Multiscale modeling of magnetorheological elastomers: From magneto-mechanical actuators to magneto-electric sensors

by Marc-André Keip

Institute of Applied Mechanics Department of Civil and Environmental Engineering, University of Stuttgart



We discuss some recent results in the field of magento-electro-mechanical coupling of soft solids based on continuum theories and corresponding numerical simulations. The point of departure is the continuum modeling of magnetorheological elastomers (MREs) across several length scales. MREs are soft composite materials that are composed of a soft elastomer matrix and embedded magnetizable inclusions [1]. We investigate the micro-, meso- and macroscopic response of MREs with a particular focus on the evolution of magnetic microstructures in soft elastic surroundings [2], the homogenization of micro-magnetically informed mesostructures [3,4] and on the multiscale analysis of instabilities [5]. The view is then extended towards the application of MREs as soft magneto-electric sensors [6]. Here, we employ computational and semi-analytical techniques to the estimation of possible magneto-electric coupling coefficients of soft MRE bodies. Appropriate numerical examples across different length scales showcase multiscale features of MREs in the field of magneto-electro-elasticity.
The financial funding of the DFG in the framework of the Research Group 1509 (Ferroic Functional Materials; project KE 1849/2-2) and the Cluster of Excellence EXC 2075 (390740016) at the University of Stuttgart is gratefully acknowledged.

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References [1] K. Danas, S. V. Kankanala & N. Triantafyllidis. Experiments and modeling of iron-particlefilled magnetorheological elastomers. J. Mech. Phys. Solids, 60:120-138, 2012. [2] M.-A. Keip & A. Sridhar. A variationally consistent phase-field approach for micro-magnetic domain evolution at finite deformations, J. Mech. Phys. Solids, 125:805-824, 2019. [3] M.-A. Keip and M. Rambausek, Computational and analytical investigations of shape effects in the experimental characterization of magnetorheological elastomers, Int. J. Solids Struct., 121:1-20, 2017. [4] M. Rambausek, F. S. Göküzüm, L. T. K. Nguyen & M.-A. Keip. A two‐scale FE‐FFT approach to nonlinear magneto‐elasticity. Int. J. Numer. Meth. Eng., 117:1117-1142, 2019. [5] E. Polukhov & M.-A. Keip. Multiscale stability analysis of periodic magnetorheological elastomers. Mech. Mater., 103699, 2021. [6] M. Rambausek & M.-A. Keip. Analytical estimation of non-local deformation-mediated magneto-electric coupling in soft composites. Proc. R. Soc. A, 474:20170803, 2018.

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Prof. Dr. Eckhard Quandt

Kiel University
Institute for Materials Science


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Christian-Albrechts-Universität zu Kiel (CAU)

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