Time dependent Contact modeling with Automatic Remeshing

Hi
I am trying to model a Sand grain which is pressed completely into a hyperelastic material (rubber).
My sand grain has a diameter of 200 µm.
I am using a prescribed displacement to move it into the rubber.
I also tried to use a stationary study. There I used the Stop condition and remeshing a deformed mesh and a parametric sweep.
I am able to move the sand grain about 105µm out of 200 into the rubber.
After this the mesh starts overlapping and is not converging any more.

As it is complicated to remesh by hand lots of time I tried to put my model in a time dependent study
with an automatic remeshing condition.
I am also using a prescribed displacement there. I want to move my sand grain with 10µm per second into the rubber.
When I try to use the augmented Lagrangian contact it does not converge at all.
Then I tried it with penalty. Now it solves for the first two seconds. After this it starts to remesh but doesn`t get a solution and fails.

I am also not sure which boundary conditions I have to use with the moving mesh.

I attach my two models.
Please have look at it and tell me how to solve my problems.

Any helb would be appreciatet.

Thanks in advance
Carolin Rüss