<title>Nonlinear finite element modeling of phase transitions in electromechanically coupled material</title>

Abstract

A finite element approach has been used to model phase transitions in electro-mechanically coupled material. The approach is applicable to modeling a broad range of material behavior, including repolarizations in ferroelectrics as well as ferroelectric-antiferroelectric phase transitions in electroceramics such as lead lanthanum zirconate stannate titanate. A 3D 8 node element with nodal displacement and voltage degrees of freedom has been formulated using standard isoparametric shape functions. The elements utilize nonlinear constitutive relations for more accurate representation of material response at high electric fields. The phase/polarization state of the material is represented by internal variables in each element, which are updated at each simulation step based on phenomenological model. The model reproduces strain and electric displacement hysteresis loops observed in the material. The approach allows modeling of complex actuator geometries subject to non-uniform electric fields. An a sample application, the response of a piezoelectric wafer with interdigitated electrodes is analyzed. Such a geometry leads to stresses arising from non-uniform poling in the sample which can be computed using the finite element model.