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An energetic material model for time‐dependent ferroelectric behaviour: existence and uniqueness
Author(s) -
Mielke Alexander,
Timofte Aida M.
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.731
Subject(s) - uniqueness , ferroelectricity , mathematics , constitutive equation , polarization (electrochemistry) , mathematical analysis , statistical physics , thermodynamics , physics , dielectric , chemistry , finite element method , optoelectronics
We discuss rate‐independent engineering models for the multi‐dimensional behaviour of ferroelectric materials. These models capture the non‐linear and hysteretic behaviour 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 on 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. Copyright © 2006 John Wiley & Sons, Ltd.