A numerical and theoretical study on crushing behaviours of variable thickness 12 right-angles section tubes

References

• White MD, Jones N, Abramowicz W. A theoretical analysis for the quasi-static axial crushing of top-hat and double-hat thin-walled sections [J]. Int J Mech Sci. 1999;41(2):209–233.
   Web of Science ®Google Scholar
• Zhang X, Zhang H. Relative merits of conical tubes with graded thickness subjected to oblique impact loads. Int J Mech Sci. 2015;98:111–125.
   Web of Science ®Google Scholar
• Nakazawa Y, Tamura K, Yoshida M, et al. Development of crash-box for passenger car with high capability for energy absorption [C]. Paper presented at: VIII International Conference on Computation Plasticity (COMPLAS VIII), Barcelona, 2005.
   Google Scholar
• Xu Z, Xu X, Zhang Z, et al. Simulation and experimental study on bumper safety performance [J]. Automot Eng. 2014;36(03):293–297.
   Google Scholar
• Kim HS. Analysis of crash response of aluminum foam-filled front side rail of a passenger car [J]. Int J Crashworthiness. 2001;6(2):189–208.
   Web of Science ®Google Scholar
• Wierzbicki T, Abramowicz W. On the crushing mechanics of thin-walled structures [J]. J Appl Mech. 1983;50(4a):727–734.
   Web of Science ®Google Scholar
• Abramowicz W, Jones N. Dynamic progressive buckling of circular and square tubes [J]. Int J Impact Eng. 1986;4(4):243–270.
   Google Scholar
• Abramowicz W, Jones N. Dynamic axial crushing of square tubes [J. Int J Impact Eng. 1984;2(2):179–208.
   Google Scholar
• Abedi MM, Niknejad A, Liaghat GH, et al. Theoretical and experimental study on empty and foam-filled columns with square and rectangular cross section under axial compression [J]. Int J Mech Sci. 2012;65(1):134–146.
   Web of Science ®Google Scholar
• Lu R, Liu X, Chen S, et al. Axial crashing analysis for tailor rolled square tubes with axially graded both wall thickness and material strength [J]. Thin-Walled Struct. 2017;117:10–24.
   Web of Science ®Google Scholar
• Guo L-C, Noda N. Fracture mechanics analysis of functionally graded layered structures with a crack crossing the interface. Mech Mater. 2008;40(3):81–99.
   Web of Science ®Google Scholar
• Hou S, Li Q, Long S, et al. Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria [J]. Finite Elem Anal Des. 2007;43(6–7):555–565.
   Web of Science ®Google Scholar
• Zhang X, Huh H. Crushing analysis of polygonal columns and angle elements [J]. Int J Impact Eng. 2010;37(4):441–451.
   Web of Science ®Google Scholar
• Tarlochan F, Samer F, Hamouda AMS, et al. Design of thin wall structures for energy absorption applications: enhancement of crashworthiness due to axial and oblique impact forces [J]. Thin-Walled Struct. 2013;71:7–17.
   Web of Science ®Google Scholar
• Mamalis AG, Manolakos DE, Ioannidis MB, et al. Finite element simulation of the axial collapse of metallic thin-walled tubes with octagonal cross-section [J]. Thin-Walled Struct. 2003;41(10):891–900.
   Web of Science ®Google Scholar
• Liu Y. Crashworthiness design of multi-corner thin-walled columns [J]. Thin-Walled Struct. 2008;46(12):1329–1337.
   Web of Science ®Google Scholar
• Bai Z, Liu J, Zhu F, et al. Optimal design of a crashworthy octagonal thin-walled sandwich tube under oblique loading [J]. Int J Crashworthiness. 2015;20(4):401–411.
   Web of Science ®Google Scholar
• Liu S, Tong Z, Tang Z, et al. Bionic design modification of non-convex multi-corner thin-walled columns for improving energy absorption through adding bulkheads. Thin-Walled Struct. 2015;88:70–81.
   Web of Science ®Google Scholar
• Zhang J, Zhang Q, Chen G, et al. Axial crushing theory of externally fiber-reinforced thin-walled twelve right-angle section tubes [J]. Thin-Walled Struct. 2016;103:244–252.
   Web of Science ®Google Scholar
• Zhang J, Wu L, Chen G, et al. Bending collapse theory of thin-walled twelve right-angle section beams [J]. Thin-Walled Struct. 2014;85:377–387.
   Web of Science ®Google Scholar
• Chen G, Chen C, Lu S, et al. Light weight design of vehicle front rails based on the theory of thin-walled beam crush and bending [J]. Automot Eng. 2016;38(10):1269–1273.
   Google Scholar
• Sun G, Zhang H, Lu G, et al. An experimental and numerical study on quasi-static and dynamic crashing behaviors for tailor rolled blank (TRB) structures [J]. Mater Des. 2017;118:175–197.
   Web of Science ®Google Scholar
• Zhang X, Wen Z, Zhang H. Axial crushing and optimal design of square tubes with graded thickness [J]. Thin-Walled Struct. 2014;84:263–274.
   Web of Science ®Google Scholar
• An X, Gao Y, Fang J, et al. Crashworthiness design for foam-filled thin-walled structures with functionally lateral graded thickness sheets [J]. Thin-Walled Struct. 2015;91:63–71.
   Web of Science ®Google Scholar
• Sun G, Pang T, Xu C, et al. Energy absorption mechanics for variable thickness thin-walled structures [J]. Thin-Walled Struct. 2017;118:214–228.
   Web of Science ®Google Scholar
• Hanssen AG, Langseth M, Hopperstad OS. Static and dynamic crushing of square aluminum extrusions with aluminum foam filler [J]. Int J Impact Eng. 2000;24(4):347–383.
   Web of Science ®Google Scholar
• Yamashita M, Gotoh M, Sawairi Y. Axial crush of hollow cylindrical structures with various polygonal cross-sections: numerical simulation and experiment [J]. J Mater Process Technol. 2003;140(1–3):59–64.
   Google Scholar
• Halquist J. LS-DYNA keyword user’s manual version 971[J]. Livermore (CA): Livermore Software Technology Corporation; 2007.
   Google Scholar
• Chen Y, Clausen AH, Hopperstad OS, et al. Stress–strain behaviour of aluminium alloys at a wide range of strain rates [J]. Int J Solids Struct. 2009;46(21):3825–3835.
   Web of Science ®Google Scholar
• Fang J, Gao Y, Sun G, et al. On design of multi-cell tubes under axial and oblique impact loads [J]. Thin-Walled Struct. 2015;95:115–126.
   Web of Science ®Google Scholar
• Santosa SP, Wierzbicki T, Hanssen AG, et al. Experimental and numerical studies of foam-filled sections [J]. Int J Impact Eng. 2000;24(5):509–534.
   Web of Science ®Google Scholar
• Ghamarian A, Azarakhsh S. Axial crushing analysis of polyurethane foam-filled combined thin-walled structures: experimental and numerical analysis [J]. Int J Crashworthiness. 2019;24(6):632–644.
   Web of Science ®Google Scholar
• Rad MA, Khalkhali A. Crashworthiness multi-objective optimization of the thin-walled tubes under probabilistic 3D oblique load [J]. Mater Des. 2018;156:538–557.
   Web of Science ®Google Scholar
• Wang J, Zhang Y, He N, et al. Crashworthiness behavior of Koch fractal structures [J]. Mater Des. 2018;144:229–244.
   Web of Science ®Google Scholar
• Abramowicz W, Wierzbicki T. Axial crushing of multicorner sheet metal columns [J]. J Appl Mech. 1989;56(1):113–120.
   Web of Science ®Google Scholar