Virtual surgery is a serious game which provides an opportunity to acquire cognitive and technical surgical skills via virtual surgical training and planning. However, interactively and realistically manipulating the human organ and simulating its motion under interaction is still a challenging task in this field. The underlying reason for this issue is the conflict requirements for physical constraints with high fidelity and real-time performance. To achieve realistic simulation of human organ motion with volume conservation, smooth interpolation under large deformation and precise frictional contact mechanics of global behavior in surgical scenario. This paper presents a novel and effective patch Green coordinates based interpolation for embedded deformable model to achieve the volume-preserving and smooth interpolation effects. Besides, we resolve the frictional contact mechanics for embedded deformable model, and further provide the precise boundary conditions for mechanical solver. In addition, our embedded deformable model is based on the total lagrangian explicit dynamics (TLED) finite element method (FEM) solver, which can well handle the large biological tissue deformation with both nonlinear geometric and material properties. In real compression experiments, our method can achieve liver deformation with average accuracy of 3.02 mm. Besides, the experimental results demonstrate that our method can also achieve smoother interpolation and volume-preserving effects than original embedded deformable model, and allows complex and accurate organ motion with mechanical interactions in virtual surgery.