Nonlinear multibody dynamics and finite element modeling of occupant response: part I—rear vehicle collision

  • Mohamed T. Z. Hassan
  • Mo Gabriel Shi
  • S. A. MeguidEmail author


With the rise in vehicle ownership, the need to reduce the risk of injury among vehicle occupants that arises from vehicle collisions is important to occupants, insurers, manufacturers and policy makers alike. The human head and neck are of special interest, due to their vulnerable nature and the severity of potential injury in these collisions. This work is divided into two parts: In Part I, we focus our attention to modeling rear collision that could lead to whiplash. Specifically, two multibody dynamics (MBD) models of the cervical spine of the 50th percentile male are developed using realistic geometries, accelerations and biofidelic variable intervertebral rotational stiffness. Furthermore, nonlinear finite element (FE) simulations of two generic compact sedan vehicles in rear collision scenario were performed. Using the acceleration profiles measured at the driver’s seat of the colliding vehicles, FE simulation of a seated and restrained occupant in rear collision was performed to determine the occupant response. The resultant accelerations, measured at the T1 vertebra of the occupant model, were used as an input to the MBD models to obtain their kinematic response. Validation of the MBD models shows great agreement with experimentally published data. Comparison between the MBD and FE simulations for a 32 km/h vehicle-to-vehicle impact shows similar trends in head trajectory. However, the MBD models reported less peak head displacements compared to the FE model. This is attributed to the failure of the anterior longitudinal ligament at the mid cervical spine leading to increased intervertebral rotation in the FE model.


Whiplash Rear impact Nonlinear Finite element Multibody dynamics Occupant kinematics 



  1. Amevo, B., Worth, D., Bogduk, N.: Instantaneous axes of rotation of the typical cervical motion segments: a study in normal volunteers. Clin. Biomech. 6, 111–117 (1991). CrossRefGoogle Scholar
  2. Anderst, W., Baillargeon, E., Donaldson, W., Lee, J., Kang, J.: Motion path of the instant center of rotation in the cervical spine during in vivo dynamic flexion-extension. Spine (Phila. Pa. 1976) 38, E594–E601 (2013). CrossRefGoogle Scholar
  3. Arun, M.W., Humm, J.R., Yoganandan, N., Pintar, F.A.: Biofidelity evaluation of a restrained whole body finite element model under frontal impact using kinematics data from PMHS Sled Tests. In: IRCOBI Conference Proceedings (No. IRC-15-69) (2015)Google Scholar
  4. Biddis, E.A., Bogoch, E.R., Meguid, S.A.: Three-dimensional finite element analysis of prosthetic finger joint implants. Int. J. Mech. Mater. Des. 1, 317–328 (2004). CrossRefGoogle Scholar
  5. Bowman, B.M., Schneider, L.W., Lustick, L.S., Anderson, W.R., Thomas, D.J.: Simulation analysis of head and neck dynamic response. In: 28th Stapp Car Crash Conference, pp. 173–205 (1984)Google Scholar
  6. Brady, A.J.: The three element model of muscle mechanics: its applicability to cardiac muscle. Physiologist 10, 75–86 (1967)Google Scholar
  7. Camacho, D.L., Nightingale, R.W., Robinette, J.J., Vanguri, S.K., Coates, D.J., Myers, B.S.: Experimental flexibility measurements for the development of a computational head-neck model validated for near-vertex head impact. In: SAE Technical Paper 97334, pp. 473–486 (1997).
