Science China Physics, Mechanics and Astronomy

, Volume 56, Issue 6, pp 1209–1219 | Cite as

Accurate modelling of the crush behaviour of thin tubular columns using material point method

  • PengFei Yang
  • S. A. Meguid
  • Xiong Zhang


In this paper, we apply the material point method (MPM), also known as a meshfree method, to examine the crush behaviour of thin tubular columns. Unlike the finite element method, randomly-distributed-weak-particle triggers were used to account for the deformation behaviour of collapse modes. Both symmetric and asymmetric modes of deformation and their associated mean collapse loads are determined for an elasto-plastic constitutive law describing the tubular columns. Attention was devoted to the accuracy and the convergence of the MPM simulation, which is determined by the number of the particles and the size of the background cells used in our explicit solver. Furthermore, a novel contact approach was adopted to establish the crush behaviour of the tubular columns. Two aspects of the work were accordingly examined, including three different crush velocities (5, 10 and 15 m/s) and varied geometrical features of the tube (t/d and l/d) based on the deformation history. The results of our model, which were compared with existing analytical predictions and experimental findings, identify the critical geometric features of the tubular columns that would dictate the deformation mode as being either progressive collapse or following Euler’s buckling mode.


thin tubular columns crush material point method deforamtiom mode elasto-plastic mean collapse load 


