The isotropic and anisotropic magnetic permeability of Magneto-Rheological Elastomers (MREs) is identified using a simple inverse modelling approach. This involves measuring the magnetic flux density and attractive force occurring between magnets, when MRE specimens are placed in between the magnets. Tests were conducted using isotropic MREs with 10-40% and for anisotropic MREs with 10-30%, particle volume concentration. Magnetic permeabilities were then identified through inverse modelling, by

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... simulating the system using commercially available multi-physics finite element software. As expected, the effective permeability of isotropic MREs was found to be scalar-valued; increasing with increasing particle volume concentration (from about 1.6 at 10% to 3.7 at 30% particle volume concentration). The magnetic permeability of transversely isotropic MRE was itself found to be transversely isotropic, with permeabilities in the direction of particle chain alignment from 1.6 at 10% to 4.45 at 30%, which is up to 1.07-1.25 times higher than in the transverse directions. Results of this investigation are demonstrated to show good agreement with those reported in the literature.