Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T03:29:28.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Matrix laminate composites: Realizable approximations for the effective moduli of piezoelectric dispersions

Published online by Cambridge University Press:  26 July 2012

L. V. Gibiansky  and
S. Torquato
L. V. Gibiansky
Affiliation:
Department of Civil Engineering and Operations Research and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544
S. Torquato
Affiliation:
Department of Civil Engineering and Operations Research and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544
Get access

Extract

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.

Type
Articles
Information
Journal of Materials Research , Volume 14 , Issue 1 , January 1999 , pp. 49 - 63
Copyright
Copyright © Materials Research Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Klicker, K.A., Biggers, J.V., and Newnham, R.E., J. Am. Ceram. Soc. 64, 5 (1981).CrossRefGoogle Scholar
2.Newnham, R.E. and Ruschau, G.R., J. Am. Ceram. Soc. 74, 463 (1991).Google Scholar
3.Ting, R. Y., Shalov, A. A., and Smith, W. A., Proc. 1990 IEEE Ultrason. Symp., 707 (1990).Google Scholar
4.Haun, M. J. and Newnham, R. E., Ferroelec. 68, 123 (1986).Google Scholar
5.Chan, H. L. W. and Unsworth, J., IEEE Tran. Ultrason. Ferro. Freq. Control 36, 434 (1989).CrossRefGoogle Scholar
6.Smith, W.A., Proc. 1991 IEEE Ultrason. Symp., 661 (1991).CrossRefGoogle Scholar
7.Smith, W.A., IEEE Tran. Ultrason. Ferro. Freq. Control 40, 41 (1993).CrossRefGoogle Scholar
8.Dunn, M. L. and Taya, M., Int. J. Solids Struct. 30, 161 (1993).Google Scholar
9.Kuo, W.S. and Huang, J.H., Int. J. Solids Struct. 34, 2445 (1997).CrossRefGoogle Scholar
10.Avellaneda, M. and Swart, P. J., working paper, Courant Institute of Mathematical Sciences (1993).Google Scholar
11.Avellaneda, M. and Olson, T., Recent Advances in Adaptive and Sensory Materials and Their Applications (Technomic Press, Lancaster, PA, 1992).Google Scholar
12.Benveniste, Y., Mech. Mater. 18, 183 (1994).Google Scholar
13.Sigmund, O., Torquato, S., and Aksay, I. A., J. Mater. Res. 13, 1038 (1998).Google Scholar
14.Gibiansky, L.V. and Torquato, S., J. Mech. Phys. Solids 45, 689 (1997).Google Scholar
15.Hashin, Z., J. Mech. Phys. Solids 13, 119 (1965).CrossRefGoogle Scholar
16.Francfort, G. and Murat, F., Arch. Rational Mech. Anal. 94, 307 (1986).Google Scholar
17.Hashin, Z. and Shtrikman, S., J. Appl. Phys. 35, 3125 (1962).CrossRefGoogle Scholar
18.Hashin, Z. and Shtrikman, S., J. Mech. Phys. Solids 11, 127 (1963).Google Scholar
19.Willis, J. R., J. Mech. Phys. Solids 25, 185 (1977).CrossRefGoogle Scholar
20.Avellaneda, M., SIAM J. Appl. Math. 47, 1216 (1987).Google Scholar
21.Lurie, K.A. and Cherkaev, A.V., Proc. Roy. Soc. Edinburgh A 104, 21 (1986).Google Scholar
22.Tartar, L., in Ennio de Giorgi Colloquium, edited by Kree, P., Pitman Research Notes in Math. 125, 168 (1985).Google Scholar
23.Kohn, R.V. and Milton, G. W., J. Mech. Phys. Solids 36, 597 (1988).Google Scholar
24.Lipton, R., J. Mech. Phys. Solids 39, 663 (1991).Google Scholar
25.Milton, G.W., Homogenization and Effective Moduli of Materials and Media, edited by Ericksen, J. L., Kinderlehrer, D., Kohn, R. V., and Lions, J. L. (Springer-Verlag, New York, 1986), p. 150.CrossRefGoogle Scholar
26.Furukawa, T., Fujino, K., and Fukada, E., Jpn. J. Appl. Phys. 15, 2119 (1976).Google Scholar
27.Weng, G.J., Int. J. Eng. Sci. 28, 1111 (1990).Google Scholar
28.Mura, T., Micromechanics of Defects in Solids, 2nd ed. (Martinus Nijhoff, Dordrecht, The Netherlands, 1987).CrossRefGoogle Scholar
29.Qiu, Y.P. and Weng, G.J., Int. J. Eng. Sci. 28, 1121 (1990).Google Scholar