WIAS Preprint No. 1014, (2005)

An energetic material model for time-dependent ferroelectric behavior: Existence and uniqueness



Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Timofte, Aida M.

2010 Mathematics Subject Classification

  • 82D45 74G25 74C05

Keywords

  • Ferroelectric material model, existence of solutions, energetic formulation.

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.

Appeared in

  • Math. Methods Appl. Sci., 29 (2006) pp. 1393--1410.

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