## 1 Introduction
The magnetizable particles are arranged in different ways based on different needs, such as chain and uniform arrangement. The polymer with different particle arrangement is usually regarded as isotropic and anisotropic body. A wide range of applications for this type of MRE has been reported in the literature [34; 35; 36; 37]. A series of investigations and reviews of MRE-type modeling have also been carried out. Mechanical and magnetic properties were simulated and developed by establishing a mechanism of the distribution of magnetic effect [3]. The mechanical response of nanocomposites filled with carbon nanotubes was studied with a viscoelastic interface model [4; 5]. A few research studies on theoretical models of MREs were conducted by considering several determinant factors such as magnetic strength, strain amplitude, and loading frequency [6; 7; 8; 9; 10; 11]. With the excitation of both compressive and shear loading, experimental work was further implemented to modify and validate the conventional magnetorheological model which only took shear effect into account [12; 13]. In order to investigate the viscoelastic property of MRE under wider amplitude and variable frequencies, a new revised nonlinear rheological Bouc-Wen model was proposed to consider displacement-, velocity- and acceleration-dependent behavior [14]. These research results show that the mechanical properties of MRE affects the frequency, temperature, magnetic strength, and field dependence modulus. Extensive work on modeling MREs has not been carried out in the literature due to the complexity of this problem. Based on the available MRE models, an MRE with MWCNTs model is studied in this manuscript. One of the objectives of this paper, is how to assess different constituencies of these materials by using energy distribution. This is a particularly important problem that has not been adequately or methodically addressed, and remains an important research question. A proposed approach to address this problem is to collect microscale images of polymers and analyze them by image recognition methods. The micro-scale image of the edge of mixture is multisingular. In order to solve the shortage of two-dimensional wavelet transform in identifying the Linear Singularity of the edge, a new anisotropic and multiscale curvelet transform is proposed. This approach offers a mapping method which maps a two-dimensional function to a group of two-dimensional directional plane wavelets to obtain curvelet coefficients. Different components of the microstructure of MRE composites need to be clearly differentiated to reveal the weights of each constituent. This is an important task that helps to develop and identify an MRE isolator that is most suitable for seismic application. One of the effective tools that has been employed for feature extraction, in several disciplines, such as structural health monitoring, is wavelet analysis [38; 39; 40; 41; 42; 43]. Among the wider range of wavelets, the wavelet, proposed by geophysicist [PERSON] in 1981, is an advanced signal processing tool that can adaptively extract features of signals in the time-frequency domain with multiresolution analysis. Due to its unique capability of \"zoom lens with an adjustable focus\", it has been widely applied to damage detection and system identification in civil, mechanical and aerospace engineering [44; 45; 46]. For instance, considering the influence of original defect of structures, wavelet coefficient differences were employed to detect damage locations and quantify specific damages of a beam structure by choosing an optimal scale. As a further development, curvelet performs a better identification efficiency and accuracy in that its anisotropic behavior allows it to \"track\" the behavior of singularities along curves. This means it can identify an abnormal signal with various scales, spaces and orientations [47].