# Investigation on the Energy-Absorbing Properties of Bionic Spider Web Structure

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model of the Orb Web

#### 2.1. Analysis of Spider Silk Deformation Energy Absorption

#### 2.2. Number of Diameter Lines and Number of Spiral Coils Study

## 3. Simulation Analysis of Energy Absorption of Bionic Spider Web

#### 3.1. Finite Element Modeling

#### 3.1.1. Simulation Model Construction and Boundary Condition Setting

#### 3.1.2. Parameter Settings of the Simulation Model

#### 3.2. Dynamic Response Process of Energy Absorption of Spider Web

#### 3.2.1. Deformation Analysis for Spider Web Simulation

#### 3.2.2. Analysis of Energy Absorption in Spider Web Simulation

#### 3.3. Spider Web Energy Absorption Effect Evaluation Index

#### 3.4. Simulation Test Data Analysis Based on the Response Surface Method

#### 3.4.1. Simulation Design and Results of the Effect of Cobweb Structure Parameters on Energy Absorption

#### 3.4.2. Total Energy Absorption Significance Analysis

#### 3.4.3. Establishing Regression Equations with a Normal Probability Distribution of Residuals

#### 3.4.4. Response Surface Analysis

#### 3.4.5. Prediction of the Highest Total Energy Absorption Parameter Combination

## 4. Conclusions

- (1)
- Spider web radial structure factors have a more significant impact on energy absorption than spiral structure factors. The total absorbed energy of a spider web is inversely proportional to the radial line length of the web.
- (2)
- The number of spiral lines and spiral spacing have negligible effects on the total energy absorption of spider webs. The radial line cross-sectional diameter and spiral cross-sectional diameter have insignificant effects on both complete energy absorption and peak stress.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) Standardized residual prediction. (

**b**) Standardized residual series. (

**c**) Residual distribution. (

**d**) Comparison of predicted and true values.

**Table 1.**Spider web simulation material parameter settings [17].

Material Properties | Numerical Value (after UV Curing) |
---|---|

Density (kg/m^{3}) | 1080 |

Young’s modulus (pa) | 1.8 × 10^{9} |

Poisson’s ratio | 0.392 |

Volumetric modulus of elasticity (Pa) | 2.78 × 10^{9} |

Shear modulus (Pa) | 6.465 × 10^{8} |

Yield strength (Pa) | 4.8 × 10^{7} |

Tangential modulus (Pa) | 200 |

Maximum Equivalent Plastic Strain | 0.5 |

Analysis Parameters | A | B | C | D | E |
---|---|---|---|---|---|

Minimum Value | 60 mm | 0.45 mm | 6 | 4 mm | 0.45 mm |

Center Value | 70 mm | 0.5 mm | 8 | 4.75 mm | 0.5 mm |

Maximum Value | 80 mm | 0.55 mm | 10 | 5.5 mm | 0.55 mm |

Experiment Number | A mm | B mm | C Circle | D mm | E mm | EA mJ |
---|---|---|---|---|---|---|

