Why does foam dull knives? I have recently taken up prop making and just started my first foam-built costume from a video game. These kinds of costume armour builds are often built out of the various foam floor mats you can buy in say Home Depot or BJ's or Five Below for around $1 for 4 sq. foot tile.
The one thing that puzzles me is why foam dulls a sharp steel blade so easily and so quickly. 
I have tried x-acto knives, those snap-off knives, even surgical scalpels. Regardless, after cutting several linear feet (maybe in the neighborhood of 5-10?), the knife blade begins to dull rapidly and no longer produces nice cuts, but begins to tear the foam instead. You can always sharpen your blade on a stone, but in short order it will again dull and tear. 
I generally do all my cutting on one of the green, self-healing cutting mats. This could explain the tip dulling, but it is actually the whole length of the blade exposed to the foam that gets dull. 
It happens across types, thicknesses and densities of foam. The floor mats are about 0.5
" and medium density. The craft foam from Michaels is 6mm, high density and rigidity. The roll I have is 0.25" low density, low rigidity 
It absolutely baffles me how soft squishy foam just destroys the edge of a metal knife.  
I am guessing it has something to do with the molecular organization of the foam or something, but would love to know if anyone has a good explanation for why and how this happens.
 A: "Soft and squishy" is a bulk property. That's not due to either the polyurethane or the air fraction individually, but of the combination.
However, at the scale of a knife's edge, that foam is in fact locally either air or polyurethane. Cutting the air bubbles is trivially easy, but that small fraction of polyurethane is actually quite tough. So, while you're putting only a few newtons of force on the knife, at the edge those few newton are concentrated on only a few points. Let's assume that each point where you're cutting the foam is 0.1mm square and the force locally is 0.1 N. That gives a pressure on the edge of 10 MN/m2, or 10.000 bar. Quite a lot.
A: My guess is that the foam has some type of sillica in it which may stick to the knife having a detremental effect on its cutting ability possibly cleaning the blades regularly with alcohol could help this but i'm no chemist, hopefully this is helpful
A: Having previously done academic research on various aspects of knives, I agree with @MSAlters - the actual polymer you're cutting is quite tough.   The practical solution is to do what professional knife-users, like butchers, carpet layers, whatever, do:  run the blade through a hand-held sharpener after every few strokes.   I now do this when indulging hobbies, whether cooking or carpentry.   Works! 
A: Use a heat knife. Theatre folk use them religuosly to cut foam of any type. The blade wont dull, becuase a heat knife blade is already there ("butter-sharp").
