Discontinuous deformation analysis handling vertex-vertex contact based on principle of least effort

This study establishes an innovative discontinuous deformation analysis by solving the problem of frictional and cohesive contact using an implicit cone complementary formulation. In order to handle singularity associated with the vertex-vertex contact, resistances to motion trend are firstly estimated by introducing the concepts of total and partial contact forces. Based on principle of least effort, the vertex-vertex contact can be converted to a corresponding vertex-edge contact properly. In addition, unnecessary vertex-vertex contacts can be identified. The numerical scheme fully exploits geometric and dynamic conditions of the polygonal block system. As a result, determination of motion trend in the block system is penalty-free without being affected by the time step. The advantages and application prospects of the presented dynamic framework are demonstrated by using several benchmark examples.