# Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Data and Signal Filtering

#### 2.2. Piecewise Linear Lumped Parameters Model

#### 2.3. LPM Estimation and Calibration Scheme Using the Genetic Algorithm

#### 2.4. Finite Element Analysis

- Number of parts: 804,
- Number of nodes: 922,007,
- Number of beam elements: 10,
- Number of shell elements: 838,926,
- Number of solid elements: 134,468.

#### 2.5. Acceleration Severity Index (ASI)

- Class A: ASI $\le 1,$
- Class B: 1.0 ≤ ASI $\le 1.4,$
- Class C: 1.4 ≤ ASI $\le 1.9.$

## 3. Results

## 4. Discussion

## 5. Conclusions and future work

## Author Contributions

## Funding

## Conflicts of Interest

## References

- European Standard EN 1317-1. Road Restraint Systems Part 1, Terminology and General Criteria For Test Methods; Technical Report; European Committee of Standardization: Brussels, Belgium, 2010. [Google Scholar]
- Pawlus, W.; Karimi, H.R.; Robbersmyr, K.G. Development of lumped-parameter mathematical models for a vehicle localized impact. J. Mech. Sci. Technol.
**2011**, 25, 1737–1747. [Google Scholar] [CrossRef][Green Version] - Kamal, M. Analysis and Simulation of Vehicle to Barrier Impact. SAE Int. Tech. Paper
**1970**, 1–6. [Google Scholar] [CrossRef] - Marzbanrad, J.; Pahlavani, M. Calculation of vehicle-lumped model parameters considering occupant deceleration in frontal crash. Int. J. Crashworthiness
**2011**, 16, 439–455. [Google Scholar] [CrossRef] - Marler, R.T.; Kim, C.H.; Arora, J.S. System identification of simplified crash models using multi-objective optimization. Comput. Methods Appl. Mech. Eng.
**2006**, 195, 4383–4395. [Google Scholar] [CrossRef] - Kim, C.H.; Mijar, A.R.; Arora, J.S. Development of simplified models for design and optimization of automotive structures for crashworthiness. Struct. Multidiscip. Optim.
**2001**, 22, 307–321. [Google Scholar] [CrossRef] - Huang, M. Vehicle Crash Mechanics, 1st ed.; CRC PRESS: Boca Raton, FL, USA, 2002. [Google Scholar]
- Pawlus, W.; Nielsen, J.E.; Karimi, H.R.; Robbersmyr, K.G. Application of viscoelastic hybrid models to vehicle crash simulation. Int. J. Crashworthiness
**2011**, 55, 369–378. [Google Scholar] [CrossRef] - Alnaqi, A.; Yigit, A. Dynamic Analysis and Control of Automotive Occupant Restraint Systems. Jordan J. Mech. Ind. Eng.
**2011**, 5, 39–46. [Google Scholar] - Klausen, A.; Tørdal, S.S.; Karimi, H.R.; Robbersmyr, K.G.; Jecmenica, M.; Melteig, O. Firefly Optimization and Mathematical Modeling of a Vehicle Crash Test Based on Single-Mass. J. Appl. Math.
**2014**, 1–10. [Google Scholar] [CrossRef] - Klausen, A.; Tørdal, S.S.; Karimi, H.R.; Robbersmy, K.G. Mathematical Modeling and Numerical Optimization of Three Vehicle Crashes using a Single-Mass Lumped Parameter Model. In Proceedings of the 24th International Technical Conference on the Enhanced Safety of Vehicles (ESV), Gothenburg, Sweden, 8–11 June 2015; pp. 44–49. [Google Scholar]
- Ofochebe, S.M.; Ozoegwu, C.G.; Enibe, S.O. Performance evaluation of vehicle front structure in crash energy management using lumped mass spring system. Adv. Model. Simul. Eng.
