Electromechanical Response of Piezoelectric Honeycomb Foam Structures

Abstract

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 C 22 and j 22 ) 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 C 12 and C 66 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.

Highly tailorable electromechanical properties of auxetic piezoelectric ceramics with ultra‐low porosity

“…For transverse polarization, exhibits, however, limited sensitivity to . Elastic coefficients are related to different directional Poisson's ratios of structures. Distinguished from the conventional porous piezoelectric composites in Refs 1,2,3,41,44, , , associated with normal stresses in the structures can be negative due to the auxetic effect 45 The elastic coefficients of present auxetic piezoelectric ceramic, especially the "longitudinal" elastic coefficients, are smaller than bulk piezoelectric ceramic.…”

“…In macro‐scaled porous piezoelectric ceramics, the polarization distribution will be more complex than the dense piezoelectric ceramics due to the presence of low permittivity region. To improve the uniformity of polarization, the hole can be filled by the materials with much lower elastic and dielectric coefficients than the piezoelectric ceramics 2 . In small‐scaled porous piezoelectric ceramics, in addition to the porosity effect, the size‐dependent ferroelectricity will also affect the polarization distribution throughout piezoelectric ceramics 37 .…”

“…Achieving the complete polarization in small‐scaled present auxetic piezoelectric ceramics via external electric field may be very difficult. For simplicity, with reference to existing studies, 1,2,3 it is hypothesized that the present auxetic piezoelectric ceramic can be fully polarized regardless of its size.…”

“…The available references show that the piezoelectric sensitivity and acoustic impedance can increase and decrease as porosity increases in piezoelectric ceramics, respectively 1,2,3 . This implies that very large porosity in piezoelectric ceramics needs to be designed in order to achieve desirable piezoelectric sensitivity and low acoustic impedance.…”

Piezoelectric Metamaterial with Negative and Zero Poisson’s Ratios

“…We considered the linearized electromechanical coupled constitutive relations for each ligament material to obtain the homogenization electromechanical properties of the proposed cellular network. These linearized constitutive relations are simple, attractive and, arguably, the most feasible approach for describing the electromechanical response of a cellular network at the macroscale [7], [8], [9], [2]. These assumptions lead to an orthotropic linear electromechanical material model.…”