Reconfigurable intelligent surface (RIS) consisting of a large number of programmable near-passive units has been a hot topic in wireless communications due to its capability in providing smart radio environments to enhance the communication performance. However, the existing research are mainly based on simplistic channel models, which will, in principle, lead to inaccurate analysis of the system performance. In this paper, we propose a general three-dimensional (3D) wideband non-stationary end-to-end channel model for RIS assisted multiple-input multiple-output (MIMO) communications, which takes into account the physical properties of RIS, such as unit numbers, unit sizes, array orientations and array configurations. By modeling the RIS by a virtual cluster, we describe the end-to-end channel by a superposition of virtual line-of-sight (V-LoS), single-bounced non-LoS (SB-NLoS), and double-bounced NLoS (DB-NLoS) components. We also derive an equivalent cascaded channel model and show the equivalence between end-to-end and cascaded modeling of RIS channels. Then, a sub-optimal solution with low complexity is used to derive the RIS reflection phases. The impact of physical properties of RIS, such as unit numbers, unit sizes, array orientations, array configurations and array relative locations, on channel statistical characteristics has been investigated and analyzed, the results demonstrate that the proposed model is helpful for characterizing the RIS-assisted communication channels
