Homogenization of periodic 1-3 piezocomposite using wave propagation: Toward an experimental method
Résumé
1-3 piezocomposites are first choice materials for integration in ultrasonic transducers due to their high electromechanical performance, particularly, in their thickness mode. The determination of a complete set of effective electroelastic parameters through a homogenization scheme is of primary importance for their consideration as homogeneous. This allows for the simplification of the transducer design using numerical methods. The method proposed is based on acoustic wave propagation through an infinite piezocomposite, which is considered to be homogeneous material. Christoffel tensor components for the 2 mm symmetry were expressed to deduce slowness curves in several planes. Simultaneously, slowness curves of a numerical phantom were obtained using a finite element method (FEM). Dispersive curves were initially calculated in the corresponding heterogeneous structure. The subsequent identification of the effective parameters was based on a fitting process between the two sets of slowness curves. Then, homogenized coefficients were compared with reference results from a numerical method based on a fast Fourier transform for heterogeneous periodic piezoelectric materials in the quasi-static regime. A relative error of less than 2% for a very large majority of effective coefficients was obtained. As the aim of this paper is to implement an experimental procedure based on the proposed homogenization scheme to determine the effective parameters of the material in operating conditions, it is shown that simplifications to the procedure can be performed and a careful selection of only seven slowness directions is sufficient to obtain the complete database for a piezocomposite containing square-shaped fibers. Finally, further considerations to adapt the present work to a 1-3 piezocomposite with a fixed thickness are also presented.
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