Asymptotic homogenization of laminated piezocomposite materials

Abstract The objective of this paper is to apply the technique of asymptotic homogenization to determine the effective elastic, piezoelectric and dielectric moduli of a laminated piezocomposite medium with a periodic structure. Each periodic cell of the medium can possess any finite number of piezoelectric layers. The general formulae obtained are a generalization of those that appear in chapter 5 of Pobedria (Pobedria, B. E. (1984) Mechanics of Composite Materials . Moscow State University Press, Moscow (in Russian)) and involve both cases of Newnham's connectivity theory (Newnham, R. E., Skinner, D. P. and Cross, L. E. (1978) Connectivity and piezoelectric-pyroelectric composites. Materials Research Bulletin 13 , 525–536) for layered piezoelectric media. We calculate explicitly overall effective characteristics for three examples of such layered media. For the particular case of a binary layered medium, connected in parallel, with transversely isotropic constituents such formulae transform exactly to the formulae for effective constants obtained by Benveniste et al. (1992) in which a different method of homogenization was used. Finally, we apply these results to a piezocomposite material and obtain new piezoelectric with better global properties for hydrophone applications.

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