  8. Caputo, F., Lamanna, G., Soprano, A.: On the evaluation of the overloads coming from the use of seat-belts on a passenger railway seat. Int. J. Mech. Mater. Des. 8, 335–348 (2012). CrossRefGoogle Scholar
  9. Cholewicki, J., Panjabi, M.M., Nibu, K., Babat, L.B., Grauer, J.N., Dvorak, J.: Head kinematics during in vitro whiplash simulation. Accid. Anal. Prev. 30, 469–479 (1998)CrossRefGoogle Scholar
  10. Combset, J.J.: Current statues and future plans of the GHBMC (global human body models consortium). In: 6th International Symposium: Human Modeling and Simulation in Automotive Engineering, Heidelberg, Germany (2016)Google Scholar
  11. Cronin, D.S.: Finite element modeling of potential cervical spine pain sources in neutral position low speed rear impact. J. Mech. Behav. Biomed. Mater. 33, 55–66 (2014). CrossRefGoogle Scholar
  12. Cummings, J.R., Osterholt, G.D., Van Calhoun, D., Biller, B.A.: Occupant friction coefficients on various combinations of seat and clothing. In: SAE Technical Paper 2009-01-1672, p. 11 (2009)Google Scholar
  13. Davidsson, J., Deutscher, C., Hell, W., Svensson, M.Y.: Human volunteer kinematics in rear-end sled collisions. J. Crash Prev. Inj. Control 2, 319–333 (2001)CrossRefGoogle Scholar
  14. Deng, Y.-C., Li, X., Liu, Y.: Modeling of the human cervical spine using finite element techniques. In: 1999 SAE International Congress and Exposition., Detroit, MI (1999)Google Scholar
  15. Dvorak, J., Froehlich, D., Penning, L., Baumgartner, H., Panjabi, M.M.: Functional radiographic diagnosis of the cervical spine: flexion/extension. Spine (Phila. Pa. 1976) 13, 748–755 (1988)CrossRefGoogle Scholar
  16. Elemance LLC: GHBMC User Manual: M50 Detailed Occupant, Version 4.5 for LS-DYNA (2016)Google Scholar
  17. Elliott, B., Goswami, T.: Implant material properties and their role in micromotion and failure in total hip arthroplasty. Int. J. Mech. Mater. Des. 8, 1–7 (2012). CrossRefGoogle Scholar
  18. Fice, J.B., Cronin, D.S., Panzer, M.B.: Cervical spine model to predict capsular ligament response in rear impact. Ann. Biomed. Eng. 39, 2152–2162 (2011). CrossRefGoogle Scholar
  19. Forman, J.L., Kent, R.W., Mroz, K., Pipkorn, B., Bostrom, O., Segui-Gomez, M.: Predicting rib fracture risk with whole-body finite element models: development and preliminary evaluation of a probabilistic analytical framework. Ann. Adv. Automot. Med. 56, 109–124 (2012)Google Scholar
  20. Foster, J.K., Kortge, J.O., Wolanin, M.J.: Hybrid III-A biomechanically-based crash test dummy. In: 21st Stapp Car Crash Conference (1977)Google Scholar
  21. Garcia, T.: A biomechanical evaluation of whiplash using a multi-body dynamic model. J. Biomech. Eng. 125, 254 (2003). CrossRefGoogle Scholar
  22. Gayzik, F.S., Moreno, D.P., Vavalle, N.A., Rhyne, A.C., Stitzel, J.D.: Development of the global human body models consortium mid-sized male full body model. In: International Workshop on Human Subjects for Biomechanical Research, vol. 39 (2011)Google Scholar
  23. Giordano, C., Kleiven, S.: Development of a 3-year-old child fe head model, continuously scalable from 1.5- to 6-year-old. In: Proceedings of the IRCOBI Conference, Malaga, Spain, pp. 288–302 (2016)Google Scholar
  24. Giudice, J.S., Park, G., Kong, K., Bailey, A., Kent, R., Panzer, M.B.: Development of open-source dummy and impactor models for the assessment of American football helmet finite element models. Ann. Biomed. Eng. 47, 1–11 (2018). Google Scholar
