The two graphs in your last post are not plotted on the same axes, one is F vs D, the other is U2 vs what? Please label axes and include units. Also, the metastructure has 3 layers of unit cells so if you displace that 30 mm, you should compare that with a unit cell displaced 10 mm.
I have a post that lists recommendations for models that use hyperelastic materials. You need to follow that advice if you continue to use 2D Plate elements. This is not necessary if you use 3D Shell elements.
I tried 2 quadratic elements through the thickness and it did not perform well. I had to do some slicing of the domain in order to get pieces what would be easily meshed. The image below has 6 linear elements through the thickness.
Another approach to this model is to abandon the 2D meshing of a surface and replace the entire model with beam elements on line bodies. That would eliminate any concern about how many elements are through the thickness and it would reduce the node count to a very low number which would make the transient solution compute much more quickly. I built the mesh shown below, then learned that Beam188 elements do not support hyperelastic material models. So if you can use linear elastic materials, you could use this approach.
Next I extruded the line bodies into sheet bodies 10 mm wide. Shell elements increase the node count by 4 times over the line bodies above, but is still a lot fewer nodes than the 2D Plate elements.