Damping/stabilisation in implicit dynamics

[compabaq]

I am trying to model crack growth in a material using a cohesive interaction. It's basically two symmetric 3D halves that are being pulled apart in the normal direction with a cohesive zone in the symmetry plane. I want to monitor the crack growth as a function of the applied load. This works well if the fracture toughness of the cohesive zone is 50 kJ/m², but fails to converge if I increase this to 100kJ/m². I have tried all sorts of damping/stabilisation approaches, but none of them worked. Here's a list of what I tried:
-Changing the dynamic step from "Default" to "Quasi-static" (helped a bit, but not enough)
-Increasing the viscosity of the cohesive interaction (helped slightly, but only when it started to affect the force displacement diagram, which I want to avoid)
-Increasing the density by a factor of 100 (nearly no effect, and I cannot increase it anymore, otherwise the energy balance is messed up)
-I played with the "General solution controls" to allow more iterations within one increment and allowed smaller step sizes (again this helped slightly but not enough)
-I played with the mesh density (did not really help)
-I used 3D elements with and without reduced integration (did not really help)
-I turned the repeated contacts on and off (did not help at all)
-I changed the stiffness of the cohesive law (hardly helped)

I have no clue what else I can try to make my simulation converge. Any ideas or thoughts on what I can do?

 

[Mustaine3]

What about A/Explicit?

 

[compabaq]

I have not considered Explicit yet. Do you think this will lead to a more stable solution/convergence?