The effective dielectric constant, bulk modulus, and shear modulus of isotropic polycrystals with piezoelectric grains are studied using an effective medium approximation (EMA) and generalized Hashin–Shtrikman bounds. The EMA determines self-consistently the electromechanical interaction of grains with the surrounding composite. Numerical values for the moduli are computed for barium titanate and compared with available experimental data, as well as with classical estimates for the moduli. Further assessment of the EMA is made by computing numerical values of the effective moduli for ideal polycrystals, based on numerical data for crystals with strong piezoelectric coupling and comparing the resulting values with classical estimates. Similar comparisons are made for the generalized Hashin–Shtrikman bounds. On ‘‘ideal’’ polycrystals the gap between the upper and lower bounds can be 30% narrower than the corresponding gap if piezoelectric coupling is neglected.
Two examples of piezoelectricity in composite materials are studied. The first con sists of a laminate of a homogeneous piezoelectric reinforced with a non-piezoelectric material, e.g., a metal. The effective piezoelectric response tensor is computed, as well as the effective elec tromechanical coupling factors, which measure the efficiency in converting electricity into mechanical work and vice versa. The second example consists of an isotropic polycrystalline material. Here, we study the influence of the piezoelectric coupling at the grain level on the effective permittivities via an effective medium approximation. The results are compared with experimental data and with predictions of other effective medium theories. We also give a theorem which provides an absolute upper bound on the effective electromechanical coupling factor for arbitrary piezoelec tric composites.
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