Skip to main content

Mathematical Models, Computer Aided Design, and Occupant Safety

  • Chapter
  • First Online:
Accidental Injury

Abstract

Imagine what it would be like if, in the near future, we were able to take all the crash test dummies out of all the cars in all crash test labs around the world, because we no longer needed them. Imagine how quick, inexpensive, and accurate crash testing would become if we could marry the mathematical data representing all the adult male, adult female, and child vehicle occupants, and run all the crash tests as simulations. If you can imagine this scenario, you can imagine that all future cars will be capable of providing individualized restraints based on information of each occupant instead of affording safety only for a handful of anthropomorphic test devices (ATDs), also known as crash dummies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. McHenry RR (1963) Analysis of the dynamics of automobile passenger-restraint systems. In Proceedings of the 7th Stapp Car Crash Conference. Los Angles, CA, USA, paper no.1963-12-0017

    Google Scholar 

  2. King AI, Chou CC (1976) Mathematical modelling, simulation and experimental testing of biomechanical system crash response. J Biomech 9(5):301–317

    Google Scholar 

  3. Prasad P (1984) An overview of major occupant simulation models. SAE 84085. In: Mathematical simulation of occupant and vehicle kinematics. SAE Publication, Warrendale, p 146.

    Google Scholar 

  4. Prasad P, Chou CC (1989) A review of mathematical occupant simulation models. In: Crashworthiness and occupant protection in transportation systems, AMD-Vol. 106/BED, Vol 13. The American Society of Mechanical Engineers, New York, pp 96–112

    Google Scholar 

  5. Prasad P, Chou CC (1993) A review of mathematical occupant simulation models, Chapter 6. In: Accident injury – biomechanics and prevention. Springer, New York, pp 102–150

    Google Scholar 

  6. Prasad P, Chou CC (2002) A review of mathematical occupant simulation models. Chapter 7. In: Accident injury – biomechanics and prevention. Springer, New York, pp 121–186

    Google Scholar 

  7. Yang KH, Hu J, White NA, King AI, Chou CC, Prasad P (2006) Development of numerical models for injury biomechanics research: a review of 50 years of publications in the Stapp Car Crash Conference. Stapp Car Crash J 50:429–490

    PubMed  Google Scholar 

  8. DOD (1996) Verification, validation, and acceleration (VV&A) recommended practice guide. Alexandria, http://vva.dmso.mil/.

  9. AIAA (1998) Guide for the verification and validation of computational fluid dynamics simulations. American Institute of Aeronatics and Astronatics, AIAA-G-077, Reston

    Google Scholar 

  10. ASME (2006). Guide for verification and validation in computational solid mechanics. American Society of Mechanical Engineers, ASME V&V 10, New York

    Google Scholar 

  11. DOE (2008) Advanced simulation and computing (ASC) program plan. Office of Advanced Simulation & Computing, DOE/NNASA NA-114 http://www.sandia.gov/NNSA/ASC/pubs/pubs.html

  12. Jovannovski J (1981) Crash data analysis and model validation using correlation techniques. SAE 810471

    Google Scholar 

  13. Prasad P (1997) Occupant simulation models: experiment and practice. In: Computation of transportation systems: structural impact and occupant protection. Kluwer, The Netherlands, pp 209–219

    Google Scholar 

  14. Deb A, Haorongbam B, Chou CC (2010) Efficient approximate methods for predicting behaviors of steel hat section under impact axial loading. SAE 2010-01-1015

    Google Scholar 

  15. Haorongbam B, Deb A, Chou CC (2013) Numerical prediction of dynamic progressive buckling behaviors of single-hat double-hat steel components under axial loading. SAE 2013-01-0458

    Google Scholar 

  16. Zhu F, Chou CC, Yang KH, Chen X, Wagner D, Bilkhu S (2012) Obtaining material parameters for die cast AM60B magnesium alloy using optimization techniques. Int J Vehicle Safety 6(2):178–190

