Closed-form expressions for the effective coefficients of a fiber-reinforced composite with transversely isotropic constituents – II. Piezoelectric and square symmetry

Avellaneda, 1998, Calculating the performance of 1–3 piezoelectric composites for hydrophone applications: An effective medium opproach, J. Acoust. Soc. Am., 103, 1449, 10.1121/1.421306 Bensoussan, 1978 Benveniste, 1992, Uniform fields and universal relations in piezoelectric composites, J. Mech. Phys. Solids, 40, 1295, 10.1016/0022-5096(92)90016-U Bisegna, 1996, Variational bounds for the overall properties of piezoelectric composites, J. Mech. Phys. Solids, 44, 583, 10.1016/0022-5096(95)00084-4 Chan, 1989, Simple model for piezoelectric ceramic/polymer 1–3 composites used in ultrasonic transducer applications, IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 38, 434, 10.1109/58.31780 Dunn, 1993, Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites, Int. J. Solids Struct., 30, 161, 10.1016/0020-7683(93)90058-F Galka, 1992, Homogenization and thermopiezoelectricity, Mech. Res. Commun., 19, 315, 10.1016/0093-6413(92)90050-K Galka, 1996, Some computational aspects of homogenization of thermopiezoelectric composites, Comp. Assoc. Mech. Eng. Sci., 3, 113 Grekov, 1989, Effective properties of a transversely isotropic piezocomposite with cylindrical inclusions, Ferroelectrics, 99, 115, 10.1080/00150198908221444 Grigolyuk, 1970 Hill, 1964, Theory of mechanical properties of fiber-strengthened materials: I. Elastic behaviour, J. Mech. Phys. Solids, 12, 199, 10.1016/0022-5096(64)90019-5 Hori, 1998, Universal bounds for effective piezoelectric moduli, Mech. Mater., 30, 1, 10.1016/S0167-6636(98)00029-5 Hori, 1999, On two micromechanics theories for determining micro–macro relations in heterogeneous solids, Mech. Mater., 31, 667, 10.1016/S0167-6636(99)00020-4 Ikeda, 1990 Janas, 1995, Overview of fine-scale piezoelectric ceramic/polymer composite processing, J. Am. Ceram. Soc., 78, 2945, 10.1111/j.1151-2916.1995.tb09068.x Milgrom, 1989, Linear response of two-phase composites with cross moduli: Exact universal relations, Phys. Rev. A, 40, 1568, 10.1103/PhysRevA.40.1568 Nan, 1993, Comment on “Relationships between the effective properties of transversely isotropic piezoelectric composites”, J. Mech. Phys. Solids, 41, 1567, 10.1016/0022-5096(93)90040-M Parton, 1993 Rodrı́guez-Ramos, 2001, Closed-form expressions for the effective coefficients of fiber-reinforced composite with transversely isotropic constituents – I. Elastic and square symmetry, Mech. Mater., 33, 223, 10.1016/S0167-6636(00)00059-4 Sánchez-Palencia, E., 1980. Non Homogeneous Media and Vibration Theory. Lecture Notes in Physics 127, Springer, Berlin Schulgasser, 1992, Relationship between the efective properties of transversely isotropic piezoelectric composites, J. Mech. Phys. Solids, 40, 473, 10.1016/S0022-5096(05)80022-5 Smith, 1993, Modeling 1–3 composite piezoelectrics: hydrostatic response, IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 40, 41, 10.1109/58.184997 Smith, 1991, Modeling 1–3 composite piezoelectrics: thickness-mode oscillations, IEEE Trans. Ultrason. Ferroelec. Freq. Contr., 38, 40, 10.1109/58.67833 Smith, 1988, Composite piezoelectrics: Basic research to a practical device, Ferroelectrics, 87, 309, 10.1080/00150198808201393 Smith, 1985, Tailoring the properties of composite piezoelectric materials, Proc. IEEE Ultrason. Sympos., 642 Smith, 1989, Design of piezocomposites for ultrasonic transducers, Ferroelectrics, 91, 155, 10.1080/00150198908015735 Taunaumang, 1994, Electromechanical properties of 1–3 piezoelectric ceramic/piezoelectric polymer composites, J. Appl. Phys., 76, 484, 10.1063/1.357099 Telega, J.J., 1991. Piezoelectricity and homogenization. Application to biomechanics. In: Maugin, G.A. (Ed.), Continuum Models and Discrete Systems 2. Longman, London, pp. 220–229 Turbé, 1991, On the linear piezoelectricity of composite materials, Math. Meth. Appl. Sci., 14, 403, 10.1002/mma.1670140604