Finite Element Analysis with a Ferroelectric and Ferroelastic Material Model

Domain wall motion and phase transformations are driven by stress and electric field, are rate and temperature dependent, and can occur at relatively low stress and electric field levels due to field concentrators such as pores and electrode edges. Analysis of this behavior requires multiaxial material models with hysteresis in a finite element code. This work describes the current state of research in the area of constitutive modeling and finite element analysis of ferroelectric materials. It begins with a description of the large field experimental characterization of ferroelectric behavior including observed effects of field induced phase transformations. Constitutive modeling using a phenomenological approach (macroscale) is discussed followed by the micromechanical approach (microscale). These constitutive models connect the variables of stress, strain, electric field, electric displacement, temperature, and entropy. In addition to these relations, mechanics problems require satisfying electro-mechanical equilibrium and compatibility conditions. The final section presents results of finite element analysis using a ferroelectric material model.