I measured the Young's modulus of a rectangular silicone foam sample which is equivalent in material constitution to silicone rubber except that it is 80% empty. The Young's modulus for this foam was measured to be about $E_f= .02 MPA$ which is much smaller than the $E_s=1 MPA$ expected for silicone rubber. The internal geometry of the foam can be approximately described by spherical holes that are randomly distributed across space with sizes ranging from 0.0008 - 0.005 microns.
My first attempt at an explanation involves the following:
Assuming that we have a sample of silicone rubber with equivalent dimensions it would be 80% smaller in volume. Given that Volume has dimensions $L^3$ I would need to divide the Young's Modulus of Silicone Foam by $C=.2^{2/3}\approx .34$ in order to take into account that the silicone foam is mostly empty. This gives me $E_f \approx .02/.34 \approx .06$ MPA
Now, let's suppose that a rectangular sample of silicone rubber stretched along its major axis can be modeled as large number of rubber bands joined together with negligible bending. Given that the mass of the silicone rubber and silicone foam are equal the number of 'bands' in each one is also equal where these bands are taken to be of very small cross-sectional diameter. Then we must take into account that unlike the silicone rubber sample, the silicone foam sample has the strands almost always at an angle. Now, taking all of these angles $0 \leq \theta \leq \frac{\pi}{2}$ to be equally likely a force through any particular strand of the silicone foam would on average need to be divided by $cos(\frac{\pi}{4})=\frac{\sqrt2}{2}$ in order to correct for this difference. So $E_f \approx .06*\sqrt{2} \approx .08 MPA$
This still means that I am off by a factor of approximately $12$. My question is whether I can come up with a better theoretical explanation for the difference in Young's Modulus without knowing more about the internal geometry than the information I have given using first principles. Otherwise, I am also interested in research done on the elastic properties of silicone foam but I haven't found any so far.