Materials that have a negative Poisson's ratio
Auxetic metamaterials are a type of metamaterial with a negative Poisson's ratio, so that axial elongation causes transversal elongation (in contrast to an ordinary material, where stretching in one direction causes compression in the other direction). 
Auxetics can be single molecules, crystals, or a particular structure of macroscopic matter.
Auxetic materials are used in protective equipment such as body armor, helmets, and knee pads, as they absorb energy more effectively than traditional materials. They are also used in devices such as medical stents or implants. Auxetic fabrics can be used to create comfortable and flexible clothing, as well as technical fabrics for applications such as aerospace and sports equipment. Auxetic materials can also be used to create acoustic metamaterials for controlling sound and vibration.
History.
The term "auxetic" derives from the Greek word () which means 'that which tends to increase' and has its root in the word (), meaning 'increase' (noun). This terminology was coined by Professor Ken Evans of the University of Exeter.
One of the first artificially produced auxetic materials, the RFS structure (diamond-fold structure), was invented in 1978 by the Berlin researcher K. Pietsch. Although he did not use the term auxetics, he describes for the first time the underlying lever mechanism and its non-linear mechanical reaction so he is therefore considered the inventor of the auxetic net.
The earliest published example of a material with negative Poisson's constant is due to A. G. Kolpakov in 1985, "Determination of the average characteristics of elastic frameworks"; the next synthetic auxetic material was described in "Science" in 1987, entitled "Foam structures with a Negative Poisson's Ratio" by R.S. Lakes from the University of Wisconsin Madison. The use of the word "auxetic" to refer to this property probably began in 1991. Recently, cells were shown to display a biological version of auxeticity under certain conditions. 
Designs of composites with inverted hexagonal periodicity cell (auxetic hexagon), possessing negative Poisson ratios, were published in 1985.
For these reasons, gradually, many researchers have become interested in the unique properties of Auxetics. This phenomenon is visible in the number of publications (Scopus search engine), as shown in the following figure. In 1991, there was only one publication. However, in 2016, around 165 publications were released, so the number of publications has exploded - a 165-fold increase in just 25 years - clearly showing that the topic of Auxetics is drawing considerable attention. However, although Auxetics are promising structures and have a lot of potential in science and engineering, their widespread application in multiple fields is still a challenge. Therefore, additional research related to Auxetics is required for widespread applications.
Properties.
Typically, auxetic materials have low density, which is what allows the hinge-like areas of the auxetic microstructures to flex.
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. Auxetic behaviour at the macroscale can also be employed for the development of products with enhanced characteristics such as footwear based on the auxetic rotating triangles structures developed by Grima and Evans and prosthetic feet with human-like toe joint properties.
Auxetic materials also occur organically, although they are structurally different from man-made metamaterials. For example, the nuclei of mouse embryonic stem cells in a transition state display auxetic behavior. 
Examples.
Examples of auxetic materials include:
References.
 ;templatestyles src="Reflist/styles.css" / ;