  25. Goel, V.K., Clark, C.R., Gallaes, K., Liu, Y.K.: Moment–rotation relationships of the ligamentous occipito–atlanto–axial complex. J. Biomech. 21, 673–680 (1988). CrossRefGoogle Scholar
  26. Grauer, J.N., Panjabi, M.M., Cholewicki, J., Nibu, K., Dvorak, J.: Whiplash produces and S-shaped curvature of the neck with hyperextension at lower levels. Spine (Phila. Pa. 1976) 22, 2489–2494 (1997)CrossRefGoogle Scholar
  27. Hai-bin, C., Yang, K.H., Zheng-guo, W.: Biomechanics of whiplash injury. Chin. J. Traumatol. 12, 305–314 (2009). Google Scholar
  28. Hassan, M.T.Z., Meguid, S.A.: Viscoelastic multibody dynamics of whiplash. In: Proceedings of the 25th CANCAM, London, ON, Canada (2014)Google Scholar
  29. Hassan, M.T.Z., Meguid, S.A.: Effect of seat belt and head restraint on occupant’s response during rear-end collision. Int. J. Mech. Mater. Des. 14, 231–242 (2018). CrossRefGoogle Scholar
  30. Hell, W., Langwieder, K., Walz, F., Muser, M., Kramer, M., Hartwig, E.: Consequences for seat design due to read end accident analysis, sled tests, and possible test criteria for reducing cervical spine injuries after rear end collision. In: IRCOBI Conference on the Biomechanics of Impact, pp. 243–259 (1999)Google Scholar
  31. Himmetoglu, S., Acar, M., Bouazza-Marouf, K., Taylor, A.: A multi-body human model for rear-impact simulation. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 223, 623–638 (2009). CrossRefGoogle Scholar
  32. Hitosugi, M., Tokudome, S.: Injury severity of occupants in lateral collisions in standard and small vehicles: Analysis of ITARDA’s in-depth investigation data. Int. J. Crashworthiness 16, 657–663 (2011). CrossRefGoogle Scholar
  33. Hoover, J.: Dynamic analysis of whiplash, Master's Thesis, University of Toronto, Toronto (2012)Google Scholar
  34. Hoover, J., Meguid, S.A.: Analytical viscoelastic modelling of whiplash using lumped-parameter approach. Int. J. Mech. Mater. Des. 11, 125–137 (2015). CrossRefGoogle Scholar
  35. Ivancic, P.C., Ito, S., Panjabi, M.M., Pearson, A.M., Tominaga, Y., Wang, J.-L., Gimenez, S.E.: Intervertebral neck injury criterion for simulated frontal impacts. Traffic Inj. Prev. 6, 175–184 (2005). CrossRefGoogle Scholar
  36. de Jager, M.: Mathematical Head-Neck Models for Acceleration Impacts, impacts, Ph.D. Thesis. University of Technology, Eindhoven (1996)Google Scholar
  37. Katagiri, M., Zhao, J., Kerrigan, J., Kent, R., Forman, J.: Comparison of whole-body kinematic behaviour of the GHBMC occupant model to PMHS in far-side sled tests. In: 2016 IRCOBI Conference Proceedings—International Research Council on Biomechanics of Injury (2016)Google Scholar
  38. Kleinberger, M.: Anthropomorphic Test Devices for Military Scenarios. In: Franklyn, M., Lee, P.V.S. (eds.) Military Injury Biomechanics, pp. 87–102. CRC Press, Boca Raton, FL (2017)Google Scholar
  39. Krafft, M., Kullgren, A., Ydenius, A., Tingvall, C.: Influence of crash pulse characteristics on whiplash associated disorders in rear impacts-crash recording in real life crashes. Traffic Inj. Prev. 3, 141–149 (2002). CrossRefGoogle Scholar
  40. Kullgren, A., Krafft, M., Nygren, Å., Tingvall, C.: Neck injuries in frontal impacts: influence of crash pulse characteristics on injury risk. Accid. Anal. Prev. 32, 197–205 (2000). CrossRefGoogle Scholar
  41. Kuppa, S., Saunders, J., Stammen, J., Mallory, A.: Kinematically based whiplash injury criterion. In: Proceedings of 19th ESV conference, paper no. 05-0211 (2005)Google Scholar