**2015**, 2, 1–18. [Google Scholar] [CrossRef] - Munyazikwiy, B.B.; Karimi, H.R.; Robbersmyr, K.G. A Mathematical Model for Vehicle-Occupant Frontal Crash using Genetic Algorithm. In Proceedings of the 2016 UKSim-AMSS 18th International Conference on Computer Modelling and Simulation, Cambridge, UK, 6–8 April 2016. [Google Scholar]
- Munyazikwiye, B.B.; Karimi, H.R.; Robbersmyr, K.G. Optimization of Vehicle-to-Vehicle Frontal Crash Model Based on Measured Data Using Genetic Algorithm. IEEE Access
**2017**, 5, 3131–3138. [Google Scholar] [CrossRef] - Pahlavani, M.; Marzbanrad, J. Crashworthiness study of a full vehicle-lumped model using parameters optimization. Int. J. Crashworthiness
**2015**, 20, 573–591. [Google Scholar] [CrossRef] - Lim, J.M. A Consideration on the Offset Frontal Impact Modeling Using Spring-Mass Model. Int. J. Mech. Aerosp. Ind. Mech. Manuf. Eng.
**2015**, 9, 1453–1458. [Google Scholar] - Lim, J.M. Lumped Mass-Spring Model Construction for Crash Analysis using Full Frontal Impact Test Data. Int. J. Automot. Technol.
**2017**, 18, 463–472. [Google Scholar] [CrossRef] - Mentzer, S.G. The SISAME-3D Program: Structural Crash Model Extraction And Simulation; Technical Report; US Department of Transportation: Washington, DC, USA, 2007.
- Mentzer, S.; Radwan, R.; Hollowel, W. The SISAME methodology for extraction of optimal lumped parameter structural crash models. SAE Tech. Paper
**1992**. [Google Scholar] [CrossRef] - Gabler, H.C.; Hollowell, W.; Summers, S. Systems modeling of frontal crash compatibility. In Proceedings of the 2000 SAE International Congress and Exposition, Detroit, MI, USA, 13–15 January 2000; pp. 1–8. [Google Scholar]
- Mazurkiewicz, L.; Baranowski, P.; Karimi, H.R.; Damaziak, K.; Malachowski, J.; Muszynski, A.; Muszynski, A.; Robbersmyr, K.G.; Vangi, D. Improved child-resistant system for better side impact protection. Int. J. Adv. Manuf. Technol.
**2018**, 97, 3925–3935. [Google Scholar] [CrossRef][Green Version] - Vangi, D.; Cialdai, C.; Gulino, M.S.; Robbersmyr, K.G. Vehicle Accident Databases: Correctness Checks for Accident Kinematic Data. Designs
**2018**, 2, 4. [Google Scholar] [CrossRef][Green Version] - Sousa, L.; Verssimo, P.; Ambrosio, J. Development of generic multibody road vehicle models for crashworthiness. Multibody Syst. Dyn.
**2008**, 19, 133–158. [Google Scholar] [CrossRef] - Teng, T.; Chang, F.; Liu, Y.; Peng, C. Analysis of dynamic response of vehicle occupant in frontal crash using multibody dynamics method. Math. Comput. Model.
**2008**, 48, 1724–1736. [Google Scholar] [CrossRef] - Carvalho, M.; Ambrosio, J.; Eberhard, P. Identification of validated multibody vehicle models for crash analysis using a hybrid optimization procedure. Struct. Multidiscip. Optim.
