How to enforce minimum gap between two vibrating structures- FSI

Hey,

I am working on vocal fold aerodynamics. I am trying to perform 2D Fluid Structure Interaction simulations in which the air flows between the two vocal folds. The gap between them is very small(~2mm) through which the air flows. I am unable to get convergence. The error is "Failed to find consistent initial value". I am also getting a warning of inverted mesh in the gap between the two structures.
I think so the structures are coming in contact and hence the error. Can anyone help me out to understand how to enforce a minimum gap between the two.

Thanks in advance!!