We present an improvement of a unified topological-physical model which permits topological modifications during physical simulation of soft tissues. Our improvement makes the model more generic, efficient and simpler to update. The main principle of our improvement is to associate information to elements of the model, depending on the underlying physical model. Our modification of the architecture enables to easily integrate different physical models. Moreover, topological operations and physical simulations can be factorized between the different physical models. Our solution is more efficient as it leads to simpler modification algorithms after topological alterations with less changes to apply. In this paper, we present our new solution and illustrate its new properties thanks to several experiments performed on two well-known physical models: Mass-Spring System and Tensor-Mass model. The results present a comparison of our solution with the previous one for the cutting topological operation. Moreover, as our model permits to easily compare several physical models, we performed some simulations to reproduce experiments made on real tissues.