The vertex-to-vertex contact analysis in the two-dimensional discontinuous deformation analysis

In the two-dimensional discontinuous deformation analysis (DDA), contacts can be generalized into three types: vertex to edge, edge to edge, and vertex to vertex. In the vertex-edge contact, the contact reference edge is clearly and uniquely defined, while the contact reference edge for the vertex-vertex contact is not unique, which will lead to an indeterminate state. The indeterminacy of the vertex-vertex contact is a well-known problem in both the continuum-based methods and the discontinuum-based methods. The standard DDA employs the shortest path method to deal with the indeterminacy in the vertex-vertex contact, which is sensitive to the choice of analysis parameters, such as the time step size, the maximum displacement ratio and the contact spring stiffness. Two enhancements to the shortest path method are introduced in this paper. The first enhancement employs a temporary vertex-vertex contact spring to determine the moving tendency among two contact blocks. The second enhancement uses the trajectory of the vertex during a time step to find the entrance edge when the moving vertex invades into the target block. Examples show that these two enhancements to the standard DDA code work well.