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A hybrid element formulation for electromechanical problems
Author(s) -
Kurzhöfer Ingo,
Schröder Jörg
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610206
Subject(s) - ansatz , finite element method , electric field , electric potential , isotropy , transverse isotropy , microscale chemistry , anisotropy , hysteresis , constitutive equation , context (archaeology) , mechanics , physics , materials science , mathematical analysis , classical mechanics , mathematics , voltage , condensed matter physics , geology , thermodynamics , paleontology , mathematics education , quantum mechanics
The difficulty in the modeling of ferroelectric materials is the coverage of the complicated interactions between electrical and mechanical quantities on the macroscale, which are caused by switching processes on the microscale. In the present work we present an electric hybrid element formulation where the stresses and the electric fields are derived by constitutive relations as presented in [1]. Therefore the displacements, the electric potential and the electric displacements are approximated by bilinear ansatz functions. Applying a static condensation procedure we obtain a modified finite element formulation governed by the degrees of freedoms associated to the displacements and the electric potential. The anisotropic material behavior is modeled within a coordinate‐invariant formulation [6] for an assumed transversely isotropic material [4]. In this context a general return algorithm is applied to compute the remanent quantities at the actual timestep. Resulting hysteresis loops for the ferroelectric ceramics are presented. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)