Homogenization in Magnetic-Shape-Memory Polymer Composites

  • Sergio ContiEmail author
  • Martin Lenz
  • Matthäus Pawelczyk
  • Martin Rumpf
Part of the International Series of Numerical Mathematics book series (ISNM, volume 169)


Magnetic-shape-memory materials (e.g. specific NiMnGa alloys) react with a large change of shape to the presence of an external magnetic field. As an alternative for the difficult to manufacture single crystal of these alloys we study composite materials in which small magnetic-shape-memory particles are embedded in a polymer matrix. The macroscopic properties of the composite depend strongly on the geometry of the microstructure and on the characteristics of the particles and the polymer.

We present a variational model based on micromagnetism and elasticity, and derive via homogenization an effective macroscopic model under the assumption that the microstructure is periodic. We then study numerically the resulting cell problem, and discuss the effect of the microstructure on the macroscopic material behavior. Our results may be used to optimize the shape of the particles and the microstructure.


Homogenization Magnetic shape memory Micromagnetism Calculus of variations Shape optimization 

Mathematics Subject Classification (2010).

Primary 74Q05; Secondary 74F15 



This work was partially supported by the Deutsche Forschungsgemeinschaft through Schwerpunktprogramm 1239 Änderung von Mikrostruktur und Form fester Werkstoffe durch äußere Magnetfelder and through Sonderforschungsbereich 1060 Die Mathematik der emergenten Effekte.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sergio Conti
    • 1
    Email author
  • Martin Lenz
    • 2
  • Matthäus Pawelczyk
    • 3
  • Martin Rumpf
    • 2
  1. 1.Institut für Angewandte MathematikUniversität BonnBonnGermany
  2. 2.Institut für Numerische SimulationUniversität BonnBonnGermany
  3. 3.Institut für GeometrieTechnische Universität DresdenDresdenGermany

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