Archive of Applied Mechanics

, Volume 89, Issue 1, pp 17–45 | Cite as

Mesoscopic characterization of magnetoelastic hybrid materials: magnetic gels and elastomers, their particle-scale description, and scale-bridging links

  • Andreas M. MenzelEmail author


Magnetic hybrid materials in the form of magnetic gels and elastomers, that is, magnetic or magnetizable colloidal particles embedded in an elastic polymer matrix, are fascinating substances. By addressing and adjusting the magnetic interactions between the particles through external magnetic fields, their overall material properties can be tuned reversibly while in operation. A central goal is to understand how these features can be optimized and which structural properties of the materials determine their overall behavior and its tunability. Mesoscopic theories and modeling are necessary for these purposes, resolving the arrangement of the embedded particles and linking it to the macroscopic scale of the overall material behavior. Here, we overview such recent developments of mesoscopic approaches. Particularly, we address coarse-grained but efficient dipole-spring models, explicit analytical calculations using linear elasticity theory, numerical approaches that allow to characterize nonlinear effects, or density functional theory. In this way, various properties and types of behavior of these materials are revealed, for instance, their reversible tunability of static and dynamic mechanical moduli by magnetic fields, elastic interactions between the embedded particles mediated through the polymeric matrix, or a pronounced and reversibly tunable nonlinear stress–strain behavior. Links from the mesoscopic to the micro- and macroscopic level are outlined. We mention combined efforts of theoretical descriptions, modeling, numerical simulations, and experimental investigations. It becomes evident from our treatment that an integrated approach of theory, simulations, and experiments will significantly increase our further understanding of these materials in the future and will draw possible applications into sight.


Ferrogels Magnetorheological elastomers Mesoscopic modeling Particle–matrix interactions Tunable elastic properties Scale bridging 



The author thanks several colleagues for fruitful collaborations that led to the different studies and effects overviewed above, namely, Hartmut Löwen, Peet Cremer, Giorgio Pessot, Mate Puljiz, Elshad Allahyarov, Sonja Babel, Mitsusuke Tarama, Rudolf Weeber, Christian Holm, Karl Kalina, Markus Kästner, Michael Orlishausen, Werner Köhler, Shilin Huang, Günter K. Auernhammer, Malte Schümann, Thomas Gundermann, Dmitry Borin, and Stefan Odenbach. The present work was supported through the Deutsche Forschungsgemeinschaft (DFG) via the SPP 1681, Grant No. ME 3571/3.

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Authors and Affiliations

  1. 1.Theoretische Physik II: Weiche MaterieHeinrich-Heine-Universität DüsseldorfDüsseldorfGermany

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