Modeling and Analytical Study for Ferroelectric Materials

Abstract

We discuss rate-independent engineering models for multi-dimensional behavior of ferroelectric materials. These models capture the non-linear and hysteretic behavior of such materials. We show that these models can be formulated in an energetic framework which is based on the elastic and the electric displacements as reversible variables and interior, irreversible variables like the remanent polarization. We provide quite general conditions on the constitutive laws which guarantee the existence of a solution. Under more restrictive assumptions we are also able to establish uniqueness results.

Keywords:

• ferroelectric material model
• existence of solutions
• energetic formulation

ACKNOWLEDGMENTS

The research was partially supported by the European Union via the Research Training Network “Smart Systems” (HPRN-CT-2002-00284).