Auxetics are materials that have a negative Poisson’s Ratio. When stretched they become thicker perpendicular to the applied force, from our own experiences when a material is stretched we expect the material to not only become longer but also thinner. Auxetics behave in a different way because of there internal structure.
Poisson’s ratio (v) of a material is the ratio of the lateral contractile strain to the longitudinal tensile strain for materials undergoing tension in the longitudinal direction. It shows how much a material becomes thinner when stretched, therefore most materials have a positive Poisson’s ratio.
The images below show modules of four structures that have Auxetic behavior. The images show the change in state of the structure as they undergo tension in the longitudinal direction.
This video shows an interesting application of an auxetic structure with inflatables by Fergal Coulter. http://fergalcoulter.eu/