The visualization of internal structures of organs in minimally invasive surgery is an important avenue for improving the perception of the surgeon, or for supporting planning and decision systems. However, current methods dealing with non-rigid augmented reality only provide augmentation when the topology of the organ is not modified. In this paper we solve this shortcoming by introducing a method for physics-based non-rigid augmented reality. Singularities caused by topo-logical changes are detected and propagated to the pre-operative model. This significantly improves the coherence between the actual laparascopic view and the model, and provides added value in terms of navigation and decision making. Our real time augmentation algorithm is assessed on a video showing the cut of a porcine liver's lobe in minimal invasive surgery.