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  1. 1.
    Mallock A. Note on the instability of tubes subjected to end pressure and on the folds in a flexible material. Proc R Soc Ser A, 1908, 81: 388–393ADSzbMATHCrossRefGoogle Scholar
  2. 2.
    Alexander J M. An approximate analysis of thin cylindrical shells under axial loading. Q J Mech Appl Math, 1960, 13: 10–15zbMATHCrossRefGoogle Scholar
  3. 3.
    Pugsley A, Macaulay M. The large scale crumpling of thin cylindrical columns. Q J Mech Appl Math, 1960, 13: 1–9CrossRefMathSciNetGoogle Scholar
  4. 4.
    Pugsley A. On the crumpling of thin tubular struts. Q J Mech Appl Math, 1979, 32(I): 1–7CrossRefGoogle Scholar
  5. 5.
    Abramowicz W, Jones N. Dynamic axial crushing of circular tubes. Int J Impact Eng, 1984, 2: 263–281CrossRefGoogle Scholar
  6. 6.
    Abramowicz W, Jones N. Dynamic progressive buckling of circular and square tubes. Int J Impact Eng, 1986, 4: 243–269CrossRefGoogle Scholar
  7. 7.
    Johnson W, Soden P D, Al-Hassani S T S. Inextensional collapse of thin-walled tubes under axial compression. J Strain Anal Eng Des, 1977, 12: 317–330CrossRefGoogle Scholar
  8. 8.
    Andrews K R F, England G L, Ghani E. Classification of the axial collapse of cylindrical tubes under quasi-static loading. Int J Mech Sci, 1983, 25(9–10): 687–696CrossRefGoogle Scholar
  9. 9.
    Singace A A, El-Sobky H. Interplay of factors influencing collapse modes in axially crushed tubes. Int J Crashworthiness, 2000, 5(3): 279–298CrossRefGoogle Scholar
  10. 10.
    Rust W, Schweizerhof K. Finite element limit load analysis of thin-walled structures by ANSYS (implicit), LS-DYNA (explicit) and in combination. Thin Wall Struct, 2003, 41: 227–244CrossRefGoogle Scholar
  11. 11.
    Marzbanrad J, Abdollahpoor A, Mashadi B. Effects of the triggering of circular aluminum tubes on crashworthiness. Int J Crashworthiness, 2009, 14(6): 591–599CrossRefGoogle Scholar
  12. 12.
    Meguid S A, Stranart J C, Heyerman J. On the layered micromechanical three-dimensional finite element modelling of foam-filled columns. Finite Elem Anal Des, 2004, 40: 1035–1057CrossRefGoogle Scholar
  13. 13.
    Meguid S A, Attia M S, Stranart J C, et al. Solution stability in the dynamic collapse of square aluminium columns. Int J Impact Eng, 2007, 34: 348–359CrossRefGoogle Scholar
  14. 14.
    Zhang X, Cheng G D, You Z, et al. Energy absorption of axially compressed thin-walled square tubes with patterns. Thin Wall Struct, 2007, 45: 737–746CrossRefGoogle Scholar
  15. 15.
    Younes M M. Finite element modeling of crushing behaviour of thin tubes with various cross-sections. In: 13th International Conference on aerospace sciences & aviation technology, Egypt, 2009Google Scholar
  16. 16.
    Fyllingen Ø, Hopperstad O S, Hanssen A G, et al. Modelling of tubes subjected to axial crushing. Thin Wall Struct, 2010, 48: 134–142CrossRefGoogle Scholar
  17. 17.
    Noguchi H, Kawashima T, Miyamura T. Element free analysis of shell and spatial structures. Int J Numer Meth Eng, 2000, 47: 1215–240zbMATHCrossRefGoogle Scholar
  18. 18.
    Li S, Hao W, Liu W K. Numerical simulations of large deformation of thin shell structures using meshfree methods. Comput Mech, 2000, 25: 102–116zbMATHCrossRefGoogle Scholar
  19. 19.
    Gato C. Meshfree analysis of dynamic fracture in thin-walled strucres. Thin Wall Struct, 2010, 48: 215–222CrossRefGoogle Scholar
  20. 20.
    Ma S, Zhang X, Qiu X M. Comparison study of MPM and SPH in modeling hypervelocity impact problems. Int J Impact Eng, 2009, 36: 272–282CrossRefGoogle Scholar
  21. 21.
    Sulsky D, Chen Z, Schreyer H L. A particle method for historyependent materials. Comput Method Appl Mech, 1994, 118: 179–196zbMATHMathSciNetGoogle Scholar
  22. 22.
    Huang P, Zhang X, Ma S. Contact algorithms for the material point method in impact and penetration simulation. Int J Numer Meth Eng, 2011, 85(4): 498–517zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Bardenhagen S G, Guilkey J E, Roessig K M, et al. An improved contact algorithmfor the material point method and application to stress propagation in granular material. CMES-Comput Modeling Eng, 2001, 2(4): 509–522zbMATHGoogle Scholar
  24. 24.
    Zhang Y T, Zhang X, Liu Y. An alternated grid updating parallel algorithm for material point method using OpenMP. CMES-Comput Modeling Eng, 2010, 69(2): 143–165Google Scholar
  25. 25.
    Lian Y P, Zhang X, Liu Y. Coupling of finite element method with material point method by local multi-mesh contact method. Comput Method Appl Mech, 2011, 200: 3482–3494zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Ma Z T, Zhang X, Huang P. An object-oriented mpm framework for simulation of large deformation and contact of numerous grains. CMES-Comput Modeling Eng, 2010, 51(1): 61–87MathSciNetGoogle Scholar
  27. 27.
    Bardi F C, Yun H D, Kyriakides S. On the axisymmetric progressive crushing of circular tubes under axial compression. Int J Solids Struct, 2003, 40: 3137–3155CrossRefGoogle Scholar
  28. 28.
    Chen Z, Schreyer H L. Secant structural solution strategies under element constraint for incremental damage. Comput Method Appl Mech, 1991 (90): 869–884Google Scholar
  29. 29.
    Deruntz J A, Hodge P G. Crushing of a tube between rigid plates. J Appl Mech, 1963, 30: 391–396CrossRefGoogle Scholar
  30. 30.
    Galib D A, Limam A. Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes. Thin Wall Struct, 2004, 42: 1103–1137CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of AerospaceTsinghua UniversityBeijingChina
  2. 2.Mechanics and Aerospace Design LaboratoryUniversity of TorontoTorontoCanada

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