# Helmet Design Based on the Optimization of Biocomposite Energy-Absorbing Liners under Multi-Impact Loading

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Certified Motorcycle Helmet

#### 2.1.1. Numerical Modelling

#### 2.1.2. Material Modelling

$p=-{\displaystyle \frac{1}{3}}\mathrm{tr}\left(\sigma \right)$ | is the pressure; |

$q=\sqrt{{\displaystyle \frac{3}{2}}\mathit{S}:\mathit{S}}$ | is the von Mises stress; |

$\mathit{S}=\sigma +p\mathbf{I}$ | is the deviatoric stress and I is the identity matrix; |

$B=\alpha A$ | is the size of the (vertical) q-axis of the yield ellipse; |

$A={\displaystyle \frac{{p}_{c}+{p}_{t}}{2}}$ | is the size of the (horizontal) p-axis of the yield ellipse; |

$\alpha =B/A$ | is the shape factor of the yield ellipse; |

${p}_{0}={\displaystyle \frac{{p}_{c}-{p}_{t}}{2}}$ | is the center of the yield ellipse on the p-axis; |

${p}_{c}$ | is the yield stress in hydrostatic compression (always positive); |

${p}_{t}$ | is the strength of the material in hydrostatic tension. |

#### 2.1.3. Comparison between EPS Liners and Agglomerated Cork Liners

#### 2.2. New Helmet and Its Optimization

#### YEAHM, the Finite Element Head Model

## 3. Results

#### 3.1. Helmet Evaluation and Optimization Based on YEAHM Response

#### 3.2. Comparison between Agglomerated Cork and EPS

#### 3.3. Lighter 40 mm Thick Liners

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Crushable foam model with volumetric hardening: yield surface and flow potential in the p-q stress plane (adapted from [54]).

**Figure 4.**Acceleration measured in the headform’s COG - ECE 22.05 test conditions: (

**a**) Impact point B. (

**b**) Impact point P. (

**c**) Impact point R. (

**d**) Impact point X.

**Figure 5.**Sagitall cut view of the helmet-headform system at the moment of maximum deformation: (

**a**) AC216. (

**b**) EPS90.

**Figure 6.**New jet helmet with constant thick liners: (

**left**) render with 40 mm thick agglomerated cork liner; (

**center**) Sagittal cut view of the FE model positioned for an impact at point B; (

**right**) FE model.

**Figure 8.**Acceleration-time history of double impacts performed with helmets composed of agglomerated cork liners with thicknesses ranging between 25 and 40 mm.

**Figure 9.**Maximum deformation of a liner with a thickness of 35 mm: (

**a**) First impact. (

**b**) Second impact.

**Figure 10.**Maximum deformation of a liner with a thickness of 40 mm: (

**a**) First impact. (

**b**) Second impact.

**Figure 12.**CSF strain energy history during the double impacts with both 40 mm thick AC and EPS solutions.

**Figure 14.**Lighter holed versions of the 40 mm thick cork liner: (

**a**) Left—render of the 15 mm diameter-holed version; Right—render of the 25 mm diameter-holed version. (

**b**) FE helmet model of the 15 mm diameter-holed version.

**Figure 15.**Comparison of the acceleration response between the solid and holed liner versions made of AC216.

Material | $\mathit{\rho}$ [kg/m${}^{3}$] | E [MPa] | $\mathit{\nu}$ | ${\mathit{k}}_{\mathit{t}}$ | k | r | m | $\mathit{\beta}$ |
---|---|---|---|---|---|---|---|---|

AC | 199 | - | 0 | - | - | 1.8 | 0.01 | 0.1 |

216 | - | 0 | - | - | 1.1 | 0.5 | 0.1 | |

EC | 159 | - | 0 | - | - | 1.01 | 0.3 | 0.1 |

EPS | 90 | 44 | 0 | 0.1 | 2.5 | - | - | - |

ABS | 1200 | 4000 | 0.37 | - | - | - | - | - |

Part | Number of Elements | Number of Nodes |
---|---|---|

Skull | 57257 | 14443 |

CSF | 98032 | 27499 |

Brain | 836328 | 153749 |

$\mathit{\rho}$ [kg/m${}^{3}$] | $\mathit{\mu}$ [MPa] | ${\mathit{\alpha}}_{1}$ | ${\mathit{D}}_{1}$ [MPa${}^{-1}$] | ${\mathit{g}}_{1}$ | ${\mathit{g}}_{2}$ | ${\mathit{\tau}}_{1}$ [s] | ${\mathit{\tau}}_{2}$ [s] |
---|---|---|---|---|---|---|---|

