A multiscale approach to the computational characterization of magnetorheological elastomers

• Published in: International journal for numerical methods in engineering Vol. 107; no. 4; pp. 338 - 360
• Main Authors: Keip, Marc-Andre, Rambausek, Matthias
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 27.07.2016; Wiley Subscription Services, Inc
• Subjects: Boundary conditions; computational homogenization; Computer simulation; Elastomers; FE2-method; finite deformations; Homogenization; Homogenizing; Inclusions; magnetic boundary conditions; Magnetic fields; magneto-mechanical coupling; magnetorheological elastomers; Microstructure
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.5178

Summary Magnetorheological elastomers are materials with a composite microstructure that consists of an elastomeric matrix and magnetizable inclusions. Because of the magnetic inclusions, magnetorheological elastomers are able to change their properties under magnetic field. Thereby, their effective behavior strongly depends on the microstructure. This calls for homogenization strategies to characterize their macroscopic response. However, for arbitrary macroscopic bodies, this is a non‐trivial task. The main difficulty stems from the fact that a magnetic body interacts with its surrounding and thus perturbs the magnetic field it is subjected to. In a multiscale simulation, this interaction has to be accounted for through a physically sound prescription of magnetic boundary conditions. Thus, the goal of this contribution is to establish a two‐scale homogenization framework that allows for both (i) the incorporation of the microstructure into the macroscopic simulation and (ii) the application of experimentally motivated boundary conditions on arbitrary macroscopic bodies. We show the capabilities of the approach in several numerical studies, in which we analyze the effective behavior of different specimens. Depending on their microstructure, we observe a contraction or extension of the specimens and find magnetically induced stiffening or weakening. All numerical predictions are in good qualitative agreement with experimental measurements. Copyright © 2016 John Wiley & Sons, Ltd.