Discontinuity of quasi-static solution in the two-node Coulomb frictional system

A single-node system introduced by Klarbring has provided insight into the non-uniqueness of solution in the quasi-static contact problem at the high coefficient of Coulomb friction. Here, we explore this issue for the two-node system under the slip displacement space in which the instantaneous condition is efficiently represented. In the paper, we identify a qualitatively different failure of the quasi-static evolution algorithm in which a more complex dynamic transition may occur. When the system evolves from the point where both-node discontinuity occurs, the transient evolution behavior involving a damping matrix is explored in order to investigate a final state of the two-node system. It is demonstrated that the final state is uniquely determined which is independent of the damping matrix.