A hybrid finite element model for phase transitions in nonlinear electro-mechanically coupled material

A finite element approach for modeling phase transitions in electro-mechanically coupled material is presented. The approach is applicable to modeling a broad range of material behavior, including repolarizations in ferroelectrics (PZTs) as well as ferroelectric-antiferroelectric phase transitions in electroceramics such as lead lanthanum zirconate stannate titanate (PLZST). A three-dimensional 4 node hybrid element has been formulated. In addition to nodal displacement and voltage degrees of freedom used in conventional coupled elements, the hybrid element also utilizes internal electric displacement degrees of freedom, resulting in improved numerical efficiency. The elements utilize energy based nonlinear constitutive relations for more accurate representation of material response at high electric fields. The phase/polarization state of each element is represented by internal variables, which are updated at each simulation step based on a phenomenological model. The material model has been roughly fitted to response of PZT-5H under free strain conditions. The model reproduces strain and electric displacement hysteresis loops observed in the material. The hybrid finite element model results are demonstrated for a complex geometry with non-uniform fields.