Fully Coupled 3-D Modelling of Ferroelectric Polycrystalline Material Behavior

Abstract

AbstractA thermodynamically consistent phenomenological model for the material behavior of polycrystalline ferroelectric ceramics is presented. The internal state of the material is described by two internal state variables. The first one is a second-order texture tensor, determining a simple orientation distribution function (ODF) for the axes of the crystal unit cells. The second is the vector of relative irreversible polarization. The irreversible strains are derived from the ODF by volume averaging. The polarization saturation states are calculated by summing up the possible contributions of all cells to the overall polarization. An invariant formulation of the piezoelectric law is applied. Analogous to the thermodynamical framework of rate-independent plasticity, driving forces and evolution laws for the internal state variables are established. Saturation and coupling of the switching behavior are governed by energy barrier functions introduced in the electric enthalpy function. Numerical examples illustrate the models capabilities.