Modeling of hysteretic response of porous piezo/ferroelectric ceramics

The hysteretic character of the electromechanic coupling in porous piezoeceramics is a fundamental issue to be investigated in order to design porous materials with enhanced functional responses and increased figure of merit. In the present work, the porosity-dependent evolution of polarization-field P(E) and strain-field s(E) hysteretic responses of porous ferro/piezoceramics are simulated by using the Jiles-Atherton model for switching, combined with Finite Element Analysis in order to determine the local electrical and mechanical responses and the effective dielectric and piezoelectric constants. By considering 2D arrays of porous structures, the local electric field, potential and strain-stress local distributions are firstly evaluated in discrete elements. The macroscopic polarization and deformation responses vs. the applied field are determined by computing the response of each dense region subjected to its corresponding local field. The obtained nonlinear decrease of polarization and deformation vs. porosity are comparatively discussed for square, hexagonal regular pore arrays and for randomly distributed porosity. Further, the effective permittivity and piezoelectric constant d33 and conversion figure of merit vs. porosity computed in different polarization states are estimated and discussed. The present approach may offer a support for the design of porous structures with enhanced piezoelectric response.