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Auxetics are typical structures of the representative mechanical meta-materials. Mechanical meta-materials are structures whose mechanical properties are artificially derived from sophisticated structures and refer to unique structures that do not take place in nature. Herein, the basic concept of meta (meta means beyond in Greek) implies something that goes beyond naturally occurring substances. Generally, materials have a positive Poisson's ratio. Unlike general materials, Auxetics are structures or materials that have a negative Poisson's ratio. In terms of general materials, it is noted that while elongating along the x axis, the length in the y axis is decreased. Interestingly, in terms of the auxetic structure, while it expands along the x axis, y axis also expands simultaneously. In other words, elongation occurs in both directions, causing a rapid decrease in volume.[1][2]


where, ε(trans) is the transverse strain and ε(axial) is the axial strain.

Auxetics can be single molecules, crystals, or a particular structure of macroscopic matter.[3][4] Expansion structures of Auxetics are being attempted in a variety of fields. Typical studies are being conducted on impact protection, medical devices, textiles, and sound vibration control. In terms of impact protection, Auxetic materials are appropriate for use in protective equipment such as body armor, helmets, and knee pads. This is because it is able to absorb energy more effectively than traditional materials. It is also actively studied in devices such as medical stents or implants. This is because its unique properties can improve the performance and longevity of stents or implants. Auxetic fabrics can be used to create comfortable and flexible clothing that conventional materials cannot embody, as well as technical fabrics for applications such as aerospace and sports equipment. Finally, as for the sound and vibration control field, Auxetic materials can be used to create acoustic meta-materials for controlling sound and vibration in diverse applications.

Meanwhile, research using auxetic structures is also ongoing in the microscopic world. Unlike the general belief that auxeticity is rarely shown in crystalline solids, most of the cubic elemental metals show when they are stretched along the [110] direction. As an example, both compliance coefficients (i.e. s11 and s12) of Zn single crystals have the same sign. As a result, as for θ = 0, ν12 = −s12/s11 around equals −0.073 < 0, so the Poisson’s ratio of mono-crystalline Zn in its underlying plane is negative. For these metals, the auxeticity allows for the existence, in the orthogonal lateral direction, of positive Poisson’s ratios until the stability limit of 2 for cubic crystals. Such metals were expected to allow for electrodes that exponentially increase the response of piezoelectric sensors.[5]


The term auxetic derives from the Greek word auxetikos (αὐξητικός) which means 'that which tends to increase' and has its root in the word auxesis (αὔξησις), meaning 'increase' (noun). This terminology was coined by Professor Ken Evans of the University of Exeter.[6][4] 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"[3] 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.[7] Recently, cells were shown to display a biological version of auxeticity under certain conditions. [8]

Designs of composites with inverted hexagonal periodicity cell (auxetic hexagon), possessing negative Poisson ratios, were published in 1985.[9]

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.[10] 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.


Typically, auxetic materials have low density, which is what allows the hinge-like areas of the auxetic microstructures to flex.[11]

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[12][13][14] and prosthetic feet with human-like toe joint properties.[15]

Auxeticity is also common in biological materials. The origin of auxeticity is very different in biological materials than the materials discussed above. One of the example is nuclei of mouse embryonic stem cells in transition state. A model has been developed by Tripathi et. al [16] to explain it.


In footwear, auxetic design allows the sole to expand in size while walking or running, thereby increasing flexibility.

Examples of auxetic materials include:

Production of auxetic metamaterials through the introduction of patterned microstructural cuts using direct laser cutting. The thin rubber surface with perforated architecture covers a spherical surface (orange)[35]
  • Tailored structures designed to exhibit special designed Poisson's ratios.[36][37][38][39][40][41]
  • Chain organic molecules. Recent researches revealed that organic crystals like n-paraffins and similar to them may demonstrate an auxetic behavior.[42]

See also[edit]


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