I am working on a 2D implicit model where I tied two different parts. A portion of the interface between two parts kept untied. In this portion, I defined cohesive interaction between two surface for step-1, which acts similar to 'Tie', and deactivated that for step-2. The red and green zone of the figure are in compression and leads to overlapping at step-2. I decided to define a contact(surface to surface) property. So I created an interaction property with normal behavior 'Linear'. Then it solves overlapping but that simulation fails at t=0.2679 due to convergency issue. And one element is also distorted too much. I tried refining mesh but it stops simulation earlier.  I have added the portion of input file about the interaction.
*Surface Interaction, name=IntProp-3
1.,
*Cohesive Behavior
0.1, 0.1, 0.1
*Surface Interaction, name=IntProp-4
1.,
*Friction
0.,
.........  .........  .........
.........  .........  .........
** Interaction: Int-5
*Contact Pair, interaction=IntProp-3, small sliding, type=SURFACE TO SURFACE
cut-2, cut-1
** Interaction: Int-6
*Contact Pair, interaction=IntProp-4, type=SURFACE TO SURFACE
cut-2-step2, cut-1-step2