Acta Mechanica Solida Sinica

, Volume 31, Issue 1, pp 1–18 | Cite as

Coupled Shell-Material Point Method for Bird Strike Simulation

  • Bo Wu
  • Zhenpeng Chen
  • Xiong ZhangEmail author
  • Yan Liu
  • Yanping Lian
Original Paper


In a bird strike, the bird undergoes large deformation like flows; while most part of the structure is in small deformation, the region near the impact point may experience large deformations, even fail. This paper develops a coupled shell-material point method (CSMPM) for bird strike simulation, in which the bird is modeled by the material point method (MPM) and the aircraft structure is modeled by the Belytschko–Lin–Tsay shell element. The interaction between the bird and the structure is handled by a particle-to-surface contact algorithm. The distorted and failed shell elements will be eroded if a certain criterion is reached. The proposed CSMPM takes full advantages of both the finite element method and the MPM for bird strike simulation and is validated by several numerical examples.


Bird strike simulation Material point method Shell element Coupling Adaptive conversion 


  1. 1.
    Heimbs S. Computational methods for bird strike simulations: a review. Comput Struct. 2011;89(23–24):2093–112.CrossRefGoogle Scholar
  2. 2.
    Hedayati R, Sadighi M, Mohammadi-aghdam M. On the difference of pressure readings from the numerical, experimental and theoretical results in different bird strike studies. Aerosp Sci Technol. 2014;32(1):260–6.CrossRefGoogle Scholar
  3. 3.
    Hedayati R, Sadighi M. Bird strike: an experimental, theoretical and numerical investigation. Amsterdam: Elsevier Science; 2015.Google Scholar
  4. 4.
    Dolbeer RA, Wright SE, Weller JR, Anderson AL, Begier MJ. Wildlife strikes to civil aircraft in the united states 1990–2014. FAA/USDA: Tech. rep; 2015.Google Scholar
  5. 5.
    Wilbeck JS. Impact behavior of low strength projectiles. Wright-Patterson Air Force Base: Tech. rep; 1978.Google Scholar
  6. 6.
    Georgiadis S, Gunnion AJ, Thomson RS, Cartwright BK. Bird-strike simulation for certification of the boeing 787 composite moveable trailing edge. Compos Struct. 2008;86(1–3):258–68.CrossRefGoogle Scholar
  7. 7.
    Anghileri M, Castelletti L-ML, Mazza V. Birdstrike: approaches to the analysis of impacts with penetration. Impact Load Lightweight Struct. 2005;49:63–74.Google Scholar
  8. 8.
    Lavoie M-A, Gakwaya A, Nejad Ensan M, Zimcik D. Validation of available approaches for numerical bird strike modeling tools. Int Rev Mech Eng. 2007;1(4):380–9.Google Scholar
  9. 9.
    Sulsky D, Chen Z, Schreyer HL. A particle method for history-dependent materials. Comput Methods Appl Mech Eng. 1994;118(1–2):179–96.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Sulsky D, Zhou S-J, Schreyer HL. Application of a particle-in-cell method to solid mechanics. Comput Phys Commun. 1995;87(1–2):236–52.CrossRefzbMATHGoogle Scholar
  11. 11.
    Lian YP, Zhang X, Liu Y. An adaptive finite element material point method and its application in extreme deformation problems. Comput Methods Appl Mech Eng. 2012;241–244(1):275–85.CrossRefzbMATHGoogle Scholar
  12. 12.
    Lian YP, Liu Y, Zhang X. Coupling of membrane element with material point method for fluid–membrane interaction problems. Int J Mech Mater Des. 2014;10(2):199–211.CrossRefGoogle Scholar
  13. 13.
    Ma S, Zhang X, Qiu XM. Comparison study of MPM and SPH in modeling hypervelocity impact problems. Int J Impact Eng. 2009;36:272–82.CrossRefGoogle Scholar
  14. 14.
    Lian YP, Zhang F, Liu Y, Zhang X. Material point method and its applications. Adv Mech. 2013;43(2):237–64.Google Scholar
  15. 15.
    Lian YP, Zhang X, Zhou X, Ma S, Zhao YL. Numerical simulation of explosively driven metal by material point method. Int J Impact Eng. 2011;38:237–45.CrossRefGoogle Scholar
  16. 16.
    Andersen S, Andersen L. Modelling of landslides with the material-point method. Comput Geosci. 2010;14:137–47.CrossRefzbMATHGoogle Scholar
  17. 17.
    Nairn JA. Material point method calculations with explicit cracks. CMES-Comput Model Eng Sci. 2003;4:649–63.zbMATHGoogle Scholar
