Different approaches to finite element modeling of effective moduli of porous piezoceramics with 3-3 (3-0) connectivity

Abstract

Theoretical aspects of the effective moduli method for an inhomogeneous piezoelectric media were examined. Four static piezoelectric problems for a representative volume that allow finding the effective moduli of an inhomogeneous body were specified. These problems differ by the boundary condi- tions which were set on a representative volume surfaces: a) mechanical displacements and electric potential, b) mechanical displacements and normal component of electric flux density vector, c) mechanical stress vector and electric potential, and d) mechanical stress vector and normal component of electric flux density vector. Respective equations for calculation of effective moduli of piezoelectric media with arbitrary anisotropy were derived. Based on these equations and using finite element method (FEM) the full set of effective moduli for PZT porous ceramics having wide porosity range was calculated. Different models of representative volume were considered: piezoelectric cubes with one cubic and one spherical pore inside, cubic volume evenly divided on partial cubic volumes a part of which randomly de- clared as pores etc. For the modeling of the porous piezoceramics with 3-3 connectivity the representative volume having skeleton structure was considered. For accounting of inhomogeneous or incomplete ceramics polarization the preliminary modeling of polarization process was performed. To determine the areas having different polarization FEM calculations of the electrostatic problem were executed. The results of FEM modeling were compared with the theoret- ical results obtained on the basis of Marutakes effective medium approximation, Bruggemans formulas and unit-cell models, as well as with the experimental results received using Piezoelec- tric Resonance Analysis Program (PRAP) for different porous ceramics in the relative porosity range of 0-70