I am not much experienced with CalculiX. I have a hyperelastic Ring to which a large prescribed displacement is given.
The model converges till a diplacement of 15, but as soon as I give displacement above 15 or 20, the model shows divergence and error stating the increment size is smaller than minimum
This is the surface interaction between the Ring and the moving metal part that stretches it
Try tying the surfaces. If the analysis completes with this setting, the reason for non-convergence lies somewhere else, not in contact (which often causes problems). Try also changing the material model or adjusting its properties, refining the mesh (if needed) and using different element type. You can also try running the study with the dynamic analysis step.