A nonlinear constitutive theory for ferroelectrics

There have been reported many phenomenological theories on the polarization switching of ferroelectric materials, but the achievements have not yet been widely applied to the field of constitutive behaviors of ferroelectrics. In this paper, we develop a constitutive model that is based on the phenomenological theory similar to the work of Y. Ishibashi et al (1971). The constitutive relations are derived from micromechanics theories, and the evolution of volume fraction of domains are determined by the phenomenological theory. By using these equations, we can predict the nonlinear constitutive behavior of ferroelectric ceramics in an easy way. The numerical calculation agree well with the experiment data.