A Homogenized Energy Model for Hysteresis in Ferroelectric Materials: General Density Formulation
Abstract
In this paper, we construct a framework for modeling hysteresis and constitutive nonlinearities in ferroelectric compounds based on energy analysis at mesoscopic scales in combination with stochastic homogenization techniques to construct macroscopic models. In the first step of the development, previous analysis is used to construct Helmholtz and Gibbs energy relations at the lattice level. This provides local polarization relations which can be extrapolated to provide constitutive models for certain homogeneous, single crystal compounds. To incorporate material and field nonhomogeneities, as well as the effects of polycrystallinity, certain parameters in the local models are assumed to be manifestations of underlying distributions having densities which must be identified for a given compound. Two techniques for estimating the unknown densities are presented, and the accuracy of the resulting model is illustrated for both symmetric major loops and biased minor loops through fits and predictions with experimental PZT4 and PZT5H data.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2004
- Accession Number
- ADA452029
Entities
People
- Andrew Hatch
- Binu Mukhergee
- Ralph C. Smith
- Shifang Liu
Organizations
- North Carolina State University