  18. 18.
    Zhang DZ, Zou Q, VanderHeyden WB, Ma X. Material point method applied to multiphase flows. J Comput Phys. 2008;227:3159–73.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Zhang X, Sze KY, Ma S. An explicit material point finite element method for hyper velocity impact. Int J Numer Meth Eng. 2006;66:689–706.CrossRefzbMATHGoogle Scholar
  20. 20.
    Lian YP, Zhang X, Zhou X, Ma ZT. A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading. Comput Methods Appl Mech Eng. 2011;200(17–20):1659–70.CrossRefzbMATHGoogle Scholar
  21. 21.
    Lian YP, Zhang X, Liu Y. Coupling of finite element method with material point method by local multi-mesh contact method. Comput Methods Appl Mech Eng. 2011;200:3482–94.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Chen ZP, Qiu XM, Zhang X, Lian YP. Improved coupling of finite element method with material point method based on a particle-to-surface contact algorithm. Comput Methods Appl Mech Eng. 2015;293:1–19.MathSciNetCrossRefGoogle Scholar
  23. 23.
    Belytschko T, Lin JI, Chen-Shyh T. Explicit algorithms for the nonlinear dynamics of shells. Comput Methods Appl Mech Eng. 1984;42(2):225–51.CrossRefzbMATHGoogle Scholar
  24. 24.
    Hallquist JO. ANSYS/LS-DYNA Theoretical Manual, Livermore Software Technology Corporation, 2006.Google Scholar
  25. 25.
    ESI Group, Theory Notes Manual, PAM System International, Paris, France, 2000.Google Scholar
  26. 26.
    Dassault Systèmes, ABAQUS 6.12 Theory manual, Dassault Systèmes, Paris, France, 2012.Google Scholar
  27. 27.
    Belytschko T, Wong BL, Chiang H-Y. Advances in one-point quadrature shell elements. Comput Methods Appl Mech Eng. 1992;96(1):93–107.CrossRefzbMATHGoogle Scholar
  28. 28.
    Mindlin RD. Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech. 1951;18:31–8.zbMATHGoogle Scholar
  29. 29.
    Flanagan DP, Belytschko T. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. Int J Numer Meth Eng. 1981;17(5):679–706.CrossRefzbMATHGoogle Scholar
  30. 30.
    Belytschko T, Lin JI. A three-dimensional impact-penetration algorithm with erosion. Comput Struct. 1987;25(1):95–104.CrossRefzbMATHGoogle Scholar
  31. 31.
    Ma Z, Zhang X, Huang P. An object-oriented MPM framework for simulation of large deformation and contact of numerous grains. CMES-Comput Model Eng Sci. 2010;55(1):61–87.Google Scholar
  32. 32.
    Zhang X, Lian YP, Liu Y, Xu Z. The Material Point Method. Beijing: Tsinghua University Press; 2013 (in Chinese).Google Scholar
  33. 33.
    McCarthy MA, Xiao JR, McCarthy CT, Kamoulakos A, Ramos J, Gallard JP, Melito V. Modelling of bird strike on an aircraft wing leading edge made from fibre metal laminates—part 2: modelling of impact with sph bird model. Appl Compos Mater. 2004;11(5):317–40.CrossRefGoogle Scholar
  34. 34.
    Hedayati R, Ziaei-Rad S. Foam-core effect on the integrity of tailplane leading edge during bird-strike event. J Aircr. 2011;48(6):2080–9.CrossRefGoogle Scholar
  35. 35.
    Langrand B, Bayart A-S, Chauveau Y, Deletombe E. Assessment of multi-physics FE methods for bird strike modelling-application to a metallic riveted airframe. Int J Crashworthiness. 2002;7(4):415–28.Google Scholar
  36. 36.
    Hanssen AG, Girard Y, Olovsson L, Berstad T, Langseth M. A numerical model for bird strike of aluminium foam-based sandwich panels. Int J Impact Eng. 2006;32(7):1127–44.CrossRefGoogle Scholar
  37. 37.
    Sun Q, Liu YJ, Jin RH. Numerical simulation of bird strike in aircraft leading edge structure using a new dynamic failure model. In: International Council of the Aeronautical Sciences, 2014.Google Scholar
  38. 38.
    Swegle J, Hicks D, Attaway S. Smoothed particle hydrodynamics stability analysis. J Comput Phys. 1995;116(1):123–34.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2018

Authors and Affiliations

  • Bo Wu
    • 1
  • Zhenpeng Chen
    • 1
  • Xiong Zhang
    • 1
    Email author
  • Yan Liu
    • 1
  • Yanping Lian
    • 1
    • 2
  1. 1.School of Aerospace EngineeringTsinghua UniversityBeijingChina
  2. 2.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA

Personalised recommendations