# Frontiers of Mechanical Engineering

 Front. Mech. Eng.    2020, Vol. 15 Issue (3) : 438-474     https://doi.org/10.1007/s11465-019-0579-1
 REVIEW ARTICLE
Review of the crushing response of collapsible tubular structures
Vivek PATEL(), Gaurav TIWARI, Ravikumar DUMPALA
Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur 440010, India
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 Abstract Studies on determining and analyzing the crushing response of tubular structures are of significant interest, primarily due to their relation to safety. Several aspects of tubular structures, such as geometry, material, configuration, and hybrid structure, have been used as criteria for evaluation. In this review, a comprehensive analysis of the important findings of extensive research on understanding the crushing response of thin-walled tubular structures is presented. Advancements in thin-walled structures, including multi-cell tube, honeycomb and foam-filled, multi wall, and functionally graded thickness tubes, are also discussed, focusing on their energy absorption ability. An extensive review of experimentation and numerical analysis used to extract the deformation behavior of materials, such as aluminum and steel, against static and dynamic loadings are also provided. Several tube shapes, such as tubes of uniform and nonuniform (tapered) cross sections of circular, square, and rectangular shapes, have been used in different studies to identify their efficacy. Apart from geometric and loading parameters, the effects of fabrication process, heat treatment, and triggering mechanism on initiating plastic deformation, such as cutouts and grooves, on the surface of tubular structures are discussed. Corresponding Author(s): Vivek PATEL Just Accepted Date: 23 February 2020   Online First Date: 20 March 2020    Issue Date: 03 September 2020
 Cite this article: Vivek PATEL,Gaurav TIWARI,Ravikumar DUMPALA. Review of the crushing response of collapsible tubular structures[J]. Front. Mech. Eng., 2020, 15(3): 438-474. URL: http://journal.hep.com.cn/fme/EN/10.1007/s11465-019-0579-1 http://journal.hep.com.cn/fme/EN/Y2020/V15/I3/438
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 Fig.1  Force vs. displacement curve of tubular structures used for measuring crashworthiness parameters. Fig.2  Classification of a tubular structure. Fig.3  Mode of collapse element: (a) Type-I and (b) Type-II. w: Width of the tube; α, γ: folding angle of corner element; N: Distance between the plastic hinges of folding element. Reproduced with permission from Ref. [6] from Elsevier. Fig.4  Front and top views of a deformed tube with two opposite holes at mid height. Reprinted with permission from Ref. [21] from Elsevier. Fig.5  Specimens with (a) alternative grooves [24] and (b) external grooves only [25]. $D ‾$, $Do$, $Di$: Mean, outer, and inner diameter of shell/tube, respectively; b, d: Width and depth of groove, respectively; λ: Groove distance; H: Length of rings between grooves.Reproduced with permission from Refs. [24,25] from Elsevier. Fig.6  Steel samples: Collapse modes at velocities of 385, 277, 227, 173, and 0 m/s (from left to right). Reprinted with permission from Ref. [27] from Elsevier. Fig.7  Geometric configuration of the ring-fitted tube under axial and oblique loading conditions. V: Velocity of striker; β: Load angle. Reproduced with permission from Ref. [30] from Elsevier. Fig.8  Schematic of circular tubes with (a) radial corrugation and (b) longitudinal corrugation. Fig.9  Schematic of specimens with developed designs of (a) tube with expanding rigid ring press-fitted at the top and (b) tube with wide external grooves. $do$, $di$: Outer and inner diameter of expanding steel ring; L1, L2: Length of tubes. Reproduced from Ref. [34] from Elsevier. Fig.10  Circular tube with buckling initiator. Reprinted with permission from Ref. [39] from Elsevier. Fig.11  Aluminum samples: Collapse mode at velocities of 361, 220, 137, and 0 m/s (from left to right). Reprinted with permission from Ref. [27] from Elsevier. Fig.12  Schematic representation of tube splitting arrangement. Reproduced with permission from Ref. [45] from Elsevier. Fig.13  Constraint used for a square box component: (a) Grooves on the sidewalls of the tube and (b) grooved end cap for end constraint. Reprinted with permission from Ref. [47] from Elsevier. Fig.14  Square hat tube with trigger. Reproduced with permission from Ref. [51] from Elsevier. Fig.15  Numerical models of (a) conventional square tube, (b) square tube with grooves on all faces, and (c) square tube with grooves on opposite faces. Reprinted with permission from Ref. [52] from Elsevier. Fig.16  Schematic of square tubes with different trigger positions: (a) Trigger at the top, (b) trigger symmetric on two planes, and (c) trigger asymmetric on three planes. Reproduced with permission from Ref. [58] from Elsevier. Fig.17  Schematic of new design structure: (a) With pyramidal element, (b) Type A, and (c) Type B