LS-DYNA: Compression of thin layered structure

Hello everyone,

I am trying to simulate the compression of very thin layered structure. It is modeled via a Shell in the middle (0.012 mm thickness), and 2 layers of Solid on each side of the Shell (thickness 0.078 mm). 
I have a measured force displacement curve, from which I derived the material parameters for MAT63 compressible foam. 

However, at one point the volumetric strain becomes very large and the elements extremely stiff. I tried other element formulations like -1 or -2 without success. I tried to modify the LCID definition without success. 

I have attached the rather small model. 
Does anyone have a suggestions how to cope with such things?

I know ideally I use 3 solids through thickness. Since this is a material calibration model, that would be possible. the final model is huge, so doing 3 solids with 0.026 mm thickness each is impossible to handle.