# Design and Optimization of Lightweight Lithium-Ion Battery Protector with 3D Auxetic Meta Structures

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## Abstract

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## 1. Introduction

_{2}emissions in the environment [2]. According to Novizayanti et al. [3], the three most prioritized factors in choosing electric cars in Indonesia are vehicle range, price, and speed. This new field of use and demand from the market poses new safety challenges due to the difference in external elements that the lithium-ion battery will experience during operation and can potentially cause accidents and danger to passengers. A traffic accident could expose both passengers and the rescue party to new hazards [4]. Burning is the most common accident associated with batteries in both cars and planes [5,6].

## 2. Cell Materials, Methods, and Result

#### 2.1. Cell Validation

#### 2.1.1. Cell Validation Modeling

#### 2.1.2. Cell Validation Result

#### 2.2. Cell Modeling

#### 2.2.1. Geometry and Meshing

#### 2.2.2. Orthogonal Array

#### 2.2.3. Material and Contact Modeling

#### 2.3. Cell Optimization Result and Discussion

## 3. Battery System Materials, Methods, and Results

#### 3.1. Battery Validation

#### 3.1.1. Battery Validation Modeling

#### 3.1.2. Battery Validation Result

#### 3.2. System Modeling

#### 3.3. Result and Discussion

**second configuration**. Figure 19 shows the illustration of the second configuration.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The general configuration of double-U structure simulation; impactor as blue plane, double-U structure as pink solid, floor as turquoise plane.

**Figure 2.**Geometry parameters of the 2D double-U structure [18].

**Figure 3.**Experimental true stress–true strain curve of SS316L [18].

**Figure 5.**Reference’s experimental results (

**left**), reference’s numerical results (

**middle**), and writer’s numerical results (

**right**) of quasistatic compression of double-U structure.

**Figure 8.**The general configuration of battery simulation; indenter as purple sphere, battery as pink box, floor as brown plane.

**Figure 10.**Experimental stress–volumetric strain curve through the thickness unconfined compression [27].

**Figure 15.**Upper and lower plate dimensions [25].

**Table 1.**Double-U cell’s geometry [18].

Parameter | Value | Unit |
---|---|---|

${\theta}_{1}$ | 61 | $\mathrm{degree}$ |

${\theta}_{2}$ | 31 | $\mathrm{degree}$ |

${h}_{1}$ | 18 | $\mathrm{mm}$ |

${h}_{2}$ | 6 | $\mathrm{mm}$ |

$l$ | 10 | $\mathrm{mm}$ |

$b$ | 1 | $\mathrm{mm}$ |

$\mathrm{Thickness}$ | 1 | $\mathrm{mm}$ |

Time (ms) | Velocity (According to Final Velocity) |
---|---|

0 | 0 |

1 | 10% |

2 | 90% |

3 | 100% |

**Table 3.**SS316L material properties [18].

Variable | Value | Unit |
---|---|---|

Density $\left(\rho \right)$ | $8\times {10}^{-6}$ | $\mathrm{Kg}/{\mathrm{mm}}^{3}$ |

