Effective moduli of granular and layered composites with piezoelectric constituents

The effective elastic and dielectric moduli of a composite made from piezoelectric materials are examined, with particular emphasis on applications to unpoled piezoelectric ceramics and layered materials. Explicit formulae for the effective moduli and coupling of a layered material are derived. A self-consistent estimate of the moduli of an isotropic polycrystal is obtained through an effective medium approximation (EMA), which takes into account the interaction between each individual grain and the surrounding composite. This estimate shows that the grains behave as uncoupled grains with electric and elastic constants modified by the behavior of surrounding grains. A similar effect is also observed in bounds (established via classical variational principles) on the moduli of a statistically isotropic polycrystal. Numerical implementation of the EMA and bounds show good agreement with data for unpoled barium titanate ceramic. For a general composite with piezoelectric constituents, it is shown that the effective electromechanical coupling can be bounded by the largest coupling factor of the components.