I am not sure of the physics exactly, but my assumption was that the fibers were in some ways similar to a super cooled liquid (which will rapidly freeze when disrupted).
So you have a polymer which is totally flexible, but when it is sharply shocked in some way the outer layer will stiffen and the inner layer will convert (and expand) into something like
Aerogel.
It is a stretch but it is the best I could come up with.