1040 | 0.012 | 5.0507 | 0.04 | 0.5837 | 0.2387 | 0.02571 | 0.02570 |

$\mathit{\rho}$ [kg/m ${}^{3}$] | ${\mathit{C}}_{10}$ [MPa] | ${\mathit{C}}_{01}$ [MPa] | ${\mathit{D}}_{1}$ [MPa ${}^{-1}$] |
---|---|---|---|

1000 | 0.9 | 1 | 0.9 |

$\mathit{\rho}$ [kg/m ${}^{3}$] | E [MPa] | $\mathit{\nu}$ |
---|---|---|

1800 | 6000 | 0.21 |

Impact | 25 mm | 30 mm | 35 mm | 40 mm |
---|---|---|---|---|

First | 405.5 | 361.5 | 324.7 | 314.1 |

Second | 499.9 | 482.2 | 470.6 | 377.7 |

Parameter | 25 mm | 30 mm | 35 mm | 40 mm |
---|---|---|---|---|

Strain | 0.5125 | 0.5250 | 0.4917 | 0.3833 |

von Mises stress [kPa] | 218.7 | 204.2 | 198.8 | 134.2 |

Pressure [kPa] | 745.8 | 823.3 | 846.7 | 691.7 |

CSF pressure [kPa] | 482.5 | 483.7 | 434.2 | 291.7 |

CSF strain energy [mJ] | 15506.2 | 15488.2 | 16219.8 | 12481.2 |

Impact | AC216 | EPS90 |
---|---|---|

First | 314.1 | 328.3 |

Second | 377.7 | 438.1 |

Criterion | EPS90 | AC216 |
---|---|---|

Strain | 0.5067 | 0.3833 |

von Mises stress [kPa] | 191.7 | 134.2 |

Pressure [kPa] | 840.9 | 691.7 |

CSF pressure [kPa] | 459.4 | 291.7 |

CSF strain energy [mJ] | 12611.5 | 12481.2 |

Without Holes | 15 mm Holes | 25 mm Holes |
---|---|---|

1.01 | 0.907 | 0.703 |

Impact | Without Holes | 15 mm Holes | 25 mm Holes |
---|---|---|---|

First | 314.1 | 260.8 | 296.8 |

Second | 377.7 | 343.6 | 395.0 |

Criterion | Without Holes | 15 mm Holes | 25 mm Holes |
---|---|---|---|

Strain | 0.3833 | 0.3514 | 0.5016 |

von Mises stress [kPa] | 134.2 | 91.7 | 182.9 |

Pressure [kPa] | 691.7 | 595.8 | 829.3 |

CSF pressure [kPa] | 291.7 | 291.2 | 401.4 |

CSF strain energy [mJ] | 12481.2 | 11975.9 | 19076.6 |

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**MDPI and ACS Style**

Fernandes, F.A.O.; Alves de Sousa, R.J.; Ptak, M.; Migueis, G. Helmet Design Based on the Optimization of Biocomposite Energy-Absorbing Liners under Multi-Impact Loading. *Appl. Sci.* **2019**, *9*, 735.
https://doi.org/10.3390/app9040735

**AMA Style**

Fernandes FAO, Alves de Sousa RJ, Ptak M, Migueis G. Helmet Design Based on the Optimization of Biocomposite Energy-Absorbing Liners under Multi-Impact Loading. *Applied Sciences*. 2019; 9(4):735.
https://doi.org/10.3390/app9040735

**Chicago/Turabian Style**

Fernandes, Fábio A. O., Ricardo J. Alves de Sousa, Mariusz Ptak, and Gonçalo Migueis. 2019. "Helmet Design Based on the Optimization of Biocomposite Energy-Absorbing Liners under Multi-Impact Loading" *Applied Sciences* 9, no. 4: 735.
https://doi.org/10.3390/app9040735