Effective properties of piezoelectric composites with periodic structure

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Piezoelectric composites consisting of spherically anisotropic piezoelectric inclusions ͑i.e., piezoceramic material͒ in an infinite nonpiezoelectric matrix under a uniform electric field are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials are derived exactly. Taking account of the coupling effects of elasticity, permittivity, and piezoelectricity, formulas are derived for the effective dielectric and piezoelectric responses in the dilute limit. A piezoelectric response mechanism is revealed, in which the effective piezoelectric response vanishes irrespective of how much spherically anisotropic piezoelectric inclusions are inside. Moreover, the effective coupled responses of the piezoelectric composites show that the effective dielectric responses decrease ͑increase͒ as the inclusion elastic ͑piezoelectric͒ constants increase.

Section: Introductionmentioning

confidence: 99%

Effective properties of spherically anisotropic piezoelectric composites

Wei

Poon

et al. 2007

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“…[25][26][27][28] Thus, by taking the volumetric average over the unified constitutive Eq. ͑4͒, we have…”

Section: Effective Responses Of Anisotropic Graded Compositesmentioning

confidence: 99%

“…Bergman and Dunn 24 had proposed an integral equation in Fourier space to estimate the bulk effective properties of periodic composites. Along this line, transformation field method ͑TFM͒ was significantly extended by Gu and co-workers [25][26][27][28] to calculate the effective conductivity, photonic dispersion relation, viscosity, and piezoelectric constants of periodic composites having complex inclusion structures including inclusion fractal geometry. 29,30 In addition, the finite-difference time-domain method can be developed to investigate the dielectric behavior of complex composites having inclusion fractal structures.…”

Section: Introductionmentioning

confidence: 99%

Dielectric responses of anisotropic graded granular composites having arbitrary inclusion shapes

Wei

Poon

2008

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The transformation field method ͑TFM͒ originated from Eshelby's transformation field theory is developed to estimate the effective permittivity of an anisotropic graded granular composite having inclusions of arbitrary shape and arbitrary anisotropic grading profile. The complicated boundary-value problem of the anisotropic graded composite is solved by introducing an appropriate transformation field within the whole composite region. As an example, the effective dielectric response for an anisotropic graded composite with inclusions having arbitrary geometrical shape and arbitrary grading profile is formulated. The validity of TFM is tested by comparing our results with the exact solution of an isotropic graded composite having inclusions with a power-law dielectric grading profile and good agreement is achieved in the dilute limit. Furthermore, it is found that the inclusion shape and the parameters of the grading profile can have profound effect on the effective permittivity at high concentrations of the inclusions. It is pointed out that TFM used in this paper can be further extended to investigate the effective elastic, thermal, and electroelastic properties of anisotropic graded granular composite materials.

“…The idea of Nemat-Nasser and co-workers is theoretically rigorous and conceptually straightforward. Consequently, the idea has been subsequently used for a variety of specific problems, such as the elastic properties of solids with periodically distributed cracks 18 and of periodic masonry structures, 19 elastic stiffness and the relaxation moduli of linear viscoelastic periodic composites, 20,21 the overall stress-strain relations of rate-dependent elastic-plastic periodic composites, 22 electrical conductivity, 23 thermal conductivity, 24 dielectric, elastic, and piezoelectric constants of periodic piezoelectric composites, 25 and the dielectric response of isotropic graded composites. 26 However, the original derivations of the transformation field method 9,10 contain one considerably simplifying assumption, which has propagated through the line of works mentioned above ͑e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Analytical homogenization method for periodic composite materials

Chen

Schuh

2009

We present an easy-to-implement technique for determining the effective properties of composite materials with periodic microstructures, as well as the field distributions in them. Our method is based on the transformation tensor of Eshelby and the Fourier treatment of Nemat-Nasser et al. of this tensor, but relies on fewer limiting assumptions as compared to prior approaches in the literature. The final system of linear equations, with the unknowns being the Fourier coefficients for the potential, can be assembled easily without a priori knowledge of the concepts or techniques used in the derivation. The solutions to these equations are exact to a given order, and converge quickly for inclusion volume fractions up to 70%. The method is not only theoretically rigorous but also offers flexibilities for numerical evaluations.