# Numerical Analysis of Bicycle Helmet under Blunt Behavior

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2})); gt is the maximum g acceleration of each standard (m/s

^{2}).

## 2. Materials and Methods

#### 2.1. Introduction to the Development of Numerical Model

#### 2.1.1. Helmet Model

#### 2.1.2. Human Head Model

#### 2.1.3. Boundary Conditions

#### 2.2. Head Acceleration Response Validation in Standardized Impacts

#### 2.3. Injury Predictors

#### 2.3.1. Peak Linear Acceleration (PLA)

#### 2.3.2. Gadd Severity Index (GSI)

#### 2.3.3. Generalized Acceleration Model for Brain Injury Threshold (GAMBIT)

_{max}is the maximum linear acceleration (g); a

_{cr}= 350 (g) [43]; α

_{max}is the maximum angular acceleration (rad/s

^{2}); α

_{cr}= 12,000 (rad/s

^{2}) [43].

#### 2.3.4. Head Injury Criterion (HIC15)

_{2}is the time at the end of the impact period (s); t

_{1}is the time at the start of the impact period (s); a is the acceleration (g).

#### 2.3.5. Energy Absorbed by the Helmet during Impact

#### 2.3.6. Parametric Study for the Development of an Injury Risk Curve

## 3. Results

#### 3.1. Head Acceleration Response Validation in Standardized Impacts Results

#### 3.1.1. EN 1078 Flat Anvil Validation

#### 3.1.2. EN 1078 Curbstone Anvil Validation

#### 3.1.3. Helmet–Head Numerical Simulation Validation

#### 3.2. Injury Predictors Results

#### 3.2.1. Peak Linear Acceleration (PLA)

#### 3.2.2. Gadd Severity Index (GSI)

#### 3.2.3. Generalized Acceleration Model for Brain Injury Threshold (GAMBIT)

#### 3.2.4. Head Injury Criterion (HIC15)

#### 3.3. Influence of Velocity in Cyclist Safety

#### 3.3.1. Energy Absorbed by the Helmet during Impacts

#### 3.3.2. Result of a Parametric Study for the Development of an Injury Risk Curve

## 4. Discussion

#### 4.1. Effectiveness of Current Standards to Prevent Head Injuries

_{15}), a degree of safety could be assigned to each helmet model depending on the value obtained. This would allow a more precise measurement of how effective a helmet is under different impact conditions, analogous to Euro NCAP’s system to measure safety in cars.

#### 4.2. Should a Bicycle Helmet Be Worn?

#### 4.3. Relationship between Impact Velocity and Head Injury Probability

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Severity code, adapted from Hayes et al. [44].

Europe | United States | Australia New Zealand | China | |
---|---|---|---|---|

Flat Anvil | Velocity: 5.42 m/s | Velocity: 6.2 m/s | Height: 1.5 m | Velocity: 6.2 m/s |

Max acc: 250 g | Max acc: 300 g | Max acc: 250 g | Max acc: 300 g | |

Curved Anvil | Velocity: 4.57 m/s | Velocity: 4.8 m/s | Not | Velocity: 4.8 m/s |

Max acc: 250 g | Max acc: 300 g | Tested | Max acc: 300 g |

Flat Anvil J/(100 kgm/s^{2}) | Curbstone Anvil J/(100 kgm/s^{2}) | |
---|---|---|

Europe | 5.88 | 4.17 |

America | 6.40 | 3.84 |

Australia/New Zealand | 5.88 | Not Tested |

China | 6.40 | 3.84 |

Material Model in Ls-Dyna | Material Properties | Source | |
---|---|---|---|

EPS Foam (86.8 kg/m^{3}) | mat_low_density_foam_57 | ϱ = 86 kg/m^{3}E = 22.4 MPa | [18,32] |

Straps (PET) | mat_piece wise_linear_plasticit y_24 | ϱ = 1400 kg/m^{3}ʋ = 0.44 E = 1000 MPa | [18,32] |

Shell (Fiberglass & Polyester Resin) | mat_piecewise_linear_plasticity_24 | ϱ = 2080 kg/m^{3}ʋ = 0.325 E = 8.54 GPa | [32,33] |

Anvil (Steel) | mat_rigid_20 | ϱ = 7800 kg/m^{3}ʋ = 0.3 E = 200 GPa | [19] |

Padding (PU Foam) | mat_low_density_foam_57 | ϱ = 32 kg/m^{3}E = 0.47 MPa | [18,32] |

Material Model | Material Properties | Source | |
---|---|---|---|

Scalp & Neck Flesh | Fu Chang Foam | Stress–Strain curves at 3 Strain rates | Human cadaver Scalp in Compression, McElhaney [37] |

Skull Tables | Piece-Wise Linear Plasticity | E = 6.48 GPa | Human Skull Tables in Shear, McElhaney [37] |

Skull Diploe | Isotropic Elastic Plastic | E = 40 MPa | McElhaney [37] |

Dura Mater | Elastic | E = 40 MPa | Human Dura in Tension Melvin [38] |

Pia Mater | Elastic | E = 12.5 MPa | Bovine Pia-Arachnoid in Shear [39] |

Cerebrospinal Fluid (CSF) | Elastic Fluid | K = 2.1 GPa υ = 0.4999 | McElhaney [37] |

Brain | Brain Linear Viscoelastic | G0 = 1.6 kPa G1 = 0.9 kPa | Porcine Brain Tissue in Shear Arbogast & Margulies [40] |

Falx & Tentorium | Elastic | E = 12.5 MPa | Jin et al. [39] |

Vertebrae | Rigid | - | - |

Intervertebral Discs & Facet Joints | Elastic | E = 10 MPa | Brolin et al. [41] |

Neck Ligaments | Elastic | E = 43.8 MPa | Yoganandan [42] |

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**MDPI and ACS Style**

Sepulveda-Lopez, D.; Antona-Makoshi, J.; Rubio, I.; Rodríguez-Millán, M. Numerical Analysis of Bicycle Helmet under Blunt Behavior. *Appl. Sci.* **2020**, *10*, 3692.
https://doi.org/10.3390/app10113692

**AMA Style**

Sepulveda-Lopez D, Antona-Makoshi J, Rubio I, Rodríguez-Millán M. Numerical Analysis of Bicycle Helmet under Blunt Behavior. *Applied Sciences*. 2020; 10(11):3692.
https://doi.org/10.3390/app10113692

**Chicago/Turabian Style**

Sepulveda-Lopez, David, Jacobo Antona-Makoshi, Ignacio Rubio, and Marcos Rodríguez-Millán. 2020. "Numerical Analysis of Bicycle Helmet under Blunt Behavior" *Applied Sciences* 10, no. 11: 3692.
https://doi.org/10.3390/app10113692