Animated GIF’s from recent 3D printed Auxetic material tests :
Auxetics are materials that have a negative Poisson’s ratio. When stretched, they become thicker perpendicular to the applied force. This occurs due to their hinge-like structures, which flex when stretched. Auxetic materials can be singlemolecules or a particular structure of macroscopic matter. Such materials are expected to have mechanical properties such as high energy absorption and fracture resistance. Auxetics may be useful in applications such as body armor,packing material, knee and elbow pads, robust shock absorbing material, and sponge mops.
Auxetics can be illustrated with an inelastic string wound around an elastic cord. When the ends of the structure are pulled apart, the inelastic string straightens while the elastic cord stretches and winds around it, increasing the structure’s effective volume.
The term auxetic derives from the Greek word αὐξητικός (auxetikos) which means “that which tends to increase” and has its root in the word αὔξησις, or auxesis, meaning “increase” (noun). This terminology was coined by Professor Ken Evans of the University of Exeter.
The earliest published example of a synthetic auxetic material was in Science in 1987, entitled “Foam structures with a Negative Poisson’s Ratio”  by R.S. Lakes from the University of Iowa. The use of the word auxetic to refer to this property probably began in 1991.
Designs of composites with inverted hexagonal periodicity cell (auxetic hexagon), possessing negative Poisson’s ratio, were published in 1985,  , , , 
Typically, auxetic materials have low density, which is what allows the hinge-like areas of the auxetic microstructures to flex.