patterns. p, q: Side of pyramidal element; s: Apex height. Reproduced with permission from Ref. [59] from Elsevier. Fig.18  Schematic of a square tube with a hole at mid length. $ds$: Slot diameter. Reproduced with permission from Ref. [60] from Taylor & Francis. Fig.19  Mechanism of deformation. Reproduced with permission from Ref. [69] from Elsevier. Fig.20  Schematic of tapered tubes (a) without cutouts and (b) with circular cutouts. $Ds$, $Dl$: Smaller and larger end diameter of frusta tube respectively; φ: Taper angle of frusta tube. Reproduced with permission from Ref. [79] from Elsevier. Fig.21  Collapse modes of combined tube: (a) Compound diamond, (b) compound fragmentation, (c) delamination, and (d) catastrophic failure. Reprinted with permission from Ref. [86] from Elsevier. Fig.22  Modes of failure of specimens under compressive loading: (a) Mode-I, (b) Mode-II, and (c) Mode-III. Reprinted with permission from Ref. [97] from Elsevier. Fig.23  Spot-welded steel–CFRP SHS tube. Reprinted with permission from Ref. [102] from Elsevier. Fig.24  Deformed specimens: (a) Non-compact form and (b) compact form. Reprinted with permission from Ref. [109] from Elsevier. Fig.25  Crushed specimens: (a) Square, (b) hexagonal, and (c) octagonal filled with aluminum foam. Reprinted with permission from Ref. [112] from Elsevier. Fig.26  Constrained multi-tube structure: (a) Hexagonal packed empty, (b) hexagonal packed aluminum foam filled, (c) square packed empty, and (d) square packed aluminum foam filled tube. Reproduced with permission from Ref. [113] from Elsevier. Fig.27  (a) Aluminum foam-filled tube, (b) polystyrene foam-filled tube, and (c) concertina collapse mode. Reprinted with permission from Ref. [120] from Elsevier. Fig.28  (a) Finite element model under oblique loading condition and (b) experimental setup for oblique loading. P: Applied load. Reproduced with permission from Ref. [122] from Elsevier. Fig.29  Geometric configurations of honeycomb sandwich columns: (a) Kagome, (b) triangle, (c) hexagon, (d) square-3, (e) square-4, and (f) diamond. Reprinted with permission from Ref. [125] from Elsevier. Fig.30  Configuration of honeycomb-filled single and bi-tubular polygonal tubes (N = 3, 4, 5, 6, 7, 8, and ∞): (a) Single polygon tubes and (b) bi-tubular polygon tubes. Reprinted with permission from Ref. [126] from Elsevier. Fig.31  Prepared samples: (a) Empty square aluminum tube, (b) aluminum honeycomb-filled tube, (c) polyurethane-filled tube, and (d) tube filled with honeycomb and foam. Reprinted with permission from Ref. [127] from Elsevier. Fig.32  Division of multi-cell section: (a) Corner, (b) crisscross, and (c) T-shaped. Reprinted with permission from Ref. [131] from Elsevier. Fig.33  Multi-cell tube cross section with different angle elements. Reprinted with permission from Ref. [132] from Elsevier. Fig.34  (a) Angle element with varying cross sections and (b) specimen for axial testing. Reprinted with permission from Ref. [134] from Elsevier. Fig.35  Multi-cell tube with different sections. Reprinted with permission from Ref. [135] from Elsevier. Fig.36  Schematic representation of foam-filled tubular structures with different cell configurations. Reprinted with permission from Ref. [137] from Elsevier. Fig.37  Multi-cell tubes: (a) Triangular lattice and (b) Kagome lattice. Reprinted with permission from Ref. [138] from Elsevier. Fig.38  Schematic of a circular tube with inserts. $ti$: Insert wall thickness; R: Radius of shell/tube. Reproduced with permission from Ref. [139] from Elsevier. Fig.39  FGT variation in tubes: (a) Longitudinal direction and (b) transverse direction. Fig.40  (a) Thickness nonuniformity and (b) structural layout of CTGTs under oblique load. Reproduced with permission from Ref. [147] from Elsevier. Fig.41  Prepared specimens: (a) Square tube with uniform and graded thickness and (b) two configurations of graded thickness. Reproduced with permission from Ref. [144] from Elsevier. Fig.42  FGT multi-cell tubes: (a) 3D view and (b) 2D view. Reprinted with permission from Ref. [149] from Elsevier. Fig.43  Configuration of bi-tubular specimens: (a) Parallel and (b) diamond arrangements. Reprinted with permission from Ref. [151] from Elsevier. Fig.44  Schematic of (a) the dumbbell-shaped novel tube, (b) cross-sectional view, and (c) self-locking tube. Reprinted with permission from Ref. [162] from Elsevier. Fig.45  Self-locking energy absorber with enclosed and unenclosed forms. Reproduced with permission from Ref. [164] from Elsevier. Fig.46  Nested tubular structures incorporating the same outer circular part with different inner parts such as: (a) An oblong cross-section, (b) two circular tubes of different diameters, and (c) two circular tubes of the same diameter. Reprinted with permission from Ref. [165] from Elsevier. Fig.47  Comparison of the load–displacement plots of multi-cell tubular structures: (a) Without foam and (b) foam-filled. Reproduced with permission from Ref. [172] from Elsevier.