# Investigation on Microstructure of Beetle Elytra and Energy Absorption Properties of Bio-Inspired Honeycomb Thin-Walled Structure under Axial Dynamic Crushing

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Specimens Selection and Preparation

#### 2.2. Scanning Electron Microscopy

#### 2.3. Microstructures of Fiber Layers

#### 2.4. Microstructure of the Honeycombs

## 3. Beetle-Based BHS

#### 3.1. Structural Crashworthiness Criteria

#### 3.2. The Design of BHSs

_{i}= 1 mm) of each level of hierarchy remain the same. In this study, three kinds of BHSs with different filling methods inspired by beetle elytra internal structure were developed as shown in Figure 6. The BHS with original honeycombs is a conventional cellular structure. BHS-1 and BHS-2 are honeycombs with first order filling mode and second order filling mode, respectively. To investigate the energy absorption properties of the three kinds of hierarchy level, structures with equal areas of cross-section and equal length have been established. The geometric size of honeycombs strongly affect the mechanical behavior of the structure under crushing. In this work, the distance d which means the wall and the center of one hexagonal unit cell is chosen as the design variables. It ranges from 0 mm to 8 mm in BHS-1 with the interval of 2 mm and ranges from 0 mm to 3 mm in BHS-2 with the interval of 1 mm.

#### 3.3. Mechanical Behavior of the BHS’s Material

^{3}kg/m

^{3}, the initial yield stress of 162 MPa, a Young’s modulus of 67.9 GPa, the ultimate stress of 191 MPa, and Poisson’s ratio of 0.3 (Table 1) [39]. The models were established with MAT24 in Ls-Dyna (Livermore Software Technology Corp., Livermore, CA, USA). This above material shows strain rate insensitivity, and the true stress-strain value of AA6063 is showed in Figure 7 [40].

## 4. Numerical Simulations

#### 4.1. Finite Element Modeling

#### 4.2. Validation of the FE Model

#### 4.3. Comparison of Energy Absorption Properties of BHS-1 with Different Filling Cell Size

_{1}= 8 mm, while the mean crushing force of cases of d

_{1}= 6 mm and d

_{1}= 8 mm are very similar. The same trend of absorbed energy of different filling cell size is apparent, as shown in Figure 12b. The BHS without filling cell absorbed the minimum internal energy. With the increase of the filling cell size, the absorbed energy of BHS-1 is increased obviously. Although the internal energy is constantly growing, the trend of growth is slowing gradually. The internal energy of cases of d

_{1}= 6 mm and d

_{2}= 8 mm are both about 2000 J, and the different between them is not obvious. That means the case of d

_{1}= 6 mm and d

_{2}= 8 mm are very similar at the view of energy absorbing ability. Table 2 shows that the SEA of cell size of d

_{1}= 6 mm is 66.79% higher than that of d

_{1}= 0 mm and 15.48% higher than that of cell size of d

_{1}= 2 mm, respectively. Compression force efficiency of cell size of d

_{1}= 6 mm is 7.95% higher than that of cell size of d

_{1}= 0 mm and 4.16% lower than that of cell size of d

_{1}= 4 mm, respectively. In the view of SEA, the cell size of d

_{1}= 6 mm is better than other cell size.

#### 4.4. Comparison of Energy Aabsorption Characteristics of BHS-2 with Different Filling Cell Size

_{2}= 3 mm, while the gaps of crushing force between all cases are relatively close. The same trend of absorbed energy of different filling cell size is obvious, as shown in Figure 13b. The BHS-1with d

_{1}= 6 mm absorbed the minimum impact energy. With the increase of the filling cell size, the absorbed energy of BHS-2 is increased obviously. Unlike the trend of energy absorbing ability of BHS-1, the gaps of internal energy curves of different sizes of BHS-2 change closely with the increase of filling cell size. The internal energy of cases of d

_{2}= 0 mm and d

_{2}= 1 mm are 2000 J and 3000 J, respectively. The internal energy of cases of d

_{2}= 2 mm and d

_{2}= 3 mm are both more than 3500 J. Table 3 shows that the SEA of the cell size of d

_{2}= 3 mm is 44.02% higher than that of d

_{2}= 0 mm and 4.86% higher than that of cell size of d

_{2}= 2 mm, respectively. Compression force efficiency of cell size of d

_{2}= 3 mm is 11.72% higher than that of cell size of d

_{2}= 0 mm and 5.79% higher than that of cell size of d

_{2}= 2 mm, respectively. In the view of SEA and CFE, the cell size of d

_{2}= 3 mm is better than the other cell sizes.

_{1}= 6 mm and BHS-2 with d

_{2}= 2 mm under low velocity loading are shown in Figure 14. The buckling of hollow thin-walled tubes occurs from the top to the bottom along the vertical direction in all numerical simulations. The red circle means the three connections of honeycomb corner in BHS-1, while it is observed that the stress of the connections is higher than that of other structures. In BHS-2, it is difficult to obtain that the stress changes of honeycomb corner. The structure is crushing and the wall of the corner is linked together.

#### 4.5. Comparison of Energy Absorption Properties of BHSs with Different Impact Velocity

_{1}= 6 mm and d

_{2}= 8 mm are very close. Figure 15b shows the energy absorption ability of BHS-2 increase moderately with the growth of the impact speed. It could be obtained that the impact velocity increases 5 m/s, the internal energy will increase by 0.5%–4%. It can be also observed that the energy absorption property of case of d

_{2}= 3 mm is the best of all cases.