    Article  Google Scholar 

  17. ISO TR9790, ISO/TC22/SC120/WG5 (2000) Road vehicles – anthropomorphic side impact dummy – lateral impact response requirements to assess the biofidelity of the dummy

    Google Scholar 

  18. Cesari D, Compigne S, Scherer R, Xu L, Takahashi N, Page M, Asakawa K, Kostyniuk G, Hautmann E, Bortenschlager K, Sakurai M, Harigae T (2001) WorldSID prototype dummy biomechanical responses. Stapp Car Crash J 45:285–318

    CAS  PubMed  Google Scholar 

  19. Ruan JS, El-Jawahri R, Rouhana SW, Barbat S, Prasad P (2006) Analysis and evaluation of the biofidelity of the human body finite element model in lateral impact simulations according to ISO-TR9790 procedures. Stapp Car Crash J 50:491–507

    PubMed  Google Scholar 

  20. Oberkampf WL, Barone MF (2006) Measures of agreement between computation and experiment. Validation metrics. J Comput Phys 217(1):5–36

    Article  Google Scholar 

  21. Jiang X, Yang RJ, Barbat S, Weerappuli P (2009) Bayesian probabilistic PCA approach for model validation of dynamic systems. SAE 2009-01-1404

    Google Scholar 

  22. Kokkolaras J, Hulbert G, Papalambros P, Mourelatos Z, Yang RJ, Brudnak M, Gorsich D (2013) Towards a comprehensive framework for simulation-based design validation of vehicle systems. Int J Vehicle Design 61(1/2/3/4):233–248

    Article  Google Scholar 

  23. Blum P (1997) Passenger vehicle rollover – model development, test method design and sensor algorithm assessment. Master’s thesis at Chalmers University of technology, Mechanical Engineering Department of Injury Prevention, Chalmers University of Technology, 41296 Goteborg

    Google Scholar 

  24. Aljundi B, Skidmore M, Poeze E, Alaats P (1997) Rollover impact. In Proceedings of the 35th annual symposium. SAFE Association, Phoenix, pp. 395–96, Sept 8–10

    Google Scholar 

  25. Yaniv G, Duffy S, Summers S (1998) Rollover ejection mitigation using an inflatable tubular structures. 16th Enhanced Safety Vehicles (ESV). Winsor, June 1–4, paper no. 98-S8-W18

    Google Scholar 

  26. Sharma D (1997) Status of research on restraint systems for rollover protection. Presented by G. Rains of Vehcile Research Transportation Center (VRTC) in Government/Industry meeting at Washington, DC

    Google Scholar 

  27. Renfroe DA, Partain J, Lafferty J (1998) Modeling of vehicle rollover and evaluation of occupant injury potential using MADYMO. SAE 980021

    Google Scholar 

  28. Chou CC, Wu F (2001) MADYMO-based rollover simulations. 17th international technical conference on the enhanced safety vehicles, Amsterdam, June 4–7

    Google Scholar 

  29. Takagi H, Maruyama A, Dix J, Kawaguchi K (2003) MADYMO modeling methods of rollover event and occupant behavior in each rollover initiation type. 18th international technical conference on the enhanced safety of vehicles, Nagoya, paper no. 236

    Google Scholar 

  30. Chou CC, Wu F, Gu L, Wu SR (1998) A review of mathematical models for rollover simulation. In: Crashworthiness, occupant protection and biomechanics in transportation systems, AMD-Vol. 230/BED-Vol 41, pp. 223–239. Presented at the 1998 ASME Winter Annual Meeting, California

    Google Scholar 

  31. Chou CC, Wagner CD, Yang KH, King AI, Hu J, Hope K, Arepally S (2008) A review of math-based CAE tools for rollover simulations. Int J Vehicle Safety 3(3):236–275

    Article  Google Scholar 

  32. Chou CC (2003) CAE methodology for rollover simulation – current status and future trends, presented at the SAE Government/Industry Meeting, May 12–14

