Claudio Pedrazzi

I do not necessarily agree that you should use a transient, as I wrote above, I would at first try with a static analysis, and when it works, step the complexity up and go to a transient. But since you insist: give us an idea of the speed of this phenomenon: is this a "shock"? how long does one "touch" take? 1 second, 1 tenth of a second? how is the speed of the moving part? 

A transient IMHO is appropriate when there are comparatively large kinetic energies involved. 

And I do not understand the question "can I set the accumulation of slides for the material there for multiple touches of two parts?

What do you mean with "set"? If the simulation works as expected, the increasing amount of deformation will be a result of the simulation itself, you will not have to "set" anything.