In Computer Graphics, physically-based simulation of deformable objects is a current challenge, and many efficient models have been developed to reach real-time performance. However, these models are often limited when complex interactions involving topological modifications are required. To overcome this, the key issue is to manage concurrently, and at minimal cost, both the topology and physical properties. Thus, this paper presents a unified topological-physical model for soft body simulation. The complete embedding of physical and topological models will facilitate operations like piercing, fracture or cutting, as well as adaptive refinement. Indeed, the difficulty is to treat topological changes during the simulation, requiring combined geometric and physics considerations. Rigorous topological operations guarantee the validity of the mesh, while direct access to the adjacent and incident relations will ease the update of physical properties of new elements created during these operations. These features are illustrated on an embedded mass-spring system undergoing topological modifications performed during simulation. Different levels of subdivision are also presented.