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Finite Element Modeling of the Ferroelectroelastic Material Behavior in Consideration of Domain Wall Motions

Published online by Cambridge University Press:  01 February 2011

Albrecht C. Liskowsky ,
Artem S. Semenov ,
Herbert Balke  and
Robert M. McMeeking
Albrecht C. Liskowsky
Affiliation:
Institute for Solid Mechanics (IFKM) Technical University Dresden, 01069 Dresden, Germany
Artem S. Semenov
Affiliation:
Institute for Solid Mechanics (IFKM) Technical University Dresden, 01069 Dresden, Germany
Herbert Balke
Affiliation:
Institute for Solid Mechanics (IFKM) Technical University Dresden, 01069 Dresden, Germany
Robert M. McMeeking
Affiliation:
Department of Mechanical and Environmental Engineering and Materials DepartmentUniversity of California, Santa Barbara, CA 93106, U.S.A.
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Abstract

A simulation of the nonlinear electromechanical macroscopic behavior of ferroelectric materials by means of the finite element method is presented. A material point is depicted by a representative volume element, for which homogeneous boundary conditions are valid. The evolution of integral averages over the representative volume element is to homogenize the results. For this homogenization we favor a finite element model in which each Gauss point represents exactly one single crystal. Their number of internal variables is limited to the lattice orientation and the volume fractions of the domains. The former are randomly distributed in space. It is possible to calculate the material behavior for arbitrary coupled and nonlinear electromechanical loading cases, but the model is not effective for the solution of boundary value problems for entire bodies.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 881: Symposium CC – Coupled Nonlinear Phenomena Modeling and Simulation for Smart, Ferroic and Multiferroic Materials , 2005 , CC4.2
Copyright
Copyright © Materials Research Society 2005

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References

[1] Allik, H., Hughes, T.J.R.. Finite Element Method for Piezoelectric Vibration. International Journal for Numerical Methods in Engineering, 2:151–157, 1970.Google Scholar
[2] Huber, J.E., Fleck, N.A., Landis, C.M., McMeeking, R.M.. A Constitutive Model for Ferroelectric Polycrystals. Journal of the Mechanics and Physics of Solids, 47(8):1663–1697, 1999.Google Scholar
[3] Hwang, S.C., Lynch, C.S., McMeeking, R.M.. Ferroelectric/ Ferroelastic Interactions and a Polarization Switching Model. Acta Metallurgica et Materialia, 43(5):2073–2084, 1995.Google Scholar
[4] Hwang, S.C., McMeeking, R.M.. On the Potential Energy of a Piezoelectric Inclusion and the Criterion for Ferroelectric Switching. Ferroelectrics, 200:151–173, 1997.Google Scholar
[5] Kamlah, M., Liskowsky, A.C., McMeeking, R.M., Balke, H.. Finite Element Simulation of a Polycrystalline Ferroelectric Based on a Multidomain Single Crystal Switching Model. International Journal of Solids and Structures, 42(9–10):2949–2964, 2005.Google Scholar
[6] Keβler, H., Balke, H.. On the Local and Average Energy Release in Polarization Switching Phenomena. Journal of the Mechanics and Physics of Solids, 49(5):953–978, 2001.Google Scholar
[7] Landis, C.M.. A New Finite Element Formulation for Electromechanical Boundary Value Problems. International Journal for Numerical Methods in Engineering, 55:613–628, 2002.Google Scholar
[8] Landis, C.M.. Fully Coupled, Multi-Axial, Symmetric Constitutive Laws for Polycrystalline Ferroelectric Ceramics. Journal of the Mechanics and Physics of Solids, 50(1):127–152, 2002.Google Scholar
[9] Landis, C.M.. Symmetric Constitutive Laws for Polycrystalline Ferroelectric Ceramics. In: Lynch, C.S. (Ed.). Active Materials: Behavior and Mechanics, Proceedings of the SPIE, vol. 4333, 2001.Google Scholar
[10] Landis, C.M., McMeeking, R.M.. A Self Consistent Model for Switching in Polycrystalline Ferroelectrics: Electrical Polarization Only. In: Varadan, V.V. (Ed.). Mathematics and Control in Smart Structures, Proceedings of the SPIE, vol. 3667, 1999.Google Scholar