Archive of Applied Mechanics

, Volume 89, Issue 1, pp 47–62 | Cite as

Two- and three-dimensional modeling approaches in magneto-mechanics: a quantitative comparison

  • P. Metsch
  • K. A. Kalina
  • J. Brummund
  • M. KästnerEmail author


In this contribution, we present a qualitative and quantitative comparison of two- and three-dimensional finite-element simulations for magneto-rheological elastomers. Based on a general continuum formulation of the coupled magneto-mechanical boundary value problem, a microscopic modeling approach is applied. The merit of this strategy is a full resolution of the local magnetic and mechanical fields within the heterogeneous microstructure of magneto-rheological elastomers—it allows to account for systems with high particle-volume fractions and small inter-particle distances. In order to understand basic deformation mechanisms as well as local magneto-mechanical interactions of the spherical inclusions, the differences between simplified two-dimensional and realistic three-dimensional simulations are initially shown for the example of chain-like structures with varying arrangements of the particles. Afterwards, an appropriate scale transition scheme is used to connect the microscopic and macroscopic quantities: Different two- and three-dimensional, ideal and random microstructures are analyzed with regard to their effective magneto-mechanical behavior.


Magneto-rheological elastomers Magneto-mechanical coupling Nonlinear finite-element method 



The present study is funded by the German Research Foundation, Priority Programmes (SPP) 1681 and 1713: Grants KA 3309/2-3 and KA 3309/5-2. This support is gratefully acknowledged. The computations were performed on a PC-Cluster at the Center for Information Services and High Performance Computing (ZIH) at TU Dresden. The authors thank the ZIH for generous allocations of computer time.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • P. Metsch
    • 1
  • K. A. Kalina
    • 1
  • J. Brummund
    • 1
  • M. Kästner
    • 1
    Email author
  1. 1.Institute of Solid MechanicsTechnische Universität DresdenDresdenGermany

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