Phenomenological Modeling of Ferroelectric Material Behavior

In this report, a thermodynamically consistent phenomenological model for the simulation of the macroscopic material behavior of polycrystalline ferroelectric ceramies is presented. Microscopically motivated internal state variables are used to describe the texture and polarization state of the polycrystal. The admissible states are defined in terms of the internal state variables. The constitutive relations are split into a linear piezoelectric part and a nonlinear ferroelectric switching law. The linear material behavior is transversely isotropie including deformation induced changes of anisotropy. For nonlinear irreversible processes, a switching function and associated evolution rules are applied, satisfying the principle of maximum ferroelectric dissipation. Saturation is modelied by the use of energy barrier functions in the electric enthalpy density function. The models implementation into a finite element code is presented. Numerical examples dernonstrate the capability of the proposed model, to reproduce the typical experimental results and to predict the behavior in complicated inhomogeneous loading situations.