“…Various numerical methods are used to solve contact problems including the Lagrange multiplier methods (Chen and Yeh, 1990;Hu, 1997;Laursen and Chawla, 1997;Jiang and Rogers, 1988;Simo et al, 1985), penalty methods (Kanto and Akawa, 1990;Peric and Owen, 1992;Chen et al, 2015), contact element methods (Dowling and Hall, 1989), contact force methods (Wang et al, 2007), etc. Most conventional numerical methods for dynamic contact first assume the contact status, then solve the problem, and finally check if the assumption is correct.…”