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Research Papers

Effective Electromechanical Properties of 622 Piezoelectric Medium With Unidirectional Cylindrical Holes

[+] Author and Article Information
Adair Roberto Aguiar

PPG Interunidades Bioengenharia
- EESC/FMRP/IQSC
Departamento de Engenharia de Estruturas, EESC
Universidade de São Paulo – USP
São Carlos, Brasil
e-mail: aguiarar@sc.usp.br

Julián Bravo Castillero

e-mail: jbravo@matcom.uh.cu

Reinaldo Rodríguez Ramos

e-mail: reinaldo@matcom.uh.cu
Facultad de Matemática y Computación
Universidad de La Habana
San Lázaro y L. Vedado
Habana 4, CP-10400, Cuba

Uziel Paulo da Silva

PPG Interunidades Bioengenharia
- EESC/FMRP/IQSC
Universidade de São Paulo – USP
São Carlos, Brasil
e-mail: uziel@sc.usp.br

1Corresponding author.

2See, for instance, [2] for the classification of crystal classes.

Manuscript received July 10, 2012; final manuscript received December 6, 2012; accepted manuscript posted January 22, 2013; published online July 19, 2013. Assoc. Editor: Martin Ostoja-Starzewski.

J. Appl. Mech 80(5), 050905 (Jul 19, 2013) (11 pages) Paper No: JAM-12-1316; doi: 10.1115/1.4023475 History: Received July 10, 2012; Revised December 06, 2012; Accepted January 22, 2013

The asymptotic homogenization method (AHM) yields a two-scale procedure to obtain the effective properties of a composite material containing a periodic distribution of unidirectional circular cylindrical holes in a linear transversely isotropic piezoelectric matrix. The matrix material belongs to the symmetry crystal class 622. The holes are centered in a periodic array of cells of square cross sections and the periodicity is the same in two perpendicular directions. The composite state is antiplane shear piezoelectric, that is, a coupled state of out-of-plane shear deformation and in-plane electric field. Local problems that arise from the two-scale analysis using the AHM are solved by means of a complex variable method. For this, the solutions are expanded in power series of Weierstrass elliptic functions, which contain coefficients that are determined from the solutions of infinite systems of linear algebraic equations. Truncating the infinite systems up to a finite, but otherwise arbitrary, order of approximation, we obtain analytical formulas for effective elastic, piezoelectric, and dielectric properties, which depend on both the volume fraction of the holes and an electromechanical coupling factor of the matrix. Numerical results obtained from these formulas are compared with results obtained by the Mori–Tanaka approach. The results could be useful in bone mechanics.

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Figures

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Fig. 1

(a) Periodic structure of identical parallel empty circular cylinders. (b) Cell occupying the region R = R1∪R2 with R1∩R2 = ∅⁣.

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Fig. 2

The effective material constants for the piezoelectric composite versus the area fraction V1. (a) Normalized elastic and dielectric permittivity constants. (b) Normalized piezoelectric constants.

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Fig. 3

The ratio between the effective coupling factor σe and the coupling factor of the matrix σ versus the area fraction V1

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Fig. 4

Effective material constants for the piezoelectric composite versus the piezoelectric coupling factor σ for V1 = 0.2. (a) Normalized elastic and dielectric permittivity constants. (b) Normalized piezoelectric constants.

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Fig. 5

Effective material constants for the piezoelectric composite versus piezoelectric coupling factor σ for V1 = 0.785. (a) Normalized elastic and dielectric permittivity constants. (b) Normalized piezoelectric constants.

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