### Abstract

The linear strong-property-fluctuation theory (SPFT) was developed in order to estimate the constitutive parameters of certain homogenized composite materials (HCMs) in a long-wavelength regime. The component materials of the HCM were generally orthorhombic mm2 piezoelectric materials, which were randomly distributed as oriented ellipsoidal particles. At the second-order level of approximation, wherein a two-point correlation function and its associated correlation length characterize the component material distributions, the SPFT estimates of the HCM constitutive parameters were expressed in terms of numerically tractable two-dimensional integrals. Representative numerical calculations revealed that (i) the lowest order SPFT estimates are qualitatively similar to those provided by the corresponding Mori-Tanaka homogenization formalism, but differences between the two estimates become more pronounced as the component particles become more eccentric in shape, and (ii) the second-order SPFT estimate provides a significant correction to the lowest order estimate, which accommodates attenuation due to scattering losses.

Original language | English (US) |
---|---|

Article number | 165402 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 16 |

DOIs | |

State | Published - Jul 27 2009 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(16), [165402]. https://doi.org/10.1088/1751-8113/42/16/165402

}

*Journal of Physics A: Mathematical and Theoretical*, vol. 42, no. 16, 165402. https://doi.org/10.1088/1751-8113/42/16/165402

**The homogenization of orthorhombic piezoelectric composites by the strong-property-fluctuation theory.** / Duncan, Andrew J.; MacKay, Tom G.; Lakhtakia, Akhlesh.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The homogenization of orthorhombic piezoelectric composites by the strong-property-fluctuation theory

AU - Duncan, Andrew J.

AU - MacKay, Tom G.

AU - Lakhtakia, Akhlesh

PY - 2009/7/27

Y1 - 2009/7/27

N2 - The linear strong-property-fluctuation theory (SPFT) was developed in order to estimate the constitutive parameters of certain homogenized composite materials (HCMs) in a long-wavelength regime. The component materials of the HCM were generally orthorhombic mm2 piezoelectric materials, which were randomly distributed as oriented ellipsoidal particles. At the second-order level of approximation, wherein a two-point correlation function and its associated correlation length characterize the component material distributions, the SPFT estimates of the HCM constitutive parameters were expressed in terms of numerically tractable two-dimensional integrals. Representative numerical calculations revealed that (i) the lowest order SPFT estimates are qualitatively similar to those provided by the corresponding Mori-Tanaka homogenization formalism, but differences between the two estimates become more pronounced as the component particles become more eccentric in shape, and (ii) the second-order SPFT estimate provides a significant correction to the lowest order estimate, which accommodates attenuation due to scattering losses.

AB - The linear strong-property-fluctuation theory (SPFT) was developed in order to estimate the constitutive parameters of certain homogenized composite materials (HCMs) in a long-wavelength regime. The component materials of the HCM were generally orthorhombic mm2 piezoelectric materials, which were randomly distributed as oriented ellipsoidal particles. At the second-order level of approximation, wherein a two-point correlation function and its associated correlation length characterize the component material distributions, the SPFT estimates of the HCM constitutive parameters were expressed in terms of numerically tractable two-dimensional integrals. Representative numerical calculations revealed that (i) the lowest order SPFT estimates are qualitatively similar to those provided by the corresponding Mori-Tanaka homogenization formalism, but differences between the two estimates become more pronounced as the component particles become more eccentric in shape, and (ii) the second-order SPFT estimate provides a significant correction to the lowest order estimate, which accommodates attenuation due to scattering losses.

UR - http://www.scopus.com/inward/record.url?scp=67650881927&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650881927&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/16/165402

DO - 10.1088/1751-8113/42/16/165402

M3 - Article

AN - SCOPUS:67650881927

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 16

M1 - 165402

ER -