    Google Scholar 

  33. Chou CC, Wu F (2005) Development of MADYMO-based model for simulation of laboratory rollover test modes. 19th ESV, June 6–9, Washington, DC, paper no. 05–0347

    Google Scholar 

  34. Gopal M, Baron K, Shah M (2004) Simulation and testing of a suite of field relevant rollovers. SAE 2004 world congress and exhibition, Detroit, Michigan, SAE 2004-01-0335

    Google Scholar 

  35. Le J, Chou CC (2007) Assessment tool development for rollover SAE signal analysis. SAE 2007-01-0681

    Google Scholar 

  36. TNO – MADYMO, V6.0 User’s Manual 3-D. TNO Road-Vehicles Research Institute (2003)

    Google Scholar 

  37. McCoy RW, Chou CC, van de Velde R, Twisk D, van Schie C (2007) Vehicle and rollover sensor test modeling. SAE 2007-01-0686

    Google Scholar 

  38. Huang Y, King AI, Cavanaugh JM (1994) A MADYMO model of near-side human occupants in side impacts. J Biomech Eng 116(2):228–235

    Article  CAS  PubMed  Google Scholar 

  39. Happee R, Morsink P, Wismans J (1999) Mathematical human body modeling for impact simulation. SAE 1999-01-1909

    Google Scholar 

  40. Van der Horst MJ, Thunnissen JG, Happer R, van Haastere RM (1997) The influence of muscle activity on head-neck response during impact. SAE 973346. 41st Stapp Car Crash Conference, pp 487–507

    Google Scholar 

  41. De Jager M, Sauren A, Thunissen J, Wismans J (1997) A global and a detailed mathematical model for head-neck dynamics. In: Proceedings of the 35th SAFE symposium, Phoenix

    Google Scholar 

  42. Padgaonkar AJ, Prasad P (1982) A Mathematical analysis of side impact using the CAL3D simulation model. In: Proceedings of the 9th international ESV conference, Nagoya, Japan

    Google Scholar 

  43. Wijk J, Wismans J, Wittrebrood L (1983) MADYMO pedestrian simulations. SAE 830060

    Google Scholar 

  44. Janssen EG, Wismans J (1986) Experimental and mathematical simulation of pedestrian-vehicle and cyclist-vehicle accidents. In: Proceedings of 10th international tech conference on experimental safety vehicles, Oxford, UK

    Google Scholar 

  45. Ishikawa H, Kajzer J, Schroeder G (1993) Computer simulation of impact response of the human body in car-pedestrian accidents. SAE 933129. In: Proceedings of 37th Stapp Car Crash Conference, SanAntonio, Texas, USA

    Google Scholar 

  46. Yoshida S, Matsuhashi T, Matsuoka Y (1995) Simulation of car-pedestrian accident for evaluating car structure. In: Proceedings of 16th international technical conference on the enhanced safety of vehicles, Ontario

    Google Scholar 

  47. Mizuno Y, Ishikawa H (2001) Summary of IHRA Pedestrian Safety WG activities-proposed test methods to evaluate pedestrian protection afforded by passenger cars. In: Proceedings of 17th technical conference on the enhanced safety of vehicles, Amsterdam

    Google Scholar 

  48. Anderson R, Mclean J (2001) Vehicle design and speed and pedestrian injury: Australia’s involvement in the Harmonization Research Activities. In: Proceedings of 2001 road safety conference, Australia

    Google Scholar 

  49. Yang JK, Lovsund P, Cavallero C, Bonnoit J (2000) A Human-body 3D mathematical model for simulation of car-pedestrian impacts. J Crash Prev Inj Cont 2(2):131–149

    Article  Google Scholar 

  50. Liu XJ, Yang JK (2002) Development of child pedestrian mathematical models and evaluation with accident reconstruction. Traffic Inj Prev 4(4):337–344

