## 1 Introduction  
Materials whose rheological properties can vary by the application of external stimulus belong to the class of smart materials [1]. Smart materials can respond rapidly and reversibly to changes in the surrounding environment. Magnetorheological elastomers (MRE) falls in the category of this branch, which is composed of filler particles within the elastomer matrix [2]. This material not only displays viscoelastic properties but also undergoes deformation during the transition process. The distribution, size and shape of the filler particles and the state of the interface between the particles and matrix affect the macroscopic behavior of the composite materials [3, 4]. The composite filled with particles are typically exhibiting the Payne effect at small deformation and the Mullins effect at high deformation [5, 6]. Moreover, debonding acts as a distinct failure phenomenon at critical stress levels due to polymer containing rigid inclusion. Therefore, particle-matrix interface is one of the key factors to investigate in the polymer composite.  
The presence of an anisotropic particle in the fluid creates unsteady flows. The unsteadiness behind such a body consists of unordered eddies of all sizes that create drag on the body. In contrast, the turbulence in the thin boundary layers next to the isotropic or anisotropic body of filler creates only weak disturbances of flow [7, 8]. It is important to predict the particle movement and speed within the volume of the matrix to study the effect of isotropic and anisotropic particle movements within the incompressible flow of a fluid. A key factor to understanding the nature of the flow is the Reynolds number, for values of which between 10 and 100 the flow are considered steady. The viscous forces of the fluid are proportional to the gradient of the velocity. The drag and lift forces are not of interest, as the dimensionless drag and lift coefficients. These depend only on the Reynoldsnumber and by the object's shape and not by its size [9; 10]. The coefficients of drag (\(C_{D}\)) and lift (\(C_{L}\)) are defined as below:  
\[C_{D}=\frac{2F_{D}}{\rho U_{mean}^{2}A} \tag{1}\]  
\[C_{L}=\frac{2F_{L}}{\rho U_{mean}^{2}A} \tag{2}\]  
where \(F_{D}\) and \(F_{L}\) are the drag and lift forces, \(\rho\) is the fluid's density and \(U_{mean}\) is the mean velocity. A is the projected area within the fluid.  
As the size of the particles is not considered influential, the shapes' variety, regular and/or irregular, has a significant effect with relation to particle Reynolds numbers (\(R_{ep}\)). The trajectory averaged drag forces were discussed for both the Stokes regime (\(R_{ep}\ll 1\)) and Newton regime (\(R_{ep}\gg 1\)) with keeping constant drag coefficient [11; 12]. The newton regime depends on the aspect ratio for spherical particles, such as surface area ratio for regular shape particles and min-med-max area for irregularly shaped particles. The particles with near-unity aspect ratios show a higher dependency on Reynold's number; however, particles with non-circular cross-section exhibit weaker dependence on Reynolds number, which is attributed to the more rapid transition to flow separation and turbulent boundary layer conditions [13; 14; 15].