Boundary Layer Problem in a Piezoelectric Composite

Gambin, Barbara; Gałka, A.

doi:10.1007/978-94-015-8494-4_44

Cited by 2 publications

(2 citation statements)

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“…An application in biomechanics for homogenization of piezoelectric material was presented by Telega et al [9]. Similar methods are derived in a number of publications [10][11][12]. Much of the existing literature treats single, speciÿc microstructures and is limited to certain material combinations.…”

Section: Introductionmentioning

confidence: 95%

Numerical homogenization of active material finite‐element cells

Buehler

Bettig

Parker

2003

Commun. Numer. Meth. Engng.

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SUMMARYWe present the homogenization of a parametrically deÿned periodic microstructure in which it is possible to separately control the volume fractions of conventional material, active material and void. The e ective material properties from the homogenization reduce the necessary ÿnite-element model complexity and also allow for topology optimization of smart structures or optimization of the microstructure itself. Homogenization equations for piezoelectric material including thermal e ects are derived with a ÿrst-order asymptotic approach. The homogenization problem is solved numerically for discrete values of the design parameters. An interpolation technique is used to ÿnd analytical, continuously derivable functions for material properties of the design parameters. Consideration is given to planar microstructures and the treatment of microstructures consisting of dielectrically distinct materials.

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Section: Introductionmentioning

confidence: 95%

Numerical homogenization of active material finite‐element cells

Buehler

Bettig

Parker

2003

Commun. Numer. Meth. Engng.

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“…The theory of homogenization of piezoelectric composites and exact formulae for the layered piezocomposites were described by Galka, Gambin, Telega and Wojnar (see the series of works [1][2][3][4][5][6][7]). Benveniste [8] derived a relation between the effective constants and a phase interchange connection for 2-phase piezoelectric fibrous composites in anti-plane statement.…”

Section: Introductionmentioning

confidence: 99%

Effective anti-plane properties of piezoelectric fibrous composites

Rylko

2013

Acta Mech

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Anti-plane shear of piezoelectric fibrous composites is theoretically investigated. The geometry of composites is described by the 2-dimensional geometry in a section perpendicular to the unidirectional fibers. The previous constructive results obtained for scalar conductivity problems are extended to piezoelectric antiplane problems. First, the piezoelectric problem is written in the form of the vector-matrix R-linear problem in a class of double periodic functions. In particular, application of the zeroth-order solution to the R-linear problem yields a vector-matrix extension of the famous Clausius-Mossotti approximation. The vector-matrix problem is decomposed into two scalar R-linear problems. This reduction allows us to directly apply all the known exact and approximate analytical results for scalar problems to establish high-order formulae for the effective piezoelectric constants. Special attention is paid to non-overlapping disks embedded in a two-dimensional background.

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Boundary Layer Problem in a Piezoelectric Composite

Cited by 2 publications

References 1 publication

Numerical homogenization of active material finite‐element cells

Numerical homogenization of active material finite‐element cells

Effective anti-plane properties of piezoelectric fibrous composites

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