A static discrete element method with discontinuous deformation analysis

For discrete element methods (DEMs), integrating the equation of motion based on Newton's second law is an integral part of the computation. Accelerations and velocities are involved even for modeling static mechanics problems. As a consequence, the accuracy can be ruined and numerous calculation steps are required to converge. In this study, we propose a static DEM based on discontinuous deformation analysis (DDA). The force of inertia is removed to develop a set of static equilibrium equations for distinct blocks. It inherits the advantages of DDA in dealing with distinct block system such as jointed rock structures. Furthermore, the critical numerical artifact in DDA, ie, artificial springs between contact blocks, is avoided. Accurate numerical solution can be achieved in mere one calculation step. Last but not the least, since the method is formulated in the framework of mathematical programming, the implementation can be easily conducted with standard and readily available solvers. Its accuracy and efficiency are verified against a series of benchmarks found in the literature.