Ferroelectric ceramics and composites: statistical models for effective piezoelectric and pyroelectric properties

We are concerned with the calculation of macroscopic linear thermo-electro-elastic properties for polycrystalline and composite materials. Due to the complexity of the coupled electro-mechanical field equations in 3D, in most cases exact solutions are impossible. Therefore we apply the well-known Effective field and Effective medium approximation. This can now be done since recently explicit results for the fully coupled Eshelby tensors became available. We present shortly the basics of the theory and illustrate it by numerical evaluations. The resulting effective material constants of piezoelectric ceramics depend non-monotonously on the degree of poling, and the properties of composites may strongly differ from predictions on the basis of simple rule of mixtures