Modulus of Elasticity $\text{}(E$) | 200 | $\mathrm{GPa}$ |

Yield Strength $({\sigma}_{ys}$) | 500 | $\mathrm{MPa}$ |

Poisson’s Ratio $(v$) | 0.3 |

Index | Variables | Level | |||
---|---|---|---|---|---|

1 | 2 | 3 | 4 | ||

A | Geometry | DAA | DUH | RE-A | RE-B |

B | $\mathrm{L}\text{}(\mathrm{mm}$) | 9 | 10 | 11 | 12 |

C | $\mathrm{W}\text{}(\mathrm{mm}$) | 15 | 16 | 17 | 18 |

D | $\mathrm{H}\text{}(\mathrm{mm}$) | 1.5 | 2 | 2.5 | 3 |

E | $\mathrm{Thickness}\text{}(\mathrm{mm}$) | 1 | 1.33 | 1.66 | 2 |

Variables | Noise | ||
---|---|---|---|

Increasing (+1) | Nominal | Reducing (−1) | |

Impactor Velocity (m/s) | 5.25 | 5 | 4.75 |

Material Density | 105% Rho | 100% Rho | 95% Rho |

Model No. | Factors | ||||
---|---|---|---|---|---|

Geometry | $\mathbf{L}\text{}\left(\mathbf{m}\mathbf{m}\right)$ | $\mathbf{W}\text{}\left(\mathbf{m}\mathbf{m}\right)$ | $\mathbf{H}\text{}\left(\mathbf{m}\mathbf{m}\right)$ | $\mathbf{Thickness}\text{}\left(\mathbf{m}\mathbf{m}\right)$ | |

1 | DAA | 9 | 15 | 1.5 | 1 |

2 | DAA | 10 | 16 | 2 | 1.33 |

3 | DAA | 11 | 17 | 2.5 | 1.67 |

4 | DAA | 12 | 18 | 3 | 2 |

5 | DUH | 9 | 18 | 2 | 1.67 |

6 | DUH | 10 | 17 | 1.5 | 2 |

7 | DUH | 11 | 16 | 3 | 1 |

8 | DUH | 12 | 15 | 2.5 | 1.33 |

9 | RE-A | 9 | 17 | 3 | 1.33 |

10 | RE-A | 10 | 18 | 2.5 | 1 |

11 | RE-A | 11 | 15 | 2 | 2 |

12 | RE-A | 12 | 16 | 1.5 | 1.67 |

13 | RE-B | 9 | 16 | 2.5 | 2 |

14 | RE-B | 10 | 15 | 3 | 1.67 |

15 | RE-B | 11 | 18 | 1.5 | 1.33 |

16 | RE-B | 12 | 17 | 2 | 1 |

Variable | Value | Unit |
---|---|---|

Density $(\rho $) [28] | $4.43\times {10}^{-6}$ | $\mathrm{Kg}/{\mathrm{mm}}^{3}$ |

Modulus of Elasticity $(E$) [28] | 110.32 | $\mathrm{GPa}$ |

Yield Strength $({\sigma}_{ys}$) [29] | 0.93 | $\mathrm{GPa}$ |

Poisson’s Ratio $(v$) [28] | 0.31 | |

Failure Strain $({\epsilon}_{f}$) [30] | 0.2 | |

Cowper Symond’s Constant (D) [30] | 200 | |

Cowper Symond’s Constant (q) [30] | 15 |

Geometry | $\mathbf{L}\text{}\left(\mathbf{m}\mathbf{m}\right)$ | $\mathbf{W}\text{}\left(\mathbf{m}\mathbf{m}\right)$ | $\mathbf{H}\text{}\left(\mathbf{m}\mathbf{m}\right)$ | $\mathbf{Thickness}\text{}\left(\mathbf{m}\mathbf{m}\right)$ |
---|---|---|---|---|

DUH | 10 | 17 | 3 | 2 |

Parameters | Existing (Average) | Prediction | Verification | Difference | |
---|---|---|---|---|---|

Verif- Existing | Verif- Prediction | ||||

$\mathrm{Mean}\text{}\mathrm{SEA}\text{}(\mathrm{kJ}/\mathrm{kg}$) | 19.29 | 40.62 | 42.19 | 22.91 | 1.57 |

$\mathrm{S}/\mathrm{N}\text{}\mathrm{Ratio}\text{}(\mathrm{dB}$) | 24.58 | 33.76 | 32.45 | 7.87 | −1.31 |