    Article  Google Scholar 

  51. TNO - MADYMO Database Manual, Version 6.2, TNO Road-Vehicles Research institute (2004)

    Google Scholar 

  52. Mao H, Gao H, Cao L, Genthikatti VV, Yang KH (2013) Development of high-quality hexahedral human brain meshes using feature-based multi-block approach. Comput Methods Biomech Biomed Eng 16(3):271–279. doi:10.1080/10255842.2011.617005

    Article  Google Scholar 

  53. Guan F, Han X, Mao H, Wagner C, Yeni YN, Yang KH (2011) Application of optimization methodology and specimen-specific finite element models for investigating material properties of rat skull. Ann Biomed Eng 39(1):85–95. doi:10.1007/s10439-010-0125-0

    Article  PubMed  Google Scholar 

  54. Chou CC, Neriya S, Low TC, Prasad P (1993) MADYMO2D/3D vehicle structural/occupant simulation models. AMD Vol. 169/BED Vol. 25, Crashworthiness and occupant protection in transportation systems, ASME winter annual meeting,San Francisco, CA, USA, pp 207–222

    Google Scholar 

  55. Chou CC, Chen P, Le J (2007) Development of a unified model for sensor and crash analyses. Int J Vehicle Safety 2(3):241–260

    Article  Google Scholar 

  56. Stutzler F-J, Chou CC, Le J, Chen P (2003) Development of CAE-based crash sensing algorithm and system calibration. SAE 2003-01-0509

    Google Scholar 

  57. Chou CC (2004) Chapter 4: Fundamental principles for vehicle/occupant system analysis In: P Prasad and J Belwafa (ed) Vehicle crashworthiness and occupant safety. American Iron and Steel Institute (AISI), Southfield, MI. The book can be downloaded through the link: http://www.autosteel.org/~/media/Files/Autosteel/Research/Safety/safety_book.pdf

  58. Low TC, Prasad P, Lim GG, Chou CC, Sundararajan S (1991) An integrated three-dimensional side impact model, ASME AMD-Vol. 126/BED-Vol 19, pp 155–168

    Google Scholar 

  59. Lim GG, Prasad P, Chou CC, Walker LA, Sundararajan S, Fletcher GD, Chicola JA (1996) Development of deployable door trim system. Automotive body interior & safety systems, IBEC (International engineering body conference), Detroit, MI, USA, Oct 1–3

    Google Scholar 

  60. Ruckert J, Marcault P, Lasry D, Haug E, Cesari D, Bermond F, Bouquet R (1992) A finite element model of the EuroSID dummy. SAE 922528

    Google Scholar 

  61. Midoun DE, Abramoski E, Rao MK, Kalidindi R (1993) Development of a finite element based model of the side impact dummy. SAE 930444

    Google Scholar 

  62. Kirkpatrick SW, Homies B, Hollowell WT, Gabler HC, Trella T (1993) Finite element modeling of the Side Impact Dummy (SID). SAE 930104

    Google Scholar 

  63. Fountain M, Altamore P, Skarakis J, Spiess O (1994) Mathematical modeling of the BioSID dummy. SAE 942226

    Google Scholar 

  64. Pal C, Ichikawa H, Sagawa K (1997) Development and improvement of finite element side impact dummy (EuroSID) model based on experimental verifications. SAE 971041

    Google Scholar 

  65. Shkolnikov MB, Bhaisod D (1997) LS-DYNA3D finite element model of side impact dummy SID. SAE 971525

    Google Scholar 

  66. Khan A, Subbian T, O'Conner C (1997) Finite element model development of the BioSID. SAE 971140

    Google Scholar 

  67. Chai L, Subbian T, Khan A, Barabt S, O’Conner C, McCoy R, Prasad P (1999) Finite element model development of SIDIIs. SAE 99SC06

    Google Scholar 

  68. Kobayashi M, Matsuoka Y, Matsumoto T (2003) Validation of SIDIIs dummy FE-model and study of relation between design parameter and injury. SAE 2003-01-2820

    Google Scholar 

  69. Liu Y, Zhu F, Wang ZH, van Ratingen M (2007) Development of advanced finite element models of WorldSID 5th and 50th – the next generation side impact dummies. SAE 2007-01-0891

