Homogenization and thermopiezoelectricity

Gałka, A.; Telega, Józef Joachim; Wojnar, R.

doi:10.1016/0093-6413(92)90050-k

Cited by 54 publications

(21 citation statements)

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“…The fact that the ÿrst three problems do not include k ij and d i is consistent with the derivation by Sigmund et al [4]. The results also agree to the solution obtained by Ga lka et al [18].…”

Section: Homogenization Equationssupporting

confidence: 92%

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: Homogenization Equationssupporting

confidence: 92%

Numerical homogenization of active material finite‐element cells

Buehler

Bettig

Parker

2003

Commun. Numer. Meth. Engng.

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“…However, in general, s 0 depends on both x and y. See [Galka et al 1992] for a complete description in the thermopiezoelectric case. Due to the linearity of this problem and assuming both regularity of the inclusions' shapes and smoothness in the variation of coefficients, we have…”

Section: Introductionmentioning

confidence: 99%

Homogenization and effective properties of periodic thermomagnetoelectroelastic composites

Bravo‐Castillero

Rodrı́guez-Ramos

Mechkour

et al. 2009

JOMMS

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Using asymptotic homogenization, we derive the local problems and the corresponding homogenized coefficients of periodic thermomagnetoelectroelastic heterogeneous media. The theory is applied to obtain analytical expressions for all effective properties of an important class of periodic multilaminated composites. Universal relations involving homogenized thermal coefficients of two-phase laminated and fibrous piezoelectric/piezomagnetic periodic composites, with transversely isotropic constituents, are obtained. Theoretical evidence is shown for the existence of pyroelectric and pyromagnetic effects even if neither phase exhibits them. Numerical calculations and comparisons with others theories are included.

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“…Substituting (18) into the microscopic equation and seeking its solution, we obtain two sets of equations (see Telega 1990, and Galka et al 1992):…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…Periodic materials are composed of a periodic repetition of unit cells. The homogenization theory applied to piezoelectricity was developed by Telega (1990), and Galka et al (1992). The numerical implementation of the theory is discussed and homogenization is compared with differential effective medium theory (DEM).…”

Section: Homogenization In Piezoelectricitymentioning

confidence: 99%

Optimal design of piezoelectric microstructures

Silva

Fonseca

Kikuchi

1997

Computational Mechanics

138

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Application of piezoelectric materials requires an improvement in their performance characteristics which can be obtained by designing new topologies of microstructures (or unit cells) for these materials. The topology of the unit cell (and the properties of its constituents) determines the effective properties of the piezocomposite. By changing the unit cell topology, better performance characteristics can be obtained in the piezocomposite. Based on this idea, we have proposed in this work an optimal design method of piezocomposite microstructures using topology optimization techniques and homogenization theory. The topology optimization method consists of ®nding the distribution of material phase and void phase in a periodic unit cell, that optimizes the performance characteristics, subject to constraints such as property symmetry and stiffness. The optimization procedure is implemented using sequential linear programming. In order to calculate the effective properties of a unit cell with complex topology, a general homogenization method applied to piezoelectricity was implemented using the ®nite element method. This method has no limitations regarding volume fraction or shape of the composite constituents. Although only two-dimensional plane strain topologies of microstructures have been considered to show the implementation of the method, this can be extended to threedimensional topologies. Microstructures obtained show a large improvement in performance characteristics compared to pure piezoelectric material or simple designs of piezocomposite unit cells. IntroductionPiezoelectric materials have the property of converting electrical energy (electric ®eld and applied electrical charge) into mechanical energy (strain and stress) and vice versa. They are widely used in electromechanical sensors and actuators such as robotics sensors, ultrasonic transducers for medical imaging and non destructive evaluation (NDE), underwater acoustics (some hydrophones and naval sonars), and other applications. The main goal in the transducer design in all these applications is to increase the response of the transducer which can be achieved, for example, by increasing the electromechanical energy conversion. The energy conversion depends on many factors, one of the most important being the properties of the piezoelectric material. In this work, we consider ultrasonic imaging and naval sonar applications. In these applications, it is well known that materials such as``1±3 piezocomposite'' (piezoceramic rods embedded in a soft polymer matrix) allow greater sensitivity, in both low and high frequency applications, than pure piezoceramic (see Auld 1991, andSmith 1993). This improvement occurs because the composite material provides effective properties (elastic, piezoelectric, and dielectric) that produce a better performance than pure piezoelectric materials. These effective (homogenized) properties can be determined by considering the topology of the composite microstructure (or unit cell, the smallest structure that is periodic ...

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Homogenization and thermopiezoelectricity

Cited by 54 publications

References 1 publication

Numerical homogenization of active material finite‐element cells

Numerical homogenization of active material finite‐element cells

Homogenization and effective properties of periodic thermomagnetoelectroelastic composites

Optimal design of piezoelectric microstructures

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