## 2 Materials and Methods  
NR (CV-60, Standard Vietnam Rubber) was used as the rubber matrix. Carbon black (N990, Cancarb, Alberta, Canada) was used as the reinforcement to improve the mechanical properties. Spherical CIPs (CC grade, BASF, Ludwigshafen, Germany) with a mean particle size of 3-5 \(\upmu\)m were used as the soft magnetic particles. Processing oil (N-2, Michang, Busan, Korea), sulphur (MIDAS SP 325, Miwon, Anyang, Korea), thiuram disulphide (ORICELL TT, OCI, Seoul, Korea), and sulphonamide (ORICELL CZ, OCI, Seoul, Korea) were used as the curing agents and accelerators.  
A Banbury mixer (HYB-3L, Hyupyoung Machinery, Kimpo, Korea) was used to prepare the MRE samples. First, 150 parts per hundred rubber (phr) CIPs, 15 phr carbon black, 20 phr processing oil, 1.5 phr sulphur, 1.5 phr thiuram disulphide, and 2.0 phr sulphonamide were compounded with NR at 50 \({}^{\circ}\)C for 15 min. The resulting mixture was moulded into disks with a thickness of 3.0 mm and diameter of 7.0 mm under approximately 10 MPa in a magnetic field with an intensity of 1000 mT at 160 \({}^{\circ}\)C for 400 s. As a result, an anisotropic MRE sample with CIPs aligned out-of-plane along the magnetic field direction in the matrix was obtained.  
Cyclic shear fatigue tests were performed using a modified electromechanical fatigue system (Fatigue tester, Daekyung engineering, Bucheon, Korea) equipped with an electromagnet that can generate a magnetic field under uniaxial shear loading (Figure 1a). The shear direction was perpendicular to the direction of the magnetic field and aligned CIPs. The system was designed to maintain a constant magnetic flux density during fatigue tests. A relatively weak magnetic flux density of 300 mT was applied to confirm the effect of the magnetic field on the MRE and generate a constant magnetic field for up to 500,000 fatigue cycles. Based on the test conditions, such as engine mounts where MRE can be applied, a strain amplitude of 50% and frequency of 5 Hz at an ambient temperature of 23 \({}^{\circ}\)C was set. The maximum load applied to the sample was recorded. The changes in the morphology, specific gravity, and dynamic viscoelastic properties of the anisotropic MRE samples were measured after subjecting them to cyclic shear fatigue. The cross-sectional morphologies of the MREs were observed using a laser confocal microscope (OLS5000, Olympus, Shinjuku, Japan). An analytical balance (MS204 TS, Mettler Toledo, Greifensee, Switzerland) was used to obtain the specific gravity according to ISO 1183-1. The rheological properties of the samples were examined using the modified dynamic mechanical analysis system presented in our previous work [27]. Three types of properties were measured: storage modulus, loss modulus, and loss factor. When an external magnetic field was applied, the direction of the magnetic field was perpendicular to the surface of the tested sample and parallel to the aligned structure of the CIPs within the anisotropic MRE. Thus, the modulus measured under the magnetic field detected the response of the sample in the perpendicular direction. The strain amplitude sweep test was performed by varying the strain from 0.1 to 5.0% with 1 Hz at an ambient temperature of 23 \({}^{\circ}\)C. In the on-statemeasurement, a magnetic flux density of 1200 mT was applied for the sufficient saturated magnetisation of the magnetic particles.