    Google Scholar 

  70. Wang ZJ, Been BW, Barness AS, Burleigh MJ, Schmidt A, Dotinga M, van Ratingen MR (2007) WorldSID 5th percentile prototype dummy development. SAE 2007-01-0701

    Google Scholar 

  71. Clements D (2005) Sub-system testing method for evaluation of the protective potential of door structures during side impact. Crash Expo, Novi, Oct 26

    Google Scholar 

  72. Chou CC, Aekbote K, Le J (2007) A review of side impact component test methodology. Int J Vehicle Safety 2(1/2):141–184

    Article  Google Scholar 

  73. Aekbote K, Sobick J, Zhao L, Abramczyk J, Maltarich M, Stiyer M, Bailey T (2007) A dynamic sled-to-sled methodology for simulating dummy responses in side impact. SAE 2007-01-0710

    Google Scholar 

  74. Hu J, Yang KH, Chou CC, King AI (2007a) Development of a finite element model for simulation of rollover crashes. Proceedings of the ASME mechanical engineering congress and exposition, Crashworthiness, occupant protection and biomechanics in transportation systems. In: Proceedings of IMECE’07 2007 ASME international mechanical engineering congress Nov 10–16, 2007, Seattle, Washington. Paper no IMECE2007-44083

    Google Scholar 

  75. Chou CC, Hu J, Yang KH, King AI (2008) A Method for determining the vehicle-to-ground contact load during laboratory-based rollover tests. SAE 2008-01-0351

    Google Scholar 

  76. Lee C-R, Kim J-W, Hallquist JO, Zhang Y, Farahani AD (1997) Validation of a FEA tire model for vehicle dynamic analysis and full-vehicle real-time proving ground simulations. Paper presented at the SAE International Congress and Exposition, Detroit, Michigan

    Google Scholar 

  77. Zhang Y, Xiao P, Palmer T, Farahani A (1998) Vehicle chassis/suspension dynamics analysis~Finite element model versus rigid body model. Paper presented at the SAE international congress and exposition, Detroit, Michigan

    Google Scholar 

  78. Eppinger R (2002) Occupant restraint systems. In: Accidental injury – biomechanics and prevention, 2nd edn. Springer, New York, Chapter 8, pp 187–197

    Google Scholar 

  79. Cheng Z, Rizer AL, Pellettiere JA (2003) Modeling and simulation of OOP occupant-airbag interaction. SAE 2003-01-0510

    Google Scholar 

  80. Yamagishi M, Jun Iyama J, Araki T, Natori S (2012) Numerical simulation of out-of-position front passenger injuries in frontal crashes using an accurate finite element model of the cockpit module. SAE 2012-01-0552

    Google Scholar 

  81. Midoun DE, Rao MK, Kalidindi B (1991) Dummy models for crash simulation in finite element programs. SAE 912912. Stapp conf proceedings, San Diego, pp 351–367, Nov 1–3

    Google Scholar 

  82. Lasry D, Hoffmann R, Hong P, Yang KH (1991) Mathematical modeling of the hybrid III dummy chest with chest foam. SAE 912892. Stapp conference proceedings, San Diego, pp 65–71, Nov 1–3

    Google Scholar 

  83. Yang KH, Le J (1992) Finite element modeling of Hybrid III head-neck complex. Stapp Conf Proc 36:219–233

    Google Scholar 

  84. Hu J (2007) Numerical investigation of neck injury mechanism in rollover crashes and a systematic approach of improving rollover neck protection. PhD dissertation, Wayne State University, November

    Google Scholar 

  85. Zhu F, Jin X, Guan F, Zhang L, Mao H, Yang KH, King AI (2010) Identifying the properties of ultra-soft materials using a new methodology of combined specimen-specific finite element model and optimization techniques. Mater Design 31:4704–4712

    Article  CAS  Google Scholar 

  86. Yang KH, King AI (2011) Modeling of the brain for injury simulation and prevention. In: Miller K (ed) Biomechanics of the brain. Springer, New York. ISBN 1441999965

