This is an axisymmetric insertion example in Abaqus/Standard. The procedure type is *DYNAMIC. A velocity with a user amplitude is applied in step 1. There is a sensor that monitors the contact force between the rigid ring and the top viscoelastic lip.  The UAMP subroutine ends step 1 when the contact force on the top lip falls to 0. The ring is released in step 2 and it comes to rest between the top lip and the bottom lip. The animation is from the Physics Results Explore.