  42. Liu, Y.K., Krieger, K.W., Njus, G., Ueno, K., Connors, M.P., Wakano, K., Thies, D.: Cervical spine stiffness and geometry of the young human male, Air Force Aerospace Medical Research Laboratories, AFAMRL-TR-80-138 (1980)Google Scholar
  43. Livermore Software Technology Corporation: LS-DYNA Keyword User’s Manual, Livermore, CA (2007)Google Scholar
  44. Lowrance, E.W., Latimer, H.B.: Weights and variability of components of the human vertebral column. Anat. Rec. 159, 83–88 (1967). CrossRefGoogle Scholar
  45. Martin, P.G., Crandall, J.R., Pilkey, W.D.: Injury trends of passenger car drivers in frontal crashes in the USA. Accid. Anal. Prev. 32, 541–557 (2000). CrossRefGoogle Scholar
  46. Marzougui, D., Samaha, R.R., Cui, C., Kan, Opiela, K.S.: Extended validation of the finite element model for the 2010 Toyota Yaris Passenger Sedan (2012)Google Scholar
  47. Meyer, F., Bourdet, N., Deck, C., Willinger, R., Raul, J.S.: Human neck finite element model development and validation against original experimental data. In: Stapp Car Crash Journal, vol. 48, pp. 177–206 (2004)Google Scholar
  48. Mordaka, J., Meijer, R., van Rooij, L., Żmijewska, A.E.: Validation of a finite element human model for prediction of rib fractures. in: SAE Technical Paper 2007-01-1161 (2007).
  49. National Highway Traffic Safety Administration (NHTSA): Federal Motor Vehicle Safety Standard (FMVSS) 208 (1998)Google Scholar
  50. National Highway Traffic Safety Administration (NHTSA): Toyota Yaris LS-DYNA model (2010)Google Scholar
  51. National Highway Traffic Safety Adminstration - Department of Transportation: Traffic Safety Facts 2007: a compilation of motor vehicle crash data from the fatality analysis reporting system and the general estimates system, Washington, DC (2007)Google Scholar
  52. National Highway Traffic Safety Adminstration - Department of Transportation: Traffic Safety Facts 2015—a compilation of motor vehicle crash data from the fatality analysis reporting system and the general estimates system, Washington, DC (2017)Google Scholar
  53. Nilson, G., Svensson, M.Y., Lovsund, P., Haland, Y., Wiklund, K.: Rear-end collisions—the effect of the seat belt and the crash pulse on occupant motion. In: ESV Conference., Munchen (1994)Google Scholar
  54. Oakley, E., Wrazen, B., Bellnier, D.A., Syed, Y., Arshad, H., Shafirstein, G.: A new finite element approach for near real-time simulation of light propagation in locally advanced head and neck tumors. Lasers Surg. Med. 47, 60–67 (2015). CrossRefGoogle Scholar
  55. Oda, T., Panjabi, M.M., Crisco, J.J., Bueff, H.U., Grob, D., Dvorak, J.: Role of tectorial membrane in the stability of the upper cervical spine. Clin. Biomech. 7, 201–207 (1992). CrossRefGoogle Scholar
  56. Ordway, N.R., Seymour, R.J., Donelson, R.G., Hojnowski, L.S., Edwards, W.T.: Cervical flexion, extension, protrusion, and retraction. Spine (Phila. Pa. 1976) 24, 240–247 (1999). CrossRefGoogle Scholar
  57. Östh, J., Mendoza-Vazquez, M., Linder, A., Svensson, M.Y., Brolin, K.: The VIVA OpenHBM finite element 50th percentile female occupant model: whole body model development and kinematic validation. In: IRCOBI Conference, Antwerp, Belgium (2017)Google Scholar
  58. Panjabi, M.M., Ito, S., Ivancic, P.C., Rubin, W.: Evaluation of the intervertebral neck injury criterion using simulated rear impacts. J. Biomech. 38, 1694–1701 (2005). CrossRefGoogle Scholar
