An improved discrete element method based on a variational formulation of the frictional contact law

An improved algorithm based on the contact dynamics approach is proposed. Like previous developed algorithms it involves two stages. In the first one (local stage) for each particle, forces are computed from the relative displacement using an interaction law, which models frictional contact and shock. In the second stage (global stage) Newton's second law is used to determine, for each particle, the resulting acceleration which is then time-integrated to find the new particle positions. This process is repeated for each time step until convergence is achieved. The two distinguishing features of the present algorithm are the local integration of the frictional contact law and the convergence criterion. By adopting a variational statement of the frictional contact law based on the bi-potential concept, the integration procedure is reduced to a single predictor-corrector step and a new convergence criterion is introduced. Both aspects significantly reduce the computing time and enhance the convergence. Numerical applications show the robustness of the algorithm.