Yes you want non-linear. Large Deformation and possibly Elasto-plastic material
Here is the difference in small displacement and Large displacement (small on left)
Here is how you do the 1.4mm deflection
Here is how you prevent infinite stress at the edge constraint... with a small region made rigid.
Here is the measure used to obtain the force.
Here are the Analysis definitions. If using elasto-plastic material then Plasticity will have a check mark.
Plotting the measure vs. time
Final results. If stress is above yield then you should use ELASTO-PLASTIC material. Nonlinear material + non-linear geometry. Otherwise force is generally predicted too high.
Confirmation? Run this model with found force (48N in this case) in X direction as a load in place of the enforced displacement. Confirm max displacement about 1.4mm in X direction.
BONUS - I used a Mapped Mesh (not totally necessary but results are so smooooth!)
Please show more views of your model. Is there a location with a sharp inside corner like this?
All inside corners near areas of interest should have at least a small radius. For the plastic parts I work with 0.15mm radius is used. Compared to H-elements, P-elements are less forgiving. In H-elements the stress is averaged over the element size which hides the singularity until using smaller and smaller elements. For P-elements the order of the element captures the high stress with larger elements. You can artificially limit the order of the elements near singularities but I prefer a tiny, but realistic radius.
What strain is it reporting vs. what you expect? Are you using a force or an enforced displacement. With a force this same message often comes when the design cannot reach the load applied, sometimes even failing to finish the loadsteps. I also suggest to plot a measure of plastic strain or stress vs loadstep. You can stop the analysis and view intermediate results at each loadstep.
Finally element quality/number will affect the ability to model large strains. A mapped mesh with quads and more layers through the thickness will help capture larger strains without too much element distortion. A tetra mesh with large elements could contribute to the issue.
