Abstract: Soft matters, which include liquid crystals, polymers, electro-rheological fluids, magnetic fluids, soap bubbles, bio-membranes, and granular materials, and so on, have received much academic attention recently. Among them, magneto-rheological fluids and granular materials are of particular importance in the applications of dampers and structural materials to the area of civil engineering. In this project, we will focus on the studies of magneto-rheological fluids and granular materials. The purpose of this study is two-fold. Firstly, we will discuss whether there is a useful tool for constructing the framework of the mechanics of soft matters. Secondly, we will perform experimental works on the complicated responses of granular materials and then look for a macroscopic background of these responses. The theoretical framework of this research project is the mesoscopic mixture theory to thoroughly analyze the behavior of magneto-rheological fluids. Furthermore, the extensions of this theory to the studies of other soft matters are evaluated. In addition, the differential and integral types of variational principles and the two-bracket formalism of thermodynamics are used to investigate the conservative dynamics and the dissipation structures, whereas for thermodynamics, the issue of geometric viewpoint of thermodynamics is also addressed. In the experiments, we will observe the phenomena of the settlement, segregation, and flow of granular materials under the influence of vertical vibrations. A theoretical study of the physics of segregation will also be given.