This report Stretch, but without the wrinkles of the recent paper Three-Dimensional Polymer Constructs Exhibiting a Tunable Negative Poisson’s Ratio may be interesting to mathematicians. From the report:
"A team of nanoengineers have constructed new materials that don't wrinkle when you stretch them. This makes them similar to tissue found in the human body, so they may in the future be used to repair damaged heart walls, blood vessels and skin.
The secret of the two new materials lies in their geometry. Engineered tissue is made using a porous scaffold structure. It's the shape of the pores that's important. Square and circular pores, or those shaped like regular hexagons, give you a positive Poisson ratio. But it's possible to achieve a negative ratio by cleverly tweaking such basic geometries."
The modern research in this area seems to have started with a paper of Rod Lakes in 1987, partly reproduced in his site
P.S. Videos Negative Poisson Ratio Material and The strange behaviour of auxetic foams