Romanowski, Holger; Schröder, Jörg:

Aspects of the simulation of the ferroelectric hysteresis

In: Proceedings in Applied Mathematics and Mechanics, Jg. 5 (2005) ; 1, Special Issue: GAMM Annual Meeting 2005 – Luxembourg, S. 315-316
ISSN: 1617-7061
Zeitschriftenaufsatz / Fach: Bauwissenschaften
Abstract:
In this paper we present a thermodynamically consistent phenomenological model for an assumed transversely isotropic ferroelectric crystal. Such materials become spontaneously polarized within a certain range of temperature. On the macro scale a remanent polarization and remanent strains, due to the reorientation of the polarization vectors, are observed, if an electric field above the so-called coercive field is applied. The goal of this work is to construct a thermodynamically consistent formulation of the electro-mechanically coupled ceramic on a meso scale, that takes into account the orientation of the assumed transversely isotropic unit cell, see [4]. The anisotropic behavior is governed by isotropic tensor functions, which are formulated in terms of a finite set of invariants, see [3]. Considering a simple model problem we discuss the linearization of discrete weak forms, resulting from the electromechanical boundary value problem.

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