Share Email Print
cover

Proceedings Paper

A rate-dependent incremental variational formulation of ferroelectricity
Author(s): Daniele Rosato; Christian Miehe
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

Paper Abstract

The paper presents continuous and discrete variational formulations for the treatment of the non-linear response of piezoceramics under electrical loading. The point of departure is a general internal variable formulation that determines the hysteretic response of the material as a generalized standard medium in terms of an energy storage and a rate-dependent dissipation function. Consistent with this type of standard dissipative continua, we develop an incremental variational formulation of the coupled electromechanical boundary value problem. We specify the variational formulation for a setting based on a smooth rate-dependent dissipation function which governs the hysteretic response. Such a formulation allows us to reproduce the dielectric and butterfly hysteresis responses characteristic of the ferroelectric materials together with their rate-dependency and to account for macroscopically non-uniform distribution of the polarization in the specimen. An important aspect is the numerical implementation of the coupled problem. The discretization of the two-field problem appears, as a consequence of the proposed incremental variational principle, in a symmetric format. The performance of the proposed methods is demonstrated by means of benchmark problems.

Paper Details

Date Published: 2 April 2008
PDF: 11 pages
Proc. SPIE 6929, Behavior and Mechanics of Multifunctional and Composite Materials 2008, 69290E (2 April 2008); doi: 10.1117/12.777476
Show Author Affiliations
Daniele Rosato, Univ. Stuttgart (Germany)
Christian Miehe, Univ. Stuttgart (Germany)


Published in SPIE Proceedings Vol. 6929:
Behavior and Mechanics of Multifunctional and Composite Materials 2008
Marcelo J. Dapino; Zoubeida Ounaies, Editor(s)

© SPIE. Terms of Use
Back to Top