The picture of the squished piece looks like there it was a combination of buckling failure of the sides (a geometric instability) and a material failure along

The picture of the squished piece looks like there it was a combination of buckling failure of the sides (a geometric instability) and a material failure along the sides (ripping, to allow the buckling failure of the sides). It doesn't look like a fluidlike or flow failure to me. FWIW, Plastic deformation here is in contrast to elastic, it's not the material. Elastic deformation is linear, Hooke's law deformation: f=kx. Plastic deformation is when elastic breaks down, and you can have additional deformation at the same (or lower) load. Generally, there's an elastic region, then a plastic region, and then total failure. The numbers suggest that legos are actually pretty similar to unreinforced masonry, the strength looks like about 4000 PSI in compression and nearly no tensile strength. That's about equivalent to bog standard concrete or concrete blocks (CMU). The main difference is that Legos are much less dense. It would be interesting to see something similar to Gothic architecture done in Legos though there would have to be some tweaking to deal with flying buttresses due to the density.