Penalty function method for combined finite-discrete element systems comprising large number of separate bodies

Large-scale discrete element simulations, the combined nite{discrete element method, DDA as well as a whole range of related methods, involve contact of a large number of separate bodies. In the context of the combined nite{discrete element method, each of these bodies is represented by a single discrete element which is then discretized into nite elements. The combined nite{discrete element method thus also in- volves algorithms dealing with fracture and fragmentation of individual discrete elements which result in ever changing topology and size of the problem. All these require complex algorithmic procedures and signi cant computational resources, especially in terms of CPU time. In this context, it is also necessary to have an e cient and robust algorithm for handling mechanical contact. In this work, a contact algorithm based on the penalty function method and incorporating contact kinematics preserving energy balance, is proposed and implemented into the combined nite element code.