**2011**, 44, 85–97. [Google Scholar] [CrossRef] - Carvalho, M.; Ambrósio, J. Identification of multibody vehicle models for crash analysis using an optimization methodology. Multibody Syst. Dyn.
**2010**, 24, 325–345. [Google Scholar] [CrossRef] - Ibrahim, H.K. Design Optimization of Vehicle Structures for Crashworthiness Improvement. Ph.D. Thesis, Concordia University, Montreal, QC, Canada, 2009. [Google Scholar]
- Mahmood, H.F.; Fileta, B.B. Vehicle Crashworthiness and Occupant Protection; Chapter 2; American Iron and Steel Institute: Washington, DC, USA, 2004; pp. 20–21. [Google Scholar]
- Deb, A.; Srinivas, K.C. Development of a new lumped-parameter model for vehicle side-impact safety simulation. J. Autom. Eng.
**2008**, 222, 1793–1811. [Google Scholar] [CrossRef] - Piyush Dube, M.L.J.; Suman, V.B. Lumped Parameter Model for Design of Crash Energy Absorption Tubes. MSRUAS-SAS Tech. J.
**2014**, 13, 5–7. [Google Scholar] - Ofochebe, S.; Enibe, S.; Ozoegwu, C. Absorbable energy monitoring scheme: new design protocol to test vehicle structural crashworthiness. Heliyon Elsevier
**2016**, 2, 1–33. [Google Scholar] [CrossRef] [PubMed] - Tanlak, N.; Sonmez, F.; Senaltun, M. Shape optimization of bumper beams under high-velocity impact loads. Eng. Struct.
**2015**, 95, 49–60. [Google Scholar] [CrossRef] - Lu, Q.; Karimi, H.R.; Robbersmyr, K.G. A Data-Based Approach for Modeling and Analysis of Vehicle Collision by LPV-ARMAX Models. J. Appl. Math.
**2013**, 2013, 1–10. [Google Scholar] [CrossRef] - Prasad, P.; Padgaonkar, A.J. Static-to-Dynamic Amplification Factors for Use in Lumped-Mass Vehicle Crash Models. Soc. Autom. Eng.
**1981**, 1–43. [Google Scholar] [CrossRef] - NHTSA. Vehicle Crash Test Database. 2016. Available online: http://www-nrd.nhtsa.dot.gov/database/vsr/veh/querytest.aspx (accessed on 25 May 2016).
- NHTSA. LS-DYNA FE Crash Simulation Vehicle Models. Available online: https://www.nhtsa.gov/crash-simulation-vehicle-models (accessed on 15 June 2016).
- Livermore Software Technology Corporation, Livermore, California 94551-0712. LS-DYNA Keyword User’s Manual, VOLUME II, Ls-Dyna R9.0 ed. 2016. Available online: https://www.dynamore.de/de/download/manuals/ls-dyna/ls-dyna-manual-r-9.0-vol-ii-16-mb (accessed on 24 October 2018).
- LSDYNA Supports. Available online: https://www.dynasupport.com/howtos/element/hourglass (accessed on 29 May 2018).
- European Standard EN 1317-2. Road Restraint Systems Part 2, Performance Classes, Impact Test Acceptance Criteria and Test Method for Safety Barriers Including Vehicle Parapets; Technical Report; European Committee of Standardization: Brussels, Belgium, 2010. [Google Scholar]
- Shojaat, M. Correlation between injury risk and impact severity index ASI. In Proceedings of the Swiss Transport Research Conference, Monte Verità/Ascona, Sweden, 20–22 March 2003. [Google Scholar]