**Table 10.**Material property of battery’s foam [27].

Variable | Value | Unit |
---|---|---|

Density $(\rho $) | $1.76\times {10}^{-6}$ | $\mathrm{Kg}/{\mathrm{mm}}^{3}$ |

Modulus of Elasticity $\text{}(E$) | 500 | $\mathrm{MPa}$ |

Tensile Cut-off | 55.58 | $\mathrm{MPa}$ |

Poisson’s Ratio $(v$) | 0.01 | |

DAMP Factor | 0.5 |

**Table 11.**Al2024-T351 material properties [24].

Variable | Value | Unit |
---|---|---|

Density $(\rho $) | $2.78\times {10}^{-6}$ | $\mathrm{Kg}/{\mathrm{mm}}^{3}$ |

Modulus of Elasticity $(E$) | 73.1 | $\mathrm{GPa}$ |

Yield Strength $({\sigma}_{ys}$) | 0.324 | $\mathrm{GPa}$ |

Poisson’s Ratio $(v$) | 0.33 | |

Failure Strain $({\epsilon}_{f}$) | 0.2 |

Config. | Cell Resize | Cell Arrangement | Total Dimension | Structural Volume |
---|---|---|---|---|

First Config. | 100% length | $11\times 11\times 1$ cells | $189\times 189\times 12\text{}\mathrm{mm}$ | $\mathrm{96,484.51}{\text{}\mathrm{mm}}^{3}$ |

Second Config. | 200% length | $5\times 5\times 1$ cells | $174\times 174\times 24\text{}\mathrm{mm}$ | $\mathrm{168,488.23}{\text{}\mathrm{mm}}^{3}$ |

Third Config. | 300% length | $3\times 3\times 1$ cells | $159\times 159\times 36\text{}\mathrm{mm}$ | $\mathrm{218,307.51}{\text{}\mathrm{mm}}^{3}$ |

Parameter | Noise | |||
---|---|---|---|---|

+1 | 0 | −1 | Simplified | |

$\mathrm{Volume}\text{}\left({\mathrm{mm}}^{3}\right)$ | 1187.43 | |||

$\mathrm{Mass}\text{}\left(\mathrm{g}\right)$ | 5.52 | 5.26 | 5.00 | 5.26 |

$\mathrm{EA}\text{}\mathrm{Total}\text{}\left(\mathrm{J}\right)$ | 214 | 225 | 225 | 190 |

$\mathrm{SEA}\text{}\left(\mathrm{kJ}/\mathrm{Kg}\right)$ | 38.75 | 42.78 | 45.03 | 36.13 |

Configuration | Volume $\left(\mathbf{m}{\mathbf{m}}^{3}\right)$ | Mass $\left(\mathbf{K}\mathbf{g}\right)$ | EA $\left(\mathbf{J}\right)$ | SEA $(\mathbf{k}\mathbf{J}/\mathbf{K}\mathbf{g})$ | Max Battery Deform $\left(\mathbf{m}\mathbf{m}\right)$ |
---|---|---|---|---|---|

First Configuration | 96,484.51 | 0.43 | 531.00 | 1.24 | FAIL |

Second Configuration | 168,488.23 | 0.75 | 591.00 | 0.79 | 1.92 |

Third Configuration | 218,307.51 | 0.97 | 585.00 | 0.61 | 1.36 |

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**MDPI and ACS Style**

Biharta, M.A.S.; Santosa, S.P.; Widagdo, D.; Gunawan, L.
Design and Optimization of Lightweight Lithium-Ion Battery Protector with 3D Auxetic Meta Structures. *World Electr. Veh. J.* **2022**, *13*, 118.
https://doi.org/10.3390/wevj13070118

**AMA Style**

Biharta MAS, Santosa SP, Widagdo D, Gunawan L.
Design and Optimization of Lightweight Lithium-Ion Battery Protector with 3D Auxetic Meta Structures. *World Electric Vehicle Journal*. 2022; 13(7):118.
https://doi.org/10.3390/wevj13070118

**Chicago/Turabian Style**

Biharta, Michael Alfred Stephenson, Sigit Puji Santosa, Djarot Widagdo, and Leonardo Gunawan.
2022. "Design and Optimization of Lightweight Lithium-Ion Battery Protector with 3D Auxetic Meta Structures" *World Electric Vehicle Journal* 13, no. 7: 118.
https://doi.org/10.3390/wevj13070118