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A 3D Magnetostrictive Preisach Model for the Simulation of Magneto-Electric Composites on Multiple Scales

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Multiscale Modeling of Heterogeneous Structures

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 86))

Abstract

In this contribution we derive a three dimensional ferroelectric Preisach model based on an orientation distribution function. Therefore, the classical scalar Preisach model is modified and applied on the individual orientations, which are uniformly distributed in the three dimensional space. This model is used to simulate the behavior of magneto-electric (ME) composites. Such effective multiferroic materials combine two or more ferroic characteristics and can exhibit a coupling between electric polarization and magnetization. Since most of the single-phase ME materials exhibit a weak magneto-electric coupling at low temperatures, two-phase ME composites produce an ME coupling at room temperature. The basic idea for the manufacturing of ME composites is to use the interaction of the ferroelectric and magnetostrictive phases in order to generate strain-induced ME properties. However, in contrast to single-phase multiferroics, the ME coefficient of composites significantly depends on the microscopic morphology and the electro- as well as magneto-mechanical properties of the individual constituents. Therefore, we implemented the 3D Preisach model into the FE\(^2\)-method in order to depict the realistic ferroelectric behavior and directly incorporate the microstructure by the consideration of underlying representative volume elements.

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Acknowledgements

We gratefully acknowledge the financial support of the German Research Foundation (DFG) in the framework of the research unit 1509 “Ferroic Functional Materials—Multiscale Modeling and Experimental Characterization” (SCHR 570/12-2).

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Authors and Affiliations

  1. Faculty of Engineering, Department of Civil Engineering, Institute of Mechanics, University of Duisburg-Essen, Universitätsstraße 15, 45141, Essen, Germany

    J. Schröder & M. Labusch

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  1. J. Schröder
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  2. M. Labusch
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Correspondence to J. Schröder .

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Editors and Affiliations

  1. University of Zagreb, Zagreb, Croatia

    Jurica Sorić

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

  3. LMT Cachan, Cachan, France

    Olivier Allix

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Schröder, J., Labusch, M. (2018). A 3D Magnetostrictive Preisach Model for the Simulation of Magneto-Electric Composites on Multiple Scales. In: Sorić, J., Wriggers, P., Allix, O. (eds) Multiscale Modeling of Heterogeneous Structures. Lecture Notes in Applied and Computational Mechanics, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-65463-8_15

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