An FE\(^2\)-Scheme for Magneto-Electro-Mechanically Coupled Boundary Value Problems

  • Matthias Labusch
  • Jörg Schröder
  • Marc-André Keip
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 581)


The magneto-electric coupling in materials can find several applications in future technologies and could furthermore improve devices, for instance in data storage media. Since all natural single-phase magneto-electric (ME) multiferroics and most of the synthetic single-phase ME materials show a magneto-electric coupling far below room temperature, composite materials are manufactured which consist of a ferroelectric and a magnetostrictive phase. Both phases interact with each other in consequence of transferred deformations, such that these composites produce strain-induced ME properties at room temperature. In order to predict a realistic material behavior, it is necessary to implement appropriate numerical models to reflect the natural behavior of the single phases. This chapter will focus on the numerical implementation of different numerical models for the description of ferroic materials into the two-scale finite element homogenization approach (FE\(^2\)-method) for the simulation of magneto-electro-mechanically coupled boundary value problems. In detail, we investigate the magneto-electric response in consideration of piezoelectric, electrostrictive and ferroelectric models in combination with a piezomagnetic phase. Reliable results for the ME coefficient are obtained by using a ferroelectric model which takes into account the microscopic properties over single tetragonal unit cells, which are allocated in the three dimensional space based on an orientation distribution function. As a result of switching-events of microscopic polarization vectors, we obtain the macroscopic dielectric and butterfly hysteresis curves of the ferroelectric phase. Thereby, the model for the computations of the ME coefficient is physically motivated.


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© CISM International Centre for Mechanical Sciences 2018

Authors and Affiliations

  • Matthias Labusch
    • 1
  • Jörg Schröder
    • 1
  • Marc-André Keip
    • 2
  1. 1.Institute of MechanicsUniversity of Duisburg-EssenEssenGermany
  2. 2.Institute of Applied Mechanics (CE), Chair IUniversity of StuttgartStuttgartGermany

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