    Google Scholar 

  87. Takahashi Y, Kikuchi Y, Mori F, Konosu A (2003) Advanced FE lower limb model for pedestrian. 18th international technical conference on the enhanced safety of vehicles, Nagoya

    Google Scholar 

  88. Dokko Y, Anderson R, Manavix J, Blumburgs P, Mclean J, Zhang L, Yang KH, King AI (2003) Validation of the human head FE model against pedestrian accident and its tentative application to the examination of existing tolerance curve. In: Proceedings of the 18th ESV, Nagoya

    Google Scholar 

  89. Maeno T, Hasegawa J (2001) Development of a finite element model of a total human model for safety (THUMS) and applications to car-pedestrian impacts. In: Proceedings of 17th ESV, Amsterdam

    Google Scholar 

  90. Robin S (2001) HUMOS: human model for safety – a joint effort towards the development of refined human-like car occupant models. In: Proceedings of the 17th ESV, Amsterdam

    Google Scholar 

  91. Vezin P, Verriest JP (2005) Development of a set of numerical human models for safety. In: Proceedings of 19th ESV, Washington, DC

    Google Scholar 

  92. Okamoto M, Takahashi Y, Mori F, Hitosugi M, Madeley J, Ivarsson J, Crandall J (2003) Development of finite element model for child pedestrian protection. In: Proceedings of 18th ESV, Nagoya

    Google Scholar 

  93. Shin J, Untaroiu C, Kerrigan J, Crandall J, Subi D, Takahashi Y, Akiyama A, Kikuchi Y, Longitano D (2007) Investigating pedestrian kinematics with the POLAR-II finite element model. SAE 2007-01-0756

    Google Scholar 

  94. Yao JF, Yang JK, Fredriksson R (2011) Development of a pedestrian dummy FE model for the design of pedestrian friendly vehicles. Int J of Vehicle Design 57(2/3):254–274

    Google Scholar 

  95. Untaroiu C, Shin J, Crandall J, Fredriksson R, Bostrum O, Takahashi Y, Akiyama A, Okamoto M, Kikuchi Y (2009) Development and validation of pedestrian sedan bucks using finite element simulations; applications in study the influence of vehicle automatic braking on the kinematics of the pedestrian involved in vehicle collisions. In: Proceedings of 21st ESV, Stuttgart

    Google Scholar 

  96. Untaroiu C, Shin J, Iversson J, Crandall J, Takahashi Y, Akiyama A, Kikuchi Y (2007) Pedestrian kinematics investigation with finite element dummy models based on anthropometry scaling method. In: Proceedings of 20th international technical conference on the enhanced safety of vehicles, Lyon

    Google Scholar 

  97. Huang SN, Yang JK, Fredriksson R (2008) Performance analysis of a bumper-pedestrian contact sensor system by using FE models. Int J Crashworthiness 13(2):149–157

    Article  Google Scholar 

  98. Krenn M, Mlekusch B, Wilfling C, Dobida F, Deutscher E (2003) Development and evaluation of a kinematic hood for pedestrian protection. SAE 2003-01-0897

    Google Scholar 

  99. O’Brian J (2012) Pedestrian zone. Crash Test Technology International, pp 10–16, Sept

    Google Scholar 

  100. Gupta V, Yang HK (2013) Effect of vehicle front end profiles leading to pedestrian secondary head impact to ground. Stapp Car Crash J 57:139–155

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to King H. Yang Ph.D. .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this chapter

Cite this chapter

Yang, K.H., Chou, C.C. (2015). Mathematical Models, Computer Aided Design, and Occupant Safety. In: Yoganandan, N., Nahum, A., Melvin, J. (eds) Accidental Injury. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1732-7_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-1732-7_6

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4939-1731-0

  • Online ISBN: 978-1-4939-1732-7

  • eBook Packages: MedicineMedicine (R0)

Publish with us

Policies and ethics