A frictional spring and cohesive contact model for accurate simulation of contact forces in numerical manifold method

“Open-close iteration” is a crucial algorithm for handling complex contacts in numerical manifold method (NMM) and discontinuous deformation analysis (DDA). This algorithm has proved to be robust and efficient for decades. However, as some researchers have pointed out, the original open-close iteration may involve errors in sliding tests, especially in critical sliding tests with cohesive contacts. In this study, two major problems in the original algorithm are found to be nonconvergent contact force and early removed cohesive strength. The modifications are the following: (a) a frictional spring. By avoiding the trail value of normal contact force, we added a new frictional spring to the iteration scheme. This spring can apply accurate friction and can help ensure the convergence of contact forces. (b) A cohesive contact model. The original scheme can encounter an “early failure” in cohesive contacts. After investigating how contacts provide shear resistance, we found the cause and then provided a simple correction of the cohesive issue. The new algorithms in this article are essential for accurately simulating contacts by NMM/DDA.