An Angle-Based Method Dealing with Vertex-Vertex Contact in the Two-Dimensional Discontinuous Deformation Analysis (DDA)

Due to the discontinuity of the direction of a normal vector at the corner, vertex-vertex contact is indeterminate in numerical modelling. Two classes are indeterminate in two-dimensional discontinuous deformation analysis (DDA), designated as "genuine indeterminacy" and "pseudo indeterminacy". While examining these indeterminacies, it is necessary to pre-process quasi-vertex-vertex contact and determine contact or entrance edges. On one hand, improper pre-processing not only changes the equilibrium equations of the system, but also increases the burden on open-close iteration. On the other hand, there are two kinds of quasi-contact edges, i.e. the same and different block quasi-contact edges. Certain previous distance-based methods, which are used to seek the correct entrance edge, lead to some forced contacts, including vertex-vertex or vertex-edge. New pre-processing and angle-based methods for determining entrance edges are developed in this study. Additionally, the new concept of strengthening the movement trend of blocks is presented in DDA. The new pretreatment method combining the angle-based method and a strategy for strengthening the movement trend of blocks are intended to reduce forced contacts, maintain the movement trend of blocks, and speed up open-close iterations to a certain extent. Furthermore, the new method only depends on the orientation of quasi-contact edges and the movement trend of convex corners. The effectiveness of these improvements is verified by translational motion, rotation trend, and time-step size effect tests.