Computer animations and visual effects have always been identified as human time-consuming tasks, due to the necessity to create a realistic footage from the interpolation of static key-frames. Recently, Craft Animations has developed a new technique in order to interactively create realistic physics-based animations. In this view, each frame is a static key-frame and no artificial interpolation is needed; computer animation is now becoming a machine time-consuming task, and thus a physical engine able to efficiently handle the complexity of the scenes must be created from scratch. In this talk, the task of modelling collisions and deformations is addressed; starting with the mathematical formulation of the model, we make crucial approximations to achieve real-time performance without affecting realism. We then focus on the use of existing libraries and middlewares, in order to create a robust and fast implementation of the finite element method for large deformations, with a particular attention to the communication among different solvers by means of an appropriate contact model. We also show how to reinterpret and improve our work thanks to more rigorous mathematical foundation, in order to understand where we stand given the employed models and approximations.