Effective moduli of granular and layered composites with piezoelectric constituents

Tamara Olson, Marco Avellaneda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The effective elastic and dielectric moduli of a composite made from piezoelectric materials are examined, with particular emphasis on applications to unpoled piezoelectric ceramics and layered materials. Explicit formulae for the effective moduli and coupling of a layered material are derived. A self-consistent estimate of the moduli of an isotropic polycrystal is obtained through an effective medium approximation (EMA), which takes into account the interaction between each individual grain and the surrounding composite. This estimate shows that the grains behave as uncoupled grains with electric and elastic constants modified by the behavior of surrounding grains. A similar effect is also observed in bounds (established via classical variational principles) on the moduli of a statistically isotropic polycrystal. Numerical implementation of the EMA and bounds show good agreement with data for unpoled barium titanate ceramic. For a general composite with piezoelectric constituents, it is shown that the effective electromechanical coupling can be bounded by the largest coupling factor of the components.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
PublisherPubl by Society of Photo-Optical Instrumentation Engineers
Pages214-223
Number of pages10
Volume1919
ISBN (Print)0819411523
StatePublished - 1993
EventSmart Structures and Materials 1993: Mathematics in Smart Structures - Albuquerque, NM, USA
Duration: Feb 1 1993Feb 3 1993

Other

OtherSmart Structures and Materials 1993: Mathematics in Smart Structures
CityAlbuquerque, NM, USA
Period2/1/932/3/93

Fingerprint

composite materials
Polycrystals
Composite materials
polycrystals
Barium titanate
Electromechanical coupling
Piezoelectric ceramics
Piezoelectric materials
piezoelectric ceramics
Elastic constants
estimates
variational principles
approximation
barium
modulus of elasticity
elastic properties
ceramics
interactions

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Olson, T., & Avellaneda, M. (1993). Effective moduli of granular and layered composites with piezoelectric constituents. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 1919, pp. 214-223). Publ by Society of Photo-Optical Instrumentation Engineers.

Effective moduli of granular and layered composites with piezoelectric constituents. / Olson, Tamara; Avellaneda, Marco.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 1919 Publ by Society of Photo-Optical Instrumentation Engineers, 1993. p. 214-223.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Olson, T & Avellaneda, M 1993, Effective moduli of granular and layered composites with piezoelectric constituents. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 1919, Publ by Society of Photo-Optical Instrumentation Engineers, pp. 214-223, Smart Structures and Materials 1993: Mathematics in Smart Structures, Albuquerque, NM, USA, 2/1/93.
Olson T, Avellaneda M. Effective moduli of granular and layered composites with piezoelectric constituents. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 1919. Publ by Society of Photo-Optical Instrumentation Engineers. 1993. p. 214-223
Olson, Tamara ; Avellaneda, Marco. / Effective moduli of granular and layered composites with piezoelectric constituents. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 1919 Publ by Society of Photo-Optical Instrumentation Engineers, 1993. pp. 214-223
@inproceedings{30cb4596cfb64ace932eca95ddc4da1b,
title = "Effective moduli of granular and layered composites with piezoelectric constituents",
abstract = "The effective elastic and dielectric moduli of a composite made from piezoelectric materials are examined, with particular emphasis on applications to unpoled piezoelectric ceramics and layered materials. Explicit formulae for the effective moduli and coupling of a layered material are derived. A self-consistent estimate of the moduli of an isotropic polycrystal is obtained through an effective medium approximation (EMA), which takes into account the interaction between each individual grain and the surrounding composite. This estimate shows that the grains behave as uncoupled grains with electric and elastic constants modified by the behavior of surrounding grains. A similar effect is also observed in bounds (established via classical variational principles) on the moduli of a statistically isotropic polycrystal. Numerical implementation of the EMA and bounds show good agreement with data for unpoled barium titanate ceramic. For a general composite with piezoelectric constituents, it is shown that the effective electromechanical coupling can be bounded by the largest coupling factor of the components.",
author = "Tamara Olson and Marco Avellaneda",
year = "1993",
language = "English (US)",
isbn = "0819411523",
volume = "1919",
pages = "214--223",
booktitle = "Proceedings of SPIE - The International Society for Optical Engineering",
publisher = "Publ by Society of Photo-Optical Instrumentation Engineers",

}

TY - GEN

T1 - Effective moduli of granular and layered composites with piezoelectric constituents

AU - Olson, Tamara

AU - Avellaneda, Marco

PY - 1993

Y1 - 1993

N2 - The effective elastic and dielectric moduli of a composite made from piezoelectric materials are examined, with particular emphasis on applications to unpoled piezoelectric ceramics and layered materials. Explicit formulae for the effective moduli and coupling of a layered material are derived. A self-consistent estimate of the moduli of an isotropic polycrystal is obtained through an effective medium approximation (EMA), which takes into account the interaction between each individual grain and the surrounding composite. This estimate shows that the grains behave as uncoupled grains with electric and elastic constants modified by the behavior of surrounding grains. A similar effect is also observed in bounds (established via classical variational principles) on the moduli of a statistically isotropic polycrystal. Numerical implementation of the EMA and bounds show good agreement with data for unpoled barium titanate ceramic. For a general composite with piezoelectric constituents, it is shown that the effective electromechanical coupling can be bounded by the largest coupling factor of the components.

AB - The effective elastic and dielectric moduli of a composite made from piezoelectric materials are examined, with particular emphasis on applications to unpoled piezoelectric ceramics and layered materials. Explicit formulae for the effective moduli and coupling of a layered material are derived. A self-consistent estimate of the moduli of an isotropic polycrystal is obtained through an effective medium approximation (EMA), which takes into account the interaction between each individual grain and the surrounding composite. This estimate shows that the grains behave as uncoupled grains with electric and elastic constants modified by the behavior of surrounding grains. A similar effect is also observed in bounds (established via classical variational principles) on the moduli of a statistically isotropic polycrystal. Numerical implementation of the EMA and bounds show good agreement with data for unpoled barium titanate ceramic. For a general composite with piezoelectric constituents, it is shown that the effective electromechanical coupling can be bounded by the largest coupling factor of the components.

UR - http://www.scopus.com/inward/record.url?scp=0027245364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027245364&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027245364

SN - 0819411523

VL - 1919

SP - 214

EP - 223

BT - Proceedings of SPIE - The International Society for Optical Engineering

PB - Publ by Society of Photo-Optical Instrumentation Engineers

ER -