# Resilient Mechanical Metamaterial Based on Cellulose Nanopaper with Kirigami Structure

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Fabrication of Nanopapers from Aqueous CNF Dispersion

#### 2.2. Implementation of Cut Patterns of Kirigami Structure by Laser Processing

#### 2.3. Evaluation of Resilience by Residual Strain in the Iterative Tensile Test

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagrams of (

**a**) the aqueous CNF dispersion container to dry the CNF dispersion, and (

**b**–

**d**) Kirigami structures: (

**b**) The specimen with a cut pattern of staggered dashed lines (or “Amikazari) is represented by the blue lines. (

**c**) The pattern consists of a unit where the specific set of ${L}_{x}$, ${L}_{y}$, ${S}_{x}$, and H determines the pattern, whereas w and h determine the size of specimen. The gaps of 3 mm on each side of the specimen are in direct contact with the chucks of the tensile testing system. (

**d**) Basic and versatile design variation of the Kirigami pattern with the round-edge cutting line is schematically shown. It should be noted here that the design is based on the center lines of a laser processing trajectory and the actual cut lines include round edges have finite widths.

**Figure 2.**Sequential snapshots in the tensile loading to ${\epsilon}_{\mathrm{max}}=0.5$ without iteration (i.e., ${N}_{\mathrm{c}}=1$) for different scale parameters s. Six sets of subfigures in each of (

**a**–

**d**) show the strain $\epsilon =0,0.1,0.2,0.3,0.4$, and 0.5 from left to right. A unit pair of subfigures for a specific strain value indicate the top and side views of the specimen. The scale bars indicate 10 mm.

**Figure 3.**Sequential snapshots in the iterative tensile loading cycles of specimens with $s=3$ for different maximum strains ${\epsilon}_{\mathrm{max}}$. Four sets of subfigures in each of (

**a**–

**d**) show the number ${N}_{\mathrm{c}}=1,10,100$, and 1000 of tensile loading cycles, respectively—from left to right. A unit pair of subfigures for a specific ${N}_{\mathrm{c}}$ indicate the top and side views of the specimen. It should be noted that top views correspond to the state of ${\epsilon}_{\mathrm{max}}$ whereas the side views correspond to the original end-to-end distance state. The scale bars indicate 10 mm.

**Figure 4.**The residual strain as a function of (

**a**) the number of tensile loading cycle, (

**b**) the maximum strain in a cycle, and (

**c**) the unit scale s of Kirigami structure. The parameter “s” is defined in the Section 2.

**Figure 5.**The characteristics of Kirigami design based on the cut lines with round edges: (

**a**) Digital camera images of cut lines based on the sharp edge and the round edge on nanopapers. (

**b**) Comparison of residual strain by Kirigami patterns with round edge and normal edge. The scale of Kirigami patterns is $s=3$ and the maximum strain is ${\epsilon}_{\mathrm{max}}=0.5$. The error bars indicate the maximum and minimum values in the three trials of different specimens. (

**c**,

**d**) Sequential snapshots in the tensile tests of Kirigami patterns with round edges with scale parameter $s=3$, where (

**c**) the tensile loading to ${\epsilon}_{\mathrm{max}}=0.5$ without iteration (i.e., ${N}_{\mathrm{c}}=1$), and (

**d**) iterative tensile loading cycles with ${\epsilon}_{\mathrm{max}}=0.5$. The unit pair of subfigures for a specific strain value in (

**c**,

**d**) indicate the top and side views of the specimen. It should be noted that side views in (

**c**) indicate the tensile state and those in (

**d**) indicate the state of the original end-to-end distance, while top views in (

**d**) indicate the state of ${\epsilon}_{\mathrm{max}}$. The scale bars indicate 10 mm.

**Table 1.**The combination of parameters of $s,w,h,H,{L}_{x},{L}_{y}$, and ${S}_{x}$ of the design of the Kirigami structure. The definitions of parameters are schematically shown in Figure 1b,c. H is defined as the initial specimen length relevant to the evaluation of strains. s indicates the ratio of the unit size of the Kirigami structure to the standard one in the experiments without the variation in shape. h indicates the whole specimen length.

s (-) | w $\left(\mathbf{mm}\right)$ | h $\left(\mathbf{mm}\right)$ | H $\left(\mathbf{mm}\right)$ | ${\mathit{L}}_{\mathit{x}}$ $\left(\mathbf{mm}\right)$ | ${\mathit{L}}_{\mathit{y}}$ $\left(\mathbf{mm}\right)$ | ${\mathit{S}}_{\mathit{x}}$ $\left(\mathbf{mm}\right)$ |
---|---|---|---|---|---|---|

1 | 32.0 | 60.0 | 49.2 | 4.2 | 1.2 | 0.6 |

2 | 48.0 | 8.4 | 2.4 | 1.2 | ||

3 | 46.8 | 12.6 | 3.6 | 1.8 | ||

5 | 48.0 | 21.0 | 6.0 | 3.0 |

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**MDPI and ACS Style**

Fujita, T.; Nakagawa, D.; Komiya, K.; Ohira, S.; Hanasaki, I.
Resilient Mechanical Metamaterial Based on Cellulose Nanopaper with Kirigami Structure. *Nanomaterials* **2022**, *12*, 2431.
https://doi.org/10.3390/nano12142431

**AMA Style**

Fujita T, Nakagawa D, Komiya K, Ohira S, Hanasaki I.
Resilient Mechanical Metamaterial Based on Cellulose Nanopaper with Kirigami Structure. *Nanomaterials*. 2022; 12(14):2431.
https://doi.org/10.3390/nano12142431

**Chicago/Turabian Style**

Fujita, Tadaoki, Daisuke Nakagawa, Kazuma Komiya, Shingo Ohira, and Itsuo Hanasaki.
2022. "Resilient Mechanical Metamaterial Based on Cellulose Nanopaper with Kirigami Structure" *Nanomaterials* 12, no. 14: 2431.
https://doi.org/10.3390/nano12142431