**Figure 1.**Full-scale crash test of a Ford Taurus (2004 model) at 56 km/h [35].

**Figure 2.**Noisy and filtered acceleration signals for full-scale frontal crash [35].

**Figure 5.**Deformed vehicle frontal structure through finite element analysis at impact velocities of (

**a**) 40 km/h; (

**b**) 56 km/h; and (

**c**) 72 km/h.

**Figure 6.**Convergence of the objective function using genetic algorithm (

**a**) Lumped parameters model calibrated to full-scale crash test; (

**b**) Lumped parameters model calibrated to finite element model.

**Figure 7.**Displacement, velocity, and acceleration plots comparison in case of LPM calibrated to FSCT, (

**a**,

**c**,

**e**) impact velocities lower than the calibration point (56 km/h); (

**b**,

**d**,

**f**) impact velocities higher than the calibration point.

**Figure 8.**Displacement, velocity, and acceleration plots comparison in case of LPM calibrated to FEA, (

**a**,

**c**,

**e**) impact velocities lower than the calibration point (56 km/h); (

**b**,

**d**,

**f**) impact velocities higher than the calibration point.

**Figure 9.**A summary of kinematic time histories for (

**a**) LPM calibrated to FSCT; (

**b**) LPM calibrated to FEM; (

**c**) comparison between FEA and FSCT at 56 km/h.

Parameters | LPM Calibrated to FSCT | LPM Calibrated to FEM |
---|---|---|

${k}_{1}$ | 7195 N/m | 25,718 N/m |

${k}_{2}$ | 7210 N/m | 31,444 N/m |

${k}_{3}$ | 25,386 N/m | 45,476 N/m |

${k}_{4}$ | 711,060 N/m | 467,830 N/m |

${x}_{1}$ | 0.0526 m | 0.2448 m |

${x}_{2}$ | 0.1023 m | 0.2923 m |

${c}_{1}$ | 59,444 Ns/m | 80,827 Ns/m |

${c}_{2}$ | 51,590 Ns/m | 7775 Ns/m |

${c}_{3}$ | 4997 Ns/m | 38,812 Ns/m |

${c}_{4}$ | 1382 Ns/m | 5703 Ns/m |

${\dot{x}}_{1}$ | 7.0585 m/s | 4.7855 m/s |

${\dot{x}}_{2}$ | 8.9272 m/s | 8.2880 m/s |

Impact Velocities | ||||||
---|---|---|---|---|---|---|

Approaches | Parameters | 40 km/h | 48 km/h | 56 km/h^{c} | 64 km/h | 72 km/h |

FSCT | ${t}_{m}$ [s] | - | - | 0.0723 | - | - |

${C}_{m}$ [m] | - | - | 0.7551 | - | - | |

ASI [-] | - | - | 2.5 | - | - | |

LPM calibrated to FSCT | ${t}_{m}$ [s] | 0.0736 | 0.0740 | 0.0738 | 0.0741 | 0.0741 |

${C}_{m}$ [m] | 0.5373 | 0.6429 | 0.7508 | 0.8588 | 0.9653 | |

ASI [-] | 1.7 | 2.1 | 2.6 | 2.7 | 3.1 | |

FEA | ${t}_{m}$ [s] | 0.0755 | 0.0781 | 0.0801 | 0.0804 | 0.0800 |

${C}_{m}$ [m] | 0.5077 | 0.6077 | 0.7180 | 0.8331 | 0.9408 | |

ASI [-] | 1.5 | 1.8 | 2.0 | 2.3 | 2.5 | |

LPM calibrated to FEA | ${t}_{m}$ [s] | 0.0824 | 0.0825 | 0.0793 | 0.0822 | 0.0805 |

${C}_{m}$ [m] | 0.5231 | 0.6258 | 0.7108 | 0.8360 | 0.9396 | |

ASI [-] | 1.4 | 1.6 | 2.0 | 2.3 | 2.5 |

^{c}Calibration point, ${t}_{m}$ is the time at maximum dynamic crush, ${C}_{m}$ is the maximum dynamic crush and $ASI$ is the acceleration severity index. FSCT: Full-Scale Crash Test, LPM: Lumped Parameters Model, FEA: Finite Element Analysis.

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**MDPI and ACS Style**

B. Munyazikwiye, B.; Vysochinskiy, D.; Khadyko, M.; G. Robbersmyr, K. Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models. *Designs* **2018**, *2*, 43.
https://doi.org/10.3390/designs2040043

**AMA Style**

B. Munyazikwiye B, Vysochinskiy D, Khadyko M, G. Robbersmyr K. Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models. *Designs*. 2018; 2(4):43.
https://doi.org/10.3390/designs2040043

**Chicago/Turabian Style**

B. Munyazikwiye, Bernard, Dmitry Vysochinskiy, Mikhail Khadyko, and Kjell G. Robbersmyr. 2018. "Prediction of Vehicle Crashworthiness Parameters Using Piecewise Lumped Parameters and Finite Element Models" *Designs* 2, no. 4: 43.
https://doi.org/10.3390/designs2040043