1 | 70 | 0.5 | 8 | 4.75 | 0.5 | 14.054 |

2 | 60 | 0.45 | 8 | 4.75 | 0.5 | 14.809 |

3 | 80 | 0.45 | 8 | 4.75 | 0.5 | 13.549 |

4 | 60 | 0.55 | 8 | 4.75 | 0.5 | 15.128 |

5 | 80 | 0.55 | 8 | 4.75 | 0.5 | 13.749 |

6 | 70 | 0.5 | 6 | 4 | 0.5 | 14.122 |

7 | 70 | 0.5 | 10 | 4 | 0.5 | 13.841 |

8 | 70 | 0.5 | 6 | 5.5 | 0.5 | 14.589 |

9 | 70 | 0.5 | 10 | 5.5 | 0.5 | 14.607 |

10 | 70 | 0.45 | 8 | 4.75 | 0.45 | 14.206 |

11 | 70 | 0.55 | 8 | 4.75 | 0.45 | 14.625 |

12 | 70 | 0.45 | 8 | 4.75 | 0.55 | 13.762 |

13 | 70 | 0.55 | 8 | 4.75 | 0.55 | 13.866 |

14 | 60 | 0.5 | 6 | 4.75 | 0.5 | 14.848 |

15 | 80 | 0.5 | 6 | 4.75 | 0.5 | 14.394 |

16 | 60 | 0.5 | 10 | 4.75 | 0.5 | 15.232 |

17 | 80 | 0.5 | 10 | 4.75 | 0.5 | 14.318 |

18 | 70 | 0.5 | 8 | 4 | 0.45 | 14.065 |

19 | 70 | 0.5 | 8 | 5.5 | 0.45 | 14.618 |

20 | 70 | 0.5 | 8 | 4 | 0.55 | 14.113 |

21 | 70 | 0.5 | 8 | 5.5 | 0.55 | 14.610 |

22 | 70 | 0.45 | 6 | 4.75 | 0.5 | 13.979 |

23 | 70 | 0.55 | 6 | 4.75 | 0.5 | 14.157 |

24 | 70 | 0.45 | 10 | 4.75 | 0.5 | 14.647 |

25 | 70 | 0.55 | 10 | 4.75 | 0.5 | 14.285 |

26 | 60 | 0.5 | 8 | 4 | 0.5 | 14.476 |

27 | 80 | 0.5 | 8 | 4 | 0.5 | 13.749 |

28 | 60 | 0.5 | 8 | 5.5 | 0.5 | 15.065 |

29 | 80 | 0.5 | 8 | 5.5 | 0.5 | 13.804 |

30 | 70 | 0.5 | 6 | 4.75 | 0.45 | 14.144 |

31 | 70 | 0.5 | 10 | 4.75 | 0.45 | 14.672 |

32 | 70 | 0.5 | 6 | 4.75 | 0.55 | 14.168 |

33 | 70 | 0.5 | 10 | 4.75 | 0.55 | 14.844 |

34 | 60 | 0.5 | 8 | 4.75 | 0.45 | 14.844 |

35 | 80 | 0.5 | 8 | 4.75 | 0.45 | 13.577 |

36 | 60 | 0.5 | 8 | 4.75 | 0.55 | 14.709 |

37 | 80 | 0.5 | 8 | 4.75 | 0.55 | 13.529 |

38 | 70 | 0.45 | 8 | 4 | 0.5 | 13.995 |

39 | 70 | 0.55 | 8 | 4 | 0.5 | 13.948 |

40 | 70 | 0.45 | 8 | 5.5 | 0.5 | 14.905 |

41 | 70 | 0.55 | 8 | 5.5 | 0.5 | 14.654 |

Source of Variance | Quadratic Sum | F-Value | p-Value | Significance |
---|---|---|---|---|

Models | 7.134452234 | 5.379313901 | <0.0001 | Highly significant |

A | 4.41630225 | 66.59705695 | <0.0001 | Highly significant |

B | 0.0196 | 0.295564534 | 0.5915 | Not significant |

C | 0.261376563 | 3.94151234 | 0.0582 | Not significant |

D | 1.310452563 | 19.7613929 | 0.0002 | Significant |

E | 0.08265625 | 1.246441633 | 0.2748 | Not significant |

AB | 0.00354025 | 0.053386344 | 0.8192 | Not significant |

AC | 0.0529 | 0.797722645 | 0.3803 | Not significant |

AD | 0.062001 | 0.934964116 | 0.3428 | Not significant |

AE | 0.00189225 | 0.028534795 | 0.8672 | Not significant |

BC | 0.0729 | 1.099319108 | 0.3044 | Not significant |

BD | 0.010404 | 0.15689048 | 0.6954 | Not significant |

BE | 0.02480625 | 0.374073863 | 0.5463 | Not significant |

CD | 0.02235025 | 0.337037818 | 0.5667 | Not significant |

CE | 0.005476 | 0.082577112 | 0.7762 | Not significant |

DE | 0.000784 | 0.011822581 | 0.9143 | Not significant |

A^{2} | 0.288685227 | 4.353322176 | 0.0473 | Not significant |

B^{2} | 0.024092742 | 0.363314295 | 0.5521 | Not significant |

C^{2} | 0.62585347 | 9.437759646 | 0.0051 | Significant |

D^{2} | 0.14815347 | 2.234128123 | 0.1475 | Not significant |

E^{2} | 0.031287409 | 0.471808596 | 0.4985 | Not significant |

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**MDPI and ACS Style**

Xie, B.; Wu, X.; Ji, X.
Investigation on the Energy-Absorbing Properties of Bionic Spider Web Structure. *Biomimetics* **2023**, *8*, 537.
https://doi.org/10.3390/biomimetics8070537

**AMA Style**

Xie B, Wu X, Ji X.
Investigation on the Energy-Absorbing Properties of Bionic Spider Web Structure. *Biomimetics*. 2023; 8(7):537.
https://doi.org/10.3390/biomimetics8070537

**Chicago/Turabian Style**

Xie, Baocheng, Xilong Wu, and Xuhui Ji.
2023. "Investigation on the Energy-Absorbing Properties of Bionic Spider Web Structure" *Biomimetics* 8, no. 7: 537.
https://doi.org/10.3390/biomimetics8070537