## 1 Introduction
When a magnetic field is applied, the rheological properties of these materials can be rapidly and reversibly changed [30]. These have quick responsiveness to the magnetic field, rapid reversibility, and controllable performance which make these an excellent choice for use in applications in which controlled energy dissipation is needed, e.g., brakes and clutches for exercise equipment [31] and controllable dampers for vehicle suspensions [32]. A controllable fluid damper developed with MRFs is a popular device with semi-active control. These dampers have attracted considerable attention and interest from researchers. The greatest strength of MRF dampers is their assembly with a considerably simple and thus reliable design. It does not contain any moving parts other than the piston [21]. It can be noted that all the \"smart\" base isolation strategies achieve a certain level of \"smartness\" by making use of additional variable damping through active or semi-active dampers to conventional base isolation, often known as hybrid base isolation. This supplementary damping has been studied by [PERSON] [33] in more detail who concluded with adequate satisfaction that the use of supplementary dampers in base isolation is a misplaced effort and is a source of undesirable problems. The damping primarily controls vibration responses under the circumstances of steady-state resonance and a free vibration stage [34]. Nevertheless, while operating under the impact load, which is particularly featured in near-fault earthquakes, the availability of ample time becomes a bottleneck for damping to dissipate vibrational energy. Additionally, although the supplementary damping may forcefully confine the base displacement of the passive base isolation system [35], the high-frequency accelerations as well as an increase in inter-storey drifts may be introduced to the superstructure by augmenting damping [36]. Further, the MRF-based dampers have their inherent disadvantages such as long-term particle deposition and environmental contamination, etc. [37]. In order to achieve an ideal performance of base isolation while avoiding the issues associated with additional dampers, the seismic isolator itself should be adaptable. To achieve this, magnetorheological elastomers (MREs) have been studied by researchers for use in base isolators [38; 39; 40]. MREs are controllable composites that are mainly composed of magnetic fillers (commonly iron particles) and elastomers as the dispersion matrix [41]. The efficiency of MREs has been thoroughly studied by varying different material parameters, such as matrix material [42; 43; 44], size [45; 46; 47; 39], percentage content [48; 49; 50; 42], type and shape of filler material, and operation mode of the MRE material [45; 39]. Unlike MRFs, MREs exhibit stable magnetorheological performance because the particles do not undergo sedimentation with time,. Moreover, the thermal stability of MREs is also superior as compared to MRFs. Other advantages of MREs are quick response time (less than milliseconds [51]) and having magnetic field-dependent yield stress. Due to the magnetic field-dependent properties of MREs, they have various applications in different fields of engineering [41]. In civil engineering structures, MREs have been used primarily in the development of adaptive seismic isolators [52; 39]. Studies have been conducted to investigate the suitability of MRE-based isolation systems [53; 39] which validated that MR elastomer base isolation outperforms the traditional passive system in terms of response improvement during earthquake excitations. [PERSON] et al. [40] developed a single-degree-of-freedom scaled-down structure model above an MR elastomer and performed experimental testing on the system under harmonic excitation and earthquake time histories. [PERSON] et al. [54] developed a variable stiffness and damping isolator (VSDI) for base isolation of a civil structure. Four MRE samples, each 12 mm thick and trapezoidal were proposed in the design with a shim dividing them.