, Am. ceram. soc. bull., 66, 1332-1337, (1987)
[3] Banno, H., Effects of porosity on dielectric, elastic and electromechanical properties of pb(zr, ti)O_{3} ceramics with open pores: a theoretical approach, Jpn. J. appl. phys., 33, 4214-4217, (1993)
[4] Banno, H., Effects of pore structure on depolarizing factor and dielectric constant of porous ceramics, Jpn. J. appl. phys., 33, 5518-5520, (1994)
[5] Bensoussan, A.; Lions, J.L.; Papanicolaou, G., Asymptotic analysis for periodic structures., (1978), North-Holland Amsterdam · Zbl 0411.60078
[6] Benveniste, Y., Exact results concerning the local fields and effective properties in piezoelectric composites, J. engng. mater. technol., 116, 260-267, (1994)
[7] Benveniste, Y., Piezoelectric inhomogeneity problems in anti-plane shear and inplane electric fields-how to obtain the coupled fields from the uncoupled dielectric solution, Mech. mater., 25, 59-65, (1997)
[8] Benveniste, Y.; Dvorak, G.J., Uniform fields and universal relations in piezoelectric composites, J. mech. phys. solids, 40, 1295-1312, (1992) · Zbl 0763.73046
[9] Chan, H.L.W.; Guy, I.L., Piezoelectric ceramic/polymer composites for high frequency applications, Key engng. mater., 92-93, 275-300, (1994)
[10] Chan, H.L.W.; Unsworth, J., Simple model for piezoelectric ceramic/polymer 1-3 composites used in ultrasonic transducer applications, IEEE trans. ultrason. ferroelectr. frequency control, 38, 434-441, (1989)
[11] Chen, T., Piezoelectric properties of multiphase fibrous composites: some theoretical results, J. mech. phys. solids, 41, 1781-1794, (1993) · Zbl 0798.73045
[12] Chen, T., Micromechanical estimates of the overall thermoelectroelastic moduli of multiphase fibrous composites, Int. J. solids struct., 31, 3099-3111, (1994) · Zbl 0944.74510
[13] Dunn, M.; Taya, M., Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites, Int. J. solids struct., 30, 161-175, (1993) · Zbl 0772.73068
[14] Galka, A.; Telega, J.J.; Wojnar, R., Homogenization and thermopiezoelectricity, Mech. res. commun., 19, 315-324, (1992) · Zbl 0760.73057
[15] Galka, A.; Telega, J.J.; Wojnar, R., Some computational aspects of homogenization of thermopiezoelectric composites, Comput. assisted mech. engng. sci., 3, 113-154, (1996)
[16] Gambin, B.; Galka, A., Boundary layer problem in a piezoelectric composite., (), 327-332 · Zbl 0882.73060
[17] Gibiansky, L.V.; Torquato, S., On the use of homogenization theory to optimally design piezocomposites for hydrophone applications, J. mech. phys. solids, 45, 689-708, (1997) · Zbl 0974.74549
[18] Gómez, T.E.; Montero, F., New constitutive relations for piezoelectric composites and porous piezoelectric ceramics, J. acoust. soc. am., 100, 3104-3114, (1996)
[19] Gómez, T.E.; Montero, F., Piezocomposites of complex microstructure: theory and experimental assessment of the coupling between phases, IEEE trans. ultrason. ferroelectr. frequency control, 44, 208-217, (1997)
[20] Grekov, A.A.; Kramarov, S.O.; Kuprienko, A.A., Effective properties of a transversely isotropic piezocomposite with cylindrical inclusions, Ferroelectrics, 99, 115-126, (1989)
[21] Grigolyuk, E.I., Fil’shtinskii, L.A., 1970. Perforated Plates and Shells. Nauka, Moscow (in Russian).
[22] Guinovart-Dı́az, R., Bravo-Castillero, J., Rodrı́guez-Ramos, R., Sabina, F.J., 2001. Closed-form expressions for the effective coefficients of fibre-reinforced composite with transversely isotropic constituents — I. Elastic and hexagonal symmetry. J. Mech. Phys. Solids 49, 1445-1462. · Zbl 1017.74055
[23] Hill, R., Theory of mechanical properties of fibre-strengthened materials: I. elastic behaviour, J. mech. phys. solids, 12, 199-212, (1964)
[24] Ikeda, T., Fundamentals of piezoelectricity., (1990), Oxford University Press Oxford
[25] Janas, F.V.; Safari, A., Overview of fine-scale piezoelectric ceramic/polymer composite processing, J. am. ceram. soc., 78, 2945-2955, (1995)
[26] Milgrom, M.; Shtrikman, S., Linear response of two-phase composites with cross moduli: exact universal relations, Phys. rev. A, 40, 1568-1575, (1989)
[27] Nan, C.W., Comments on “relationships between the effective properties of transversely isotropic piezoelectric composites”, J. mech. phys. solids, 41, 1567-1570, (1993) · Zbl 0782.73066
[28] Parton, V.Z., Kudryavtsev, B.A., 1993. Engineering Mechanics of Composite Structures. CRC Press, Boca Raton, FL.
[29] Pastor, J., Homogenization of linear piezoelectric media, Mech. res. commun., 24, 145-150, (1997) · Zbl 0894.73133
[30] Ramos, R.R.; Otero, J.A.; Castillero, J.B.; Sabina, F.J., Electromechanical properties of laminated piezoelectric composites, Mekh. komp. mat., 32, 410-417, (1996)
[31] Sánchez, S.; Montero, F., Modeling (2-2) piezocomposites partially sliced in the polymer phase, IEEE trans. ultrason. ferroelectr. frequency control, 44, 287-296, (1997)
[32] Sánchez-Palencia, E., Non homogeneous media and vibration theory, Lecture notes in physics, Vol. 127., (1980), Springer Berlin
[33] Schulgasser, K., Relationships between the effective properties of transversely isotropic piezoelectric composites, J. mech. phys. solids, 40, 473-479, (1992) · Zbl 0825.73629
[34] Skinner, D.P.; Newnham, R.E.; Cross, L.E., Flexible composite transducers, Mater. res. bull., 13, 599-607, (1978)
[35] Smith, W.A., Modeling 1-3 composite piezoelectrics: hydrostatic response, IEEE trans. ultrason. ferroelectr. frequency control, 40, 41-49, (1993)
[36] Smith, W.A., Shaulov, A., Auld, B.A., 1985. Tailoring the properties of composite piezoelectric materials. Proceedings of IEEE Ultrasonics Symposium, pp. 642-647.
[37] Taunaumang, H.; Guy, I.L.; Chan, H.L.W., Electromechanical properties of 1-3 piezoelectric ceramic/piezoelectric polymer composites, J. appl. phys., 76, 484-489, (1994)
[38] Telega, J.J., Piezoelectricity and homogenization. application to biomechanics., (), 220-229 · Zbl 0739.73029
[39] Turbé, N.; Maugin, G.A., On the linear piezoelectricity of composite materials, Math. methods appl. sci., 14, 403-412, (1991) · Zbl 0731.73071
[40] Wang, B., Effective behaviour of piezoelectric composites, Appl. mech. rev., 47, 112-121, (1994)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.