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14 June 2000 Effective properties of piezoelectric polycrystals
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Effective elastic, dielectric, and piezoelectric properties of piezoceramics are calculated with the finite element method using a representative volume element. A polycrystal is considered which consists of single-domain crystals defined by a 2D random Voronoi tessellation. The random orientations of the domains in the unpoled state are described by an isotropic orientation distribution. To model poled stats, simple switching criteria are applied, so that e.g. the polarization direction of the individual grains fall within a cone of a specific angle about the poling direction. Homogeneous boundary conditions are imposed and the volume averages of the local mechanical and electrical fields are calculated. The effective material properties can then be calculated as a function of the single crystal moduli and the poling degree. The main advantages of this procedure are the more realistic random geometry and the fact that interactions among the grains are taken into account. Interest is focused on basic questions such as the influence of the boundary conditions, the necessary size of the representative volume element, and the variation of the effective moduli due to the stochastic model, in particular due to the orientation distribution. The numerical results are compared to those of analytical models.
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Andreas Froehlich, Angelika Brueckner-Foit, and Stephan Weyer "Effective properties of piezoelectric polycrystals", Proc. SPIE 3992, Smart Structures and Materials 2000: Active Materials: Behavior and Mechanics, (14 June 2000);

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