A stabilized numerical solution for the dynamic contact of the bodies having very stiff constraint on the contact point

For the numerical analysis of dynamic contact problem where the contact constraint is imposed by a very stiff massless spring between the bodies, it is shown that a stabilized time integration solution can be obtained without spurious oscillations by imposing the velocity and acceleration constraints as well as the displacement constraint on the contact point. For the velocity and acceleration contact constraints which are crucial for the numerical stability, the time derivatives of the spring deformation are computed by using the Newmark time integration rule of structural dynamics. With the numerical experiments the necessity of the velocity and acceleration contact constraints and the necessity of unconditionally stable time integration rule for the very stiff spring are demonstrated.