Auxetics are structures or materials that have a negative Poisson's ratio. When stretched, they become thicker perpendicular to the applied force. This occurs due to their particular internal structure and the way this deforms when the sample is uniaxially loaded. Auxetics can be single molecules, crystals, or a particular structure of macroscopic matter. Such materials and structures 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.
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.
At the macroscale, auxetic behaviour 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.
Examples of auxetic materials include:
- Auxetic polyurethane foam
- Certain rocks and minerals
- Graphene, which can be made auxetic through the introduction of vacancy defects
- Living bone tissue (although this is only suspected)
- Tendons within their normal range of motion.
- Specific variants of polytetrafluorethylene polymers such as Gore-Tex
- Paper, all types. If a paper is stretched in an in-plane direction it will expand in its thickness direction due to its network structure.
- Folded sheet materials such as zigzag-based folded sheets. and several types of origami folds, such as miura fold.
- Tailored structures designed to exhibit special designed Poisson's ratios.
- Chain organic molecules. Recent researches revealed that organic crystals like n-paraffins and similar to them may demonstrate an auxetic behavior.
- Processed needle-punched nonwoven fabrics. Due to the network structure of such fabrics, a processing protocol using heat and pressure can convert ordinary (not auxetic) nonwovens into auxetic ones.
In 2016, Ahmad Rafsanjani described the use of Islamic geometric patterns from tomb towers in Iran to create auxetic materials from perforated rubber sheets. These are stable in either a contracted or an expanded state, and can switch between the two. The internal structure that enables this unusual behaviour is inspired by two of the 70 Islamic patterns that Rafsanjani noted on the tomb towers.
- Acoustic metamaterials
- Mechanical metamaterials
- Zetix, a type of commercially manufactured auxetic material
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