  59. Panzer, M.B., Cronin, D.S.: C4–C5 segment finite element model development, validation, and load-sharing investigation. J. Biomech. 42, 480–490 (2009). CrossRefGoogle Scholar
  60. Park, G., Kim, T., Crandall, J.R., Arregui-Dalmases, C., Luzón Narro, B.J.: Comparison of kinematics of GHBMC to PMHS on the side impact condition. In: Proceedings on IRCOBI Conference 2013, vol. 1, pp. 368–379 (2013)Google Scholar
  61. Peña, E., Calvo, B., Martínez, M.A., Doblaré, M.: An anisotropic visco-hyperelastic model for ligaments at finite strains. Formulation and computational aspects. Int. J. Solids Struct. 44, 760–778 (2007). CrossRefzbMATHGoogle Scholar
  62. Plaga, J.A., Albery, C., Boehmer, M., Goodyear, C., Thomas, G.: Design and development of anthropometrically correct head forms for joint strike fighter ejection seat testing, Dayton (2005)Google Scholar
  63. Schneider, L., Robbins, D.H., Pflüg, M.A., Snyder, R.G.: Development of anthropometrically based design specifications for an advanced adult anthropomorphic dummy family, Ann Arbor, MI, vol. 1 (1983)Google Scholar
  64. Stein, D.M., O’Connor, J.V., Kufera, J.A., Ho, S.M., Dischinger, P.C., Copeland, C.E., Scalea, T.M.: Risk factors associated with pelvic fractures sustained in motor vehicle collisions involving newer vehicles. J. Trauma Inj. Infect. Crit. Care. 61, 21–31 (2006). CrossRefGoogle Scholar
  65. Stemper, B.D., Yoganandan, N., Pintar, F.A.: Validation of a head-neck computer model for whiplash simulation. Med. Biol. Eng. Comput. 42, 333–338 (2004). CrossRefGoogle Scholar
  66. Tencer, A.F., Huber, P., Mirza, S.K. (2003): A comparison of biomechanical mechanisms of whiplash injury from rear impacts. In: 47th Annual Proceedings Association for the Advancement of Automotive Medicine, Lisbon, Portugal (2003)Google Scholar
  67. Trajkovski, A., Omerovic, S., Krasna, S., Prebil, I.: Loading rate effect on mechanical properties of cervical spine ligaments. Acta Bioeng. Biomech. 16, 13–20 (2014). Google Scholar
  68. Unnikrishnan, V.U., Unnikrishnan, G.U., Reddy, J.N.: Biomechanics of breast tumor: effect of collagen and tissue density. Int. J. Mech. Mater. Des. 8, 257–267 (2012). CrossRefGoogle Scholar
  69. van Lopik, D.W., Acar, M.: Development of a multi-body computational model of human head and neck. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 221, 175–197 (2007). CrossRefGoogle Scholar
  70. Werne, S.: Studies in spontaneous atlas dislocation. Acta Orthop. Scand. Suppl. 23, 1–150 (1957). Google Scholar
  71. White, A.A., Panjabi, M.M.: Clinical Biomechanics of the Spine. J.B. Lippincott Company, Philadelphia (1990)Google Scholar
  72. White, N.A., Danelson, K.A., Scott Gayzik, F., Stitzel, J.D.: Head and neck response of a finite element anthropomorphic test device and human body model during a simulated rotary-wing aircraft impact. J. Biomech. Eng. 136, 111001 (2014). CrossRefGoogle Scholar
  73. Yoganandan, N., Pintar, F.A., Cusick, J.F.: Biomechanical analyses of whiplash injuries using an experimental model. Accid. Anal. Prev. 34, 663–671 (2002)CrossRefGoogle Scholar
  74. Zhang, L., Meng, Q.: Study on cervical spine stresses based on three-dimensional finite element method. In: 2010 International Conference on Computational and Information Sciences, pp. 420–423 (2010).

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Mechanics and Aerospace Design LabUniversity of TorontoTorontoCanada

Personalised recommendations