If you look for the easiest model I think Hooke's law can apply: ΔL = (L0 * F) / (S*E)
ΔL--> deformation, strain
L0--> sheet thickness
S--> surface aera
E--> Young's Modulus of your material
This model is extremly simplified thought, more detailed researches are needed if you look for something serious.
This is in the case where your material has the space freely deform itself (it's not "compression" but "deformation").
If you material is completely blocked from all sides, then the force you apply will act as an Isostatic Compression, and in this situation there is actually compression of your material, and the law is different.
The formula: ΔV = (ΔP*V0) / -K
V --> Volume, P--> Pressure
K --> Bulk modulus of your material
Basically your silicon sheet will deform itself until it fills all the space avalaible and then it will compress itself.