# Cellular Auxetic Structures for Mechanical Metamaterials: A Review

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Cellular Auxetic Materials and Structures

#### 2.1. Re-Entrant Structures

_{s}is the intrinsic Young’s modulus of the material forming the cell walls.

#### 2.2. Chiral Structures

^{®}(Stratasys, Eden Prairie, MN, USA), a rubber-like additive manufacturing filament [89]. Some potential applications of the chiral models are proposed in the works of Airoldi et al. [90,91] and Budarapu et al. [92]. Airoldi et al. produced morphing wings for a variable camber wing-box using chiral honeycombs made of composite laminates. Budarapu et al. [92] proposed a framework to design an aircraft wing structure and analysed morphing air foils with chiral structure. Further studies could be carried out using an integrated approach comprising finite element modelling and additive manufacturing coupled with high-throughput methods, which could potentially accelerate the translation of chiral lattices into real-world products.

#### 2.3. Crumpled and Perforated Sheets Models

#### 2.4. Rotational (Semi-) Rigid Structures

## 3. Applications of Auxetic Structures

- Poisson’s ratio being negative or zero.
- Large shear resistance.
- Hardness improvement.
- Lower fatigue crack propagation.
- Large toughness and modulus resilience.
- Vibration absorption.

#### 3.1. Sports Science

#### 3.2. Medical Industry

#### 3.3. Sensors and Actuators

#### 3.4. Textiles

#### 3.5. Defence

## 4. Conclusions

#### 4.1. Remarks

_{4}, exhibiting a structure similar to α-cristobalite, but possessing a lower crystal symmetry due to its stoichiometry, is analytically predicted to have a Poisson’s ratio of –0.28, but needs further investigations of its auxetic behavior [15,166] Developments in additive manufacturing and computing have led the research community to the brink of a paradigm shift in the materials development and design cycle.

#### 4.2. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Classification of cellular auxetic metamaterials. Adapted from [21].

**Figure 5.**Classification of cellular auxetic metamaterials. Adapted from [21].

**Figure 9.**Hexagonal unit cell described by Masters and Evans [50].

**Figure 12.**Experimental and numerical image of the 6-hole Bucklicrystal: (

**a**) isometric and cross-sectional views of the undeformed crystal from micro-CT (micro computed tomography) X-ray imaging machine, and (

**b**) isometric and cross-sectional views of the uniaxially compressed crystal from micro-CT volumetric data sets [71,72].

**Figure 14.**(

**a**) Scanning electron microscope (SEM) image of the microstructure of polytetrafluroethylene (PTFE). (

**b**) Low vacuum scanning electron microscopy (LVSEM) micrograph of GUR

^{®}1050 ultra-high molecular weight polyethylene (UHMWPE) powder showing fibrils and nodules of approximately 1 μm size [79,80,81].

**Figure 15.**(

**a**) 2D hexachiral and 2D meta-chiral systems with different number of ribs attached to each node (

**b**) six ribs, (

**c**) four ribs, and (

**d**) three ribs [21].

**Figure 17.**Classification and representative structures of periodic chiral structures [84].

**Figure 18.**Origami metamaterials. (

**a**) ‘zipper’-coupled tube system. (

**b**) The geometrical design of Origami structure [100].

**Figure 20.**Rotating rhombi and rotating parallelogram systems; adapted from [108].

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Kelkar, P.U.; Kim, H.S.; Cho, K.-H.; Kwak, J.Y.; Kang, C.-Y.; Song, H.-C.
Cellular Auxetic Structures for Mechanical Metamaterials: A Review. *Sensors* **2020**, *20*, 3132.
https://doi.org/10.3390/s20113132

**AMA Style**

Kelkar PU, Kim HS, Cho K-H, Kwak JY, Kang C-Y, Song H-C.
Cellular Auxetic Structures for Mechanical Metamaterials: A Review. *Sensors*. 2020; 20(11):3132.
https://doi.org/10.3390/s20113132

**Chicago/Turabian Style**

Kelkar, Parth Uday, Hyun Soo Kim, Kyung-Hoon Cho, Joon Young Kwak, Chong-Yun Kang, and Hyun-Cheol Song.
2020. "Cellular Auxetic Structures for Mechanical Metamaterials: A Review" *Sensors* 20, no. 11: 3132.
https://doi.org/10.3390/s20113132