Archive of Applied Mechanics

, Volume 84, Issue 9–11, pp 1307–1323 | Cite as

A multiscale model for magneto-elastic behaviour including hysteresis effects

  • Laurent DanielEmail author
  • Mahmoud Rekik
  • Olivier Hubert
Open Access
Special Issue


Magnetic and mechanical behaviour are strongly coupled: an applied stress modifies the magnetic behaviour, and on the other hand, magnetic materials undergo a magnetisation-induced strain known as the magnetostriction strain. These coupling effects play a significant role on the overall performance of electromagnetic devices such as magnetostrictive transducers or high-performance electric machines. In order to provide engineers with accurate design tools, magneto-elastic effects must be included into constitutive laws for magnetic materials. The origin of the magneto-elastic coupling lies in the competitive contributions of stress and magnetic field to the definition of magnetic domain configurations in magnetic materials. The magnetic domain scale is then suitable to describe magneto-elastic interactions, and this is the reason why multiscale approaches based on a micro-mechanical description of magnetic domain structures have been developed in the last decades. We propose in this paper an extension of a previous anhysteretic multiscale model in order to consider hysteresis effects. This new irreversible model is fully multiaxial and allows the description of typical hysteresis and butterfly loops and the calculation of magnetic losses as a function of external magneto-mechanical loadings. It is notably shown that the use of a configuration demagnetising effect related to the initial domain configuration enables to capture the non-monotony of the effect of stress on the magnetic susceptibility. This configuration demagnetising effect is also relevant to describe the effects of stress on hysteresis losses and coercive field.


Magneto-mechanical couplings Magnetostriction Constitutive laws Micro-mechanical modelling Hysteresis loops 


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© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • Laurent Daniel
    • 1
    • 2
    Email author
  • Mahmoud Rekik
    • 2
    • 3
  • Olivier Hubert
    • 3
  1. 1.School of MaterialsUniversity of ManchesterManchesterUK
  2. 2.Laboratoire de Génie Electrique de Paris (LGEP), CNRS(UMR8507)/SUPELEC/UPMC/Univ Paris-SudGif-sur-YvetteFrance
  3. 3.LMT-Cachan, ENS Cachan/CNRS(UMR8535)/UPMC/PRES Universud ParisCachanFrance

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