Abstract
This paper is concerned with the effective piezoelectric moduli of a special class of dispersions called matrix laminates composites that are known to possess extremal elastic and dielectric moduli. It is assumed that the matrix material is an isotropic dielectric, and the inclusions and composites are transversely isotropic piezoelectrics that share the same axis of symmetry. The exact expressions for the effective coefficients of such structures are obtained. They can be used to approximate the effective properties of any transversely isotropic dispersion. The advantages of our approximations are that they are (i) realizable, i.e., correspond to specific microstructures; (ii) analytical and easy to compute even in nondegenerate cases; (iii) valid for the entire range of phase volume fractions; and (iv) characterized by two free parameters that allow one to “tune” the approximation and describe a variety of microstructures. The new approximations are compared with known ones.
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References
K.A. Klicker, J.V. Biggers, and R.E. Newnham, J. Am. Ceram. Soc. 64, 5 (1981).
R.E. Newnham and G.R. Ruschau, J. Am. Ceram. Soc. 74, 463 (1991).
R. Y. Ting, A. A. Shalov, and W. A. Smith, Proc. 1990 IEEE Ultrason. Symp., 707 (1990).
M. J. Haun and R. E. Newnham, Ferroelec. 68, 123 (1986).
H. L. W. Chan and J. Unsworth, IEEE Tran. Ultrason. Ferro. Freq. Control 36, 434 (1989).
W.A. Smith, Proc. 1991 IEEE Ultrason. Symp., 661 (1991).
W.A. Smith, IEEE Tran. Ultrason. Ferro. Freq. Control 40, 41 (1993).
M. L. Dunn and M. Taya, Int. J. Solids Struct. 30, 161 (1993).
W.S. Kuo and J.H. Huang, Int. J. Solids Struct. 34, 2445 (1997).
M. Avellaneda and P. J. Swart, working paper, Courant Institute of Mathematical Sciences (1993).
M. Avellaneda and T. Olson, Recent Advances in Adaptive and Sensory Materials and Their Applications (Technomic Press, Lancaster, PA, 1992).
Y. Benveniste, Mech. Mater. 18, 183 (1994).
O. Sigmund, S. Torquato, and I. A. Aksay, J. Mater. Res. 13, 1038 (1998).
L.V. Gibiansky and S. Torquato, J. Mech. Phys. Solids 45, 689 (1997).
Z. Hashin, J. Mech. Phys. Solids 13, 119 (1965).
G. Francfort and F. Murat, Arch. Rational Mech. Anal. 94, 307 (1986).
Z. Hashin and S. Shtrikman, J. Appl. Phys. 35, 3125 (1962).
Z. Hashin and S. Shtrikman, J. Mech. Phys. Solids 11, 127 (1963).
J. R. Willis, J. Mech. Phys. Solids 25, 185 (1977).
M. Avellaneda, SIAM J. Appl. Math. 47, 1216 (1987).
K.A. Lurie and A.V. Cherkaev, Proc. Roy. Soc. Edinburgh A 104, 21 (1986).
L. Tartar, in Ennio de Giorgi Colloquium, edited by P. Kree, Pitman Research Notes in Math. 125, 168 (1985).
R.V. Kohn and G. W. Milton, J. Mech. Phys. Solids 36, 597 (1988).
R. Lipton, J. Mech. Phys. Solids 39, 663 (1991).
G.W. Milton, Homogenization and Effective Moduli of Materials and Media, edited by J. L. Ericksen, D. Kinderlehrer, R. V. Kohn, and J. L. Lions (Springer-Verlag, New York, 1986), p. 150.
T. Furukawa, K. Fujino, and E. Fukada, Jpn. J. Appl. Phys. 15, 2119 (1976).
G.J. Weng, Int. J. Eng. Sci. 28, 1111 (1990).
T. Mura, Micromechanics of Defects in Solids, 2nd ed. (Martinus Nijhoff, Dordrecht, The Netherlands, 1987).
Y.P. Qiu and G.J. Weng, Int. J. Eng. Sci. 28, 1121 (1990).
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Gibiansky, L.V., Torquato, S. Matrix laminate composites: Realizable approximations for the effective moduli of piezoelectric dispersions. Journal of Materials Research 14, 49–63 (1999). https://doi.org/10.1557/JMR.1999.0010
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DOI: https://doi.org/10.1557/JMR.1999.0010