Bi-potential and co-rotational formulations applied for real time simulation involving friction and large deformation

This paper concerns mainly numerical aspects for the real-time manipulation of deformable objects in the context of virtual surgery. The bi-potential method in the form of augmented Lagrangian is extended to solve multiple contact problems within real time computing requirements. Nonlinearities of large deformation are also included to describe the mechanical behavior of soft tissues. To obtain both accuracy and realism, the approximated co-rotational finite element method is applied to make a compromise between accuracy and computational cost. It is difficult to detect collisions between virtual objects at interactive rates. In this work, we use an optimal bounding volume hierarchy technique to acquire a good detecting efficiency. Two numerical examples are carried out to illustrate the efficiency, robustness and accuracy of the presented approaches.