TU Darmstadt ULB TUbiblio

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

## 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 2004 Schröder, Jörg and Gross, Dietmar Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials English 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. Archive of Applied Mechanics (Ingenieur Archiv) 73 8 Piezoelectricity - Electrostriction - Invariant theory - Transverse isotropy - Nonlinear coupling 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 wallsDFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > C - ModellingDFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigueZentrale EinrichtungenDFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research CentresDFG-Collaborative Research Centres (incl. Transregio) 16 Aug 2011 14:49 http://dx.doi.org/10.1007/s00419-003-0294-5 SFB 595 C3 doi:10.1007/s00419-003-0294-5 HTML CitationEP3 XMLASCII CitationEndNoteAtomJSONRDF+XMLMODSDublin CoreReference ManagerMultiline CSVT2T_XMLBibTeXSimple Metadata TUfind oder in Google
 Send an inquiry

Options (only for editors)
 Show editorial Details