## 5. Conclusions and Discussion

_{1}= 6 mm and d

_{2}= 8 mm are both about 2000 J, and the different between them is not obvious. The internal absorbing ability of cases of d

_{1}= 6 mm and d

_{2}= 8 mm are both better than other cases. Unlike the trend of energy absorbing ability of BHS-1, the gaps of internal energy curves of different sizes of BHS-2 change slightly with the increase of filling cell size. The absorbed energy of case of d

_{2}= 3 mm which more than 3500 J has the best energy-absorbing property. Then the parameter study was carried out to study the influence of the impact velocity on energy absorption behaviors of BHS. The result shows that the impact velocity increases 5 m/s, the internal energy of BHS-1 and BHS-2 will increase by 2%–5% and 0.5%–4%, respectively.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The beetle elytra and its microstructure: (

**a**) the beetle Allomyrina dichotoma; (

**b**) micromorphology of honeycomb structure with columns. “Reproduced with permission from [CARBOHYD POLYM]. Elsevier, 2013.”.

**Figure 2.**The cross-section view SEM (scanning electron microscopy) images of fiber layers from the C. septempunctata L. elytra. (

**a**–

**c**) show the full fiber layers; (

**d**) shows higher magnification sections of fiber layers; (

**e**) shows the thickness of the exocuticle (ex) and the endocuticle (en) in the C. septempunctata L. elytra; (

**f**) shows higher magnification sections of endocuticle.

**Figure 3.**Cross-sectional SEM images of the C. septempunctata L. elytra. (

**a**) seta and pole canal in the cuticle and (

**b**) deformation of fiber layers (in white circle).

**Figure 4.**Honeycomb structures in the C. septempunctata L. elytra. (

**a**,

**b**) columns in the elytra; (

**c**) column partially immedrsed in the foam; (

**d**) internal structure of a column; (

**e**) spiral surface of acolumn; (

**f**) column and seta.

**Figure 5.**Unit cell of an evolved honeycomb: (

**a**) the original cell; (

**b**) the first order; and (

**c**) the second order.

**Figure 6.**Three types of bionic structures with different filling methods of honeycombs: (

**a**) BHS, original honeycombs; (

**b**) BHS-1, filling mode with first-order; (

**c**) BHS-2, filling mode with second-order.

**Figure 10.**Comparison of deformation patterns of structure between experimental and numerical results.

**Figure 11.**Comparison of force versus displacement curves between experimental and numerical results.

**Figure 12.**Comparisons of absorbed energy properties of BHS-1 with different filling honeycombs size: (

**a**) crushing force versus displacement curves; (

**b**) absorbed energy versus displacement curves.

**Figure 13.**Comparisons of absorbed energy properties of BHS-2 with different filling honeycombs size: (

**a**) crushing force versus displacement curves; (

**b**) absorbed energy versus displacement curves.

**Figure 15.**The absorbed energy of bionic honeycomb structures with different impact velocity: (

**a**) BHS-1; (

**b**) BHS-2.

Density (kg/m^{3}) | Young’s Modulus (GPa) | Yield Stress (MPa) | Ultimate Stress (MPa) | Poisson’s Ratio |
---|---|---|---|---|

2700 | 67.9 | 162 | 191 | 0.3 |

Cell Size | P_{m}/kN | P_{max}/kN | E_{int}/kJ | m/kg | SEA (kJ/kg) | CFE/% |
---|---|---|---|---|---|---|

0 | 23.263 | 31.714 | 0.919 | 0.074 | 12.421 | 73.353 |

2 | 36.860 | 45.620 | 1.471 | 0.082 | 17.939 | 80.801 |

4 | 48.519 | 58.723 | 1.919 | 0.091 | 21.088 | 82.624 |

6 | 52.237 | 65.969 | 2.051 | 0.099 | 20.717 | 79.185 |

8 | 52.852 | 66.545 | 2.063 | 0.108 | 19.101 | 79.423 |

Cell Size | P_{m}/kN | P_{max}/kN | E_{int}/kJ | m/kg | SEA (kJ/kg) | CFE/% |
---|---|---|---|---|---|---|

0 | 52.2375 | 65.9690 | 2.051 | 0.099 | 20.717 | 79.185 |

1 | 75.0829 | 93.9902 | 2.930 | 0.112 | 26.161 | 79.884 |

2 | 95.3310 | 114.002 | 3.699 | 0.130 | 28.454 | 83.622 |

3 | 112.560 | 127.234 | 4.386 | 0.147 | 29.837 | 88.467 |

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## Share and Cite

**MDPI and ACS Style**

Du, J.; Hao, P.
Investigation on Microstructure of Beetle Elytra and Energy Absorption Properties of Bio-Inspired Honeycomb Thin-Walled Structure under Axial Dynamic Crushing. *Nanomaterials* **2018**, *8*, 667.
https://doi.org/10.3390/nano8090667

**AMA Style**

Du J, Hao P.
Investigation on Microstructure of Beetle Elytra and Energy Absorption Properties of Bio-Inspired Honeycomb Thin-Walled Structure under Axial Dynamic Crushing. *Nanomaterials*. 2018; 8(9):667.
https://doi.org/10.3390/nano8090667

**Chicago/Turabian Style**

Du, Jianxun, and Peng Hao.
2018. "Investigation on Microstructure of Beetle Elytra and Energy Absorption Properties of Bio-Inspired Honeycomb Thin-Walled Structure under Axial Dynamic Crushing" *Nanomaterials* 8, no. 9: 667.
https://doi.org/10.3390/nano8090667