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

An implicitly coupled hydro-geomechanical model for hydraulic fracture simulation with the discontinuous deformation analysis

“…In the original DDA, contacts were divided into three different types: vertex-vertex, vertex-edge and edge-edge. A recognized problem with spring-based penalty methods is that vertexvertex contacts can lead to the inaccurate displacement of blocks by requiring the specification of a single reference line for penetration [24][25][26]. Additionally, it was found that unfractured vertex-vertex contacts would frequently struggle to converge when using the ALM, as the penetration distance and force across both reference lines of the contact would be very small.…”

“…Additionally, it was found that unfractured vertex-vertex contacts would frequently struggle to converge when using the ALM, as the penetration distance and force across both reference lines of the contact would be very small. Although some efforts have been made to resolve the first of these issues within the DDA by using a trajectorybased method for the initial selection of the reference line [25,26], a fully implicit method for resolving both problems remains elusive. In an effort to minimize these issues, vertexvertex contacts remain open in the current work until the penetration grows greater than some tolerance, here set at 1 μm.…”

Some modifications to the process of discontinuous deformation analysis

“…But this is not true, because the entrance edge should be BE and AD. The solution to this problem in Bao and Zhao (2012) is to use the trajectory of the vertex A to find the entrance edge when the moving vertex invades into the target block. However, this method is feasible only when vertex A in previous step is outside the target block.…”

Mixed linear complementarity formulation of discontinuous deformation analysis

“…During the iteration, the change in the contact mode of any contact-pair will cause a discontinuous change in the stiffness matrix, and accordingly lead to an abrupt change in degrees of freedom in two consecutive iterations. When many vertex-to-vertex contact candidates are involved in a problem, the precision is sensitive to the choice of the penalty value and the time-step size [20]. Furthermore, in considering block nonlinearity such as block nonlinear constitution or crack propagation in blocks [21], an iteration process must be carried out so as to satisfy the block nonlinearity.…”