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Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials

Schröder, Jörg and Gross, Dietmar (2004):
Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials.
In: Archive of Applied Mechanics (Ingenieur Archiv), pp. 533-552, 73, (8), ISSN 0939-1533,
[Online-Edition: http://dx.doi.org/10.1007/s00419-003-0294-5],
[Article]

Abstract

Theoretical and numerical aspects of the formulation of electromechanically coupled, transversely isotropic solids are discussed within the framework of the invariant theory. The main goal is the representation of the governing constitutive equations for reversible material behaviour based on an anisotropic electromechanical enthalpy function, which automatically fulfills the requirements of material symmetry. The introduction of a preferred direction in the argument list of the enthalpy function allows the construction of isotropic tensor functions, which reflect the inherent geometrical and physical symmetries of the polarized medium. After presenting the general framework, we consider two important model problems within this setting: i) the linear piezoelectric solid; and ii) the nonlinear electrostriction. A parameter identification of the invariant- and the common coordinate-dependent formulation is performed for both cases. The tensor generators for the stresses, electric displacements and the moduli are derived in detail, and some representative numerical examples are presented.

Item Type: Article
Erschienen: 2004
Creators: Schröder, Jörg and Gross, Dietmar
Title: Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials
Language: English
Abstract:

Theoretical and numerical aspects of the formulation of electromechanically coupled, transversely isotropic solids are discussed within the framework of the invariant theory. The main goal is the representation of the governing constitutive equations for reversible material behaviour based on an anisotropic electromechanical enthalpy function, which automatically fulfills the requirements of material symmetry. The introduction of a preferred direction in the argument list of the enthalpy function allows the construction of isotropic tensor functions, which reflect the inherent geometrical and physical symmetries of the polarized medium. After presenting the general framework, we consider two important model problems within this setting: i) the linear piezoelectric solid; and ii) the nonlinear electrostriction. A parameter identification of the invariant- and the common coordinate-dependent formulation is performed for both cases. The tensor generators for the stresses, electric displacements and the moduli are derived in detail, and some representative numerical examples are presented.

Journal or Publication Title: Archive of Applied Mechanics (Ingenieur Archiv)
Volume: 73
Number: 8
Uncontrolled Keywords: Piezoelectricity - Electrostriction - Invariant theory - Transverse isotropy - Nonlinear coupling
Divisions: DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > C - Modelling > Subproject C3: Microscopic investigations into defect agglomeration and its effect on the mobility of domain walls
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > C - Modelling
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue
Zentrale Einrichtungen
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
DFG-Collaborative Research Centres (incl. Transregio)
Date Deposited: 16 Aug 2011 14:49
Official URL: http://dx.doi.org/10.1007/s00419-003-0294-5
Additional Information:

SFB 595 C3

Identification Number: doi:10.1007/s00419-003-0294-5
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