Understanding and modeling liver biomechanics represents a significant challenge due to its complex nature. In this paper, we tackle this issue in the context of real time surgery simulation where a compromise between biomechanical accuracy and computational efficiency must be found. We describe a realistic liver model including hyperelasticity, porosity and viscosity that is implemented within an implicit time integration scheme. To optimize its computation, we introduce the Multiplicative Jacobian Energy Decomposition (MJED) method for discretizing hyperelastic materials on linear tetrahedral meshes which leads to faster matrix assembly than the standard Finite Element Method. Viscohyperelasticity is modeled by Prony series while the mechanical eff ect of liver perfusion is represented with a linear Darcy law. Dynamic mechanical analysis has been performed on 60 porcine liver samples in order to identify some visco-elastic parameters. Finally, we show that liver deformation can be simulated in real-time on a coarse mesh and study the relative eff ects of the hyperelastic, viscous and porous components on the liver biomechanics.