Contact mechanics for analysis of fracturing and fragmenting solids in the combined finite-discrete element method

The combined finite-discrete element method is a new computational method for the simulation of fracturing and fragmenting solids or particulate media where individual particles are deformable. The method combines the power of the finite element method in capturing deformability of solid particles with the power of the discrete element method to accurately represent interaction between individual particles for systems comprising millions of particles. In addition, the method is suitable for the simulation of extensive fracture and/or fragmentation processes. In recent years the method has captured the attention of researchers in a wide field of potential applications and the interest in the method has grown significantly. In this paper key features of the method are explained with special attention being paid to the processing of contact interaction. Also, the new generation of linear time complexity search algorithms has been presented including the NBS and the MR algorithm. In the computational mechanics context, these algorithms are also relevant for the discrete element method, the finite element method and grid generation.