Universal Relations in Piezoelectric Composites With Eigenstress and Polarization Fields, Part I: Binary Media—Local Fields and Effective Behavior

Benveniste, Y.

doi:10.1115/1.2900788

Cited by 66 publications

(12 citation statements)

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“…For example, Furukawa et al 1 and Wong et al 4,5 gave the simple approximation methods for 0-3 piezoelectric composites by means of the analytical stress field and the effective medium approximation. With the eigenstress, the polarization field method, and the virtual work theorems, Benveniste 6,7 proposed universal relations between effective properties of binary and multiphase piezoelectric composites. Based on the assumption of large dielectric constant of the inclusions, Jayasundere et al 2 obtained an analytical expression for the effective piezoelectric constants of 0-3 composites.…”

Section: Introductionmentioning

confidence: 99%

Effective properties of piezoelectric composites with periodic structure

et al. 2006

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The transformation field theory is developed to investigate the effective properties of piezoelectric composites consisting of anisotropic inclusions having arbitrary geometrical shapes in unit cell. The complicated boundary problem of arbitrary geometrical shapes of anisotropic inclusions is solved by introducing the transformation strain and electric fields. Motivated by theoretical investigation of the effective properties of piezoelectric composites, as an example, the effective dielectric, elastic, and piezoelectric constants of spherical periodic piezoelectric composites are discussed, and a good agreement is obtained by comparing the calculation results with the experimental data in the dilute limit.

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Section: Introductionmentioning

confidence: 99%

Effective properties of piezoelectric composites with periodic structure

et al. 2006

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“…From (10) to (1.2) it is immediately seen that tile determination of the effective thermal expansion and pyroelectric constants requires a knowledge of the jump AU across the cracks in a RAE when (8) or (9) is prescribed. For a microcrack-weakened medium an exact solution of AU is not feasible and approximate methods are usually devised to determine AU and thus the effective properties.…”

Section: Z~ = 2a = { [ L + { T ( I -3 ) ] a U ' N J +Aujn'}dlmentioning

confidence: 99%

“…To obtain the relations between the thermal and electroelastic moduli of a cracked medium, an auxiliary uniform temperature problem is considered in which following boundary conditions are prescribed: (8) or 0 ( x ) : 0% u(~=0;…”

Section: Z~ = 2a = { [ L + { T ( I -3 ) ] a U ' N J +Aujn'}dlmentioning

confidence: 99%

“…After that, Dunn [7] evaluated the effective properties of two phase composites using dilute, self-consistent, Mori-Tanaka and differential micromechanical models. Benveniste [8] and Dunn [9] showed that the effective thermal-stress constants and p)qoelectric coefficients are related to the corresponding isothermal electroelastic moduli in two-phase media. Chen[10] further obtained some simple algebraic formulae tbr the prediction of overall thermoelectroelastic moduli of multiphase fibrous composites with the self-consistent and Mori-Tanaka methods.…”

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confidence: 99%

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Using GSC theory for effective thermal expansion and pyroelectric coefficients of cracked piezoelectric solids

Qin

1996

Int J Fract

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Many brittle materials, such as concrete, piezoelectricity, have a large number of preexisting microcracks, The determination of their effective material properties has been the focus of considerable research. Current research into the development of effective material properties has mostly concentrated on the Taylor's method[l], the self-consistent method[2], the differential theory[3], the Mori-Tanaka method[4] and generalized selfconsistent(GSC) method [5]. For the themmelectroelastic problems, the first theoretical study appears to be that of Nemflmm and co-workers which is applicable to two phase thermopiezoelectric laminates that are connected in series or parallel [6]. After that, Dunn [7] evaluated the effective properties of two phase composites using dilute, self-consistent, Mori-Tanaka and differential micromechanical models. Benveniste [8] and Dunn [9] showed that the effective thermal-stress constants and p)qoelectric coefficients are related to the corresponding isothermal electroelastic moduli in two-phase media. Chen[10] further obtained some simple algebraic formulae tbr the prediction of overall thermoelectroelastic moduli of multiphase fibrous composites with the self-consistent and Mori-Tanaka methods. He indicated that when the phases have equal transverse shear rigidities, the overall moduli estimated by both methods are identical with exact solutions given by Chen[1 IJ for composites with arbitrary transverse geometry. More recently, Yu and his colleagues [12][13][14] obtained some new results of cracked thermopiezoelectric materials, additional references to work in this area can be found therein.This paper constitutes a continuation of analysis completed by the authors of those paper[12-14] on cracked thermopiezoelectric materials. In contrast to our previous studies, the present work focus on developing a GSC them T for efli:ctive thermal expansion and p3aoelectric coefficients of piezoelectric medium containing microcracks with given length and same orientation, The derivation is based on the extended Stroh formalism and a recently developed explicit solution of thermal-, electric-and elastic fields for a cracked in an infinite piezoelectric solid. In the analysis, a representative area element is adopted, which contains a microcrack surrounded by an elliptic matrix in a solid x~dth effective properties. Numerical results are given tbr a piezoelectric ceramic BatiO3.BASIC FORMULA TIONS Let us consider a two-dimensional thermopiezoelectric solid, where the material is transversely isotropic and coupling between h>plane stresses and inplane electric fields takes place. Choosing the xs-axis as the poling direction, the plane strain constitute equations are expressed by:

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“…For that reason an everincreasing number of publications are devoted to the question of prediction of characteristics for these materials [1][2][3][4][5][6][7][8][9][10][11][12][13]. A particular interest is attracted by the pyro-and piezoelectric phenomena which underlie quite a few practical applications.…”

Section: Introductionmentioning

confidence: 98%

Some specificities of the pyro- and piezoelectric phenomena in heterogeneous ferroelectric materials

Aleshin

Luchaninov

2008

J Electroceram

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A system of equations has been constructed in order to find effective pyroelectric, dielectric, piezoelectric, elastic and thermoelastic constants of heterogeneous materials using the method of self-consistency. By means of these equations the characteristics are simulated of the electrically depoled piezoceramics and of composites with antiparallel polarization of the components. Such a composite, being a mixture of BaTiO 3 and PZT-19 ceramic particles, manifests at a certain concentration of PZT-19 high pyroelectric properties but does not practically possess the piezoeffect. But at another concentration it is a strong piezoelectric without any pyroeffect.

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Universal Relations in Piezoelectric Composites With Eigenstress and Polarization Fields, Part I: Binary Media—Local Fields and Effective Behavior

Cited by 66 publications

References 0 publications

Effective properties of piezoelectric composites with periodic structure

Effective properties of piezoelectric composites with periodic structure

Using GSC theory for effective thermal expansion and pyroelectric coefficients of cracked piezoelectric solids

Some specificities of the pyro- and piezoelectric phenomena in heterogeneous ferroelectric materials

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