# An introduction to Auxetic Metamaterials

Auxetic metamaterials are a class of metamaterials that possess auxetic property. The term auxetic refers to the materials with a Negative Poisson’s ratio (NPR), contrary to the naturally occurring materials with a positive Poisson’s ratio. Generally, naturally available materials get compressed in the lateral direction when stretched in the longitudinal direction. Contrary to this, if auxetic materials are stretched longitudinally, they stretch laterally too. It results in different deformation mechanisms for auxetic and non-auxetic materials.
The structural manipulations are responsible for the auxetic behavior. It has nothing to do with the chemical composition of a material. A tailored material property can be obtained using the auxetic property.

So far, many unit cells have been developed or identified that possess auxetic behavior. These include re-entrant structures, rotating squares, chiral structures, and many more. Few research works have been carried out on combining two different unit cells to yield a modified one.

The present discussion will mainly focus on the re-entrant unit cell structure. Later, a demonstration of the rotating squares unit cell will also be carried out with the help of a model created by the author.

Poisson’s ratio is the fundamental property involved in the understanding of auxetic behavior, which is given as:

$$Poisson’s \hspace{1mm} ratio = – \frac{(Lateral \hspace{1mm} strain)}{(Longitudinal \hspace{1mm} strain)}$$

## Re-entrant Auxetic structure.

The undeformed shape of a re-entrant auxetic structure is shown in figure 1 below. Also, the deformed shape of a Re-entrant auxetic structure is shown in figure 2. In figure 2, it can be observed that a stretching provided in the vertical direction leads to stretching in the horizontal direction. This results in a Negative Poisson’s Ratio (NPR) of the materials – One can visualize it from video 1 (attached below).
In ordinary materials, the lateral and longitudinal strains are opposite. Hence, we get a positive value of Poisson’s ratio. In auxetic metamaterials, the lateral and longitudinal strains are of same nature, resulting in a negative value of Poisson’s ratio (refer to Video 1).

## A 3D unit cell of a Re-entrant structure.

The structure shown in figure 3 is a three-dimensional auxetic structure constructed using a re-entrant unit cell.

## Demonstration of Rotating square model

The deformation pattern of a rotating-square auxetic is presented in the video attached below. The white sheet of paper placed below the model shows the model’s size in the undeformed state. Upon applying stretching in the horizontal direction, a stretch is observed in the lateral direction—such deformation results in a negative Poisson’s ratio.

Categories: Metamaterials