# Numerical analysis of side airbags deployment in out-of-position situations

- D. Bendjaballah
^{1}, - A. Bouchoucha
^{1}, - M. L. Sahli
^{1, 2}Email author and - J-C. Gelin
^{2}

**12**:12

https://doi.org/10.1186/s40712-016-0070-2

© The Author(s). 2017

**Received: **5 June 2016

**Accepted: **28 December 2016

**Published: **18 March 2017

## Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

## Keywords

## Background

The passive safety of cars has become a very high priority issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases (Augenstein et al. 2003; Gabauer and Gabler 2010; Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the movement of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the occupant from having harsh contacts with interior surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of automobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision conditions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion velocity, and neck forces (neck injury risk or whiplash). Thus, new types of airbag products are being developed to handle different collision scenarios.

Extensive studies have shown that the airbag deployment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these crashes was 68.3% in comparison to front impact (48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of occupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deployment using simulation technology. Experimental and numerical studies have quantified injury risks to close-proximity occupants from deploying side airbags. These studies have focused on the prevention of the most adverse effects of airbag deployment (Duma et al. 2003). Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simulation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deformation patterns that compare most closely to the experimental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it. Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

## Methods

### Materials

Mechanical properties of the airbag

Parameters | Values |
---|---|

Density (kg/mm | 9.100E−07 |

Young’s modulus (GPa) | 2.500 |

Poisson’s ratio | 0.345 |

Thickness (mm) | 0.150 |

### Tensile tests

Physical and mechanical properties of the airbag

Properties | Airbag | |||||
---|---|---|---|---|---|---|

Peugeot | Renault | Volkswagen | ||||

P0 | P90 | R0 | R90 | VW0 | VW90 | |

Initial yield strength (MPa) | 285 | 292 | 155 | 154 | 210 | 213 |

Young’s modulus (GPa) | 2.43 | 2.46 | 2.51 | 2.53 | 2.48 | 2.52 |

Poisson’s ratio | 0.341 | 0.346 | 0.349 | 0.342 | 0.345 | 0.346 |

### Finite element model of airbag simulation

#### Theoretical background

*σ*is the normal stress and

*τ*is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also,

*ε*and

*γ*are the strain components. The material elastic constants

*Q*

_{ij}are given by the following equations:

where *E*
_{1} and *E*
_{2} are the Young’s modulus in the fill and wrap directions and *G*
_{12} is the shear modulus of the fabric material. *ν*
_{ij} is the Poisson ratio of the material.

*p*,

*ρ*, and

*e*are respectively the pressure, density, and specific internal energy, and

*γ*is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that read:

*V*is a volume,

*A*is the boundary of this volume,

*n*is the normal vector along the surface

*A*, and

*u*denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with constant entropy gives:

*u*,

*p*, and

*ρ*denote the quantities inside that part of the tube that is supplying mass. This gives

#### Materials and boundary conditions

^{2}and is shown in Fig. 4.

Material properties of airbag and rigid plate used in FE simulations (Chawla et al. 2004a)

Materials | Airbag | Rigid plate |
---|---|---|

Density of fabric [g/cm | – | 7.84 |

Young’s modulus [GPa] | 2.5 | 206 |

Poisson’s ratio | 0.34 | 0.30 |

Shear modulus [GPa] | 6.9 | – |

Initial values used for FE simulation of the swelling of passenger airbag (Deery et al. 1999)

Pressure [Pa] | 10 |
---|---|

Temperature [°C] | 25 |

Universal gas constant [kg/kmol.K] | 8.314 |

Initial pressure [Pa] | 1.01 × 10 |

Molecular weight [kg/mol] | 0.02802 |

Added initial volume [m | 3.33 × 10 |

## Results and discussion

*x*-

*x*effective strain contours computed are plotted in Fig. 7. As shown in this figure, a state of deployment and swelling of passenger airbag with highly non-uniform deformation is detected around the bag. In the present analysis, the localized elastic strains reach values far below the rupture strain that can be measured in the tensile test (Wu et al. 2005). Nevertheless, according to the global material response, the constitutive model is found to be still valid at such high deformation levels. Moreover, the development of plaice can clearly be seen during the swelling of passenger airbag.

## Conclusions

This document outlines the current possibilities and limitations of the simulation of the first stages of the airbag deployment. The studies presented have been performed using a commercial airbag. The results first have allowed us to show that the airbag has been modeled correctly with a proper filling of the gas flow. As a result of this, simulation has proved to be a valuable tool to be taken into account in tasks related to airbag deployment.

In conclusion, these technologies are able to be used not only as a tool to solve problems related to the airbag development but also to help us arrive at a better understanding of the factors that influence the deployment of the airbag and its aggressiveness and therefore get more efficient and safer designs.

Further testing with real-life airbags and comparison with experiments is required. It is also very important to model proper folding for airbag mesh for studying contact interaction of out-of-position users with an inflating airbag. These will be carried out in the near future.

## Declarations

### Acknowledgements

The authors would like to acknowledge the Applied Mechanics Department (DMA) at Franche-Comté University for support of this work.

### Authors’ contributions

All authors read and approved the final manuscript.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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