Electromechanical response of piezoelectric honeycomb foam structures

A finite element model is developed to characterize the complete electromechanical properties of the most general form of elastically anisotropic and piezoelectrically active foams with honeycomb structures. Four classes of piezoelectric honeycomb structures are identified depending on the relative orientation of the poling direction with the porosity direction (longitudinal and transverse) and the geometry of the honeycombs (isotropic and anisotropic). It is observed that: (i) Most of the elastic, dielectric, and piezoelectric constants of the longitudinally porous honeycomb foams exhibit linear dependence on the volume fraction (or relative density) of the material; (ii) The electromechanical properties of transversely porous foam structures (with the exception of C₂₂ and κ₂₂) exhibit significant dependence on the shape of the porosity; (iii) The piezoelectric figures of merit of the longitudinally porous foams do not exhibit significant dependence on the shape of the porosity; (iv) The piezoelectric figures of merit of the transversely porous foams exhibit a strong dependence on the shape of the porosity with the hexagonal foams exhibiting enhanced hydrostatic strain coefficient and lower acoustic impedance while the square foams exhibiting enhanced piezoelectric coupling constant and hydrostatic figure of merit; (v) In transversely porous anisotropic honeycomb structures, the shear elastic constants such as C₁₂ and C₆₆ and some figures of merit are enhanced significantly when compared to their isotropic counterparts. For example, in the PZT-7A transversely porous anisotropic honeycomb structures with 10% relative density, the hydrostatic figure of merit is expected to be 2485% greater than that predicted for the transversely porous isotropic honeycomb structures.