Original Article

Proc IMechE Part D:

J Automobile Engineering
2021, Vol. 235(7) 1835–1848
A basic design for automotive crash Ó IMechE 2021
Article reuse guidelines:
boxes using an efficient corrugated sagepub.com/journals-permissions
DOI: 10.1177/0954407021990921

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Alireza Mortazavi Moghaddam1, Atefeh Kheradpisheh2 and

Masoud Asgari3

Abstract
Frontal vehicle structure is of high importance through crash energy managements and crash boxes are the fundamental
structural component for vehicle safety as well as after sales issues. Similar to many other vehicle components, the detail
design of crash box is usually part of manufacture knowhow. However, some guide lines are always available. In this arti-
cle a general procedure is introduced for designing of crash box with the aid of novel thin walled structures and accord-
ing to conventional crash scenarios. The problem is followed through some basic steps. Firstly, the crash box idea is
selected through a wide range of previous investigated elements and is packaged in a real bench vehicle. Then thanks to
the protection provided by the new crash box on the other more expensive components (e.g. headlamp, cooling pack,
etc.), the effectiveness of this element are acknowledged through the low speed offset crash. Further on the robustness
of new proposed crash box is approved by high speed crash simulations. The quasi-static simulations implemented during
the analyses are carried out by finite element explicit code (Abaqus) and the FE modeling and dynamic simulation
through the next steps are also performed in ANSA and PAM CRASH respectively. Finally in addition to the general
crash box design proposed procedure, the achieved results demonstrated that the corrugated conical thin walled tubes
deforms in regular and rather stable shape under both axial and oblique loadings. They also produced a reasonable reac-
tion force versus deformations which leads to stiff and crashworthy energy absorber in comparison to traditional rectan-
gular and even some special models like as origami shapes, and so they could be a valuable selection for crash box
implementations in passenger cars.

Keywords
Crash box, automotive body developments, energy absorption, crashworthiness, passenger vehicles

Date received: 8 July 2020; accepted: 30 November 2020

Introduction the behind structure (main rails) detached from plastic

deformations, while the risk for pedestrians is low and
Nowadays, thanks to the advancements in the automo- for vehicle occupants is negligible, if correctly belted.
tive active safety as well as the improvements achieved Crash box is usually a thin-walled sacrificial element
through the roads standardization, the world seems to implemented between the vehicle bumper structure and
be safer. However, the need for vehicles structural
safety due to increased speed and traffic is still a top
priority for auto-makers and insurance companies. On 1
Department of CAE, Automotive Industries Research & Innovation
the other hands, the body in-white (BIW) weight is Center of SAIPA, Tehran, Iran
2
30%–40% of the total car weight. So, the use of opti- Amirkabir University of Technology, Tehran, Iran
3
Research Laboratory of Passive Safety Systems, Faculty of Mechanical
mal weighted elements in the car body will be of partic-
Engineering, K. N. Toosi University of Technology, Tehran, Iran
ular importance. Based on the vehicle safety standards
and insurance company’s requests, vehicle protection Corresponding author:
priorities vary with the speed of the crash. For instance, Masoud Asgari, Research Laboratory of Passive Safety Systems, Faculty of
usually up to 15 km/h, the main goal is to minimize Mechanical Engineering, K. N. Toosi University of Technology, Vanak
Square, Molla-Sadra, Pardis, P. O. Box: 19395-1999, Tehran 1999143344,
repair costs of frontal vehicle components1 (e.g. bon- Iran.
net, head lamps, cooling pack, etc) in addition keeping Email: asgari@kntu.ac.ir
1836 Proc IMechE Part D: J Automobile Engineering 235(7)

axial and oblique loadings. In another study Ahmadi

and Asgari15 surveyed the effect of corrugations on
energy absorption characteristics of conical and cylind-
rical tubes under quasi-static forces. They demon-
strated that by corrugations, one can achieve a more
stable energy absorber element under axial and oblique
loads. In addition, Azimi et al.16 desired a group of new
homo-polygonal multi-cell Finite element models under
both axial and oblique loads via studying the effect of
cell growth on energy absorption characteristics. In
parallel, hybrid and multi-sectional structures are also
Figure 1. Crash management system (crash box) between noticed. For instance, single and double (e.g. inner con-
main rails and bumper beam. ical and outer circular tubes) wall structures for crash-
worthiness are considered to introduce as energy
absorber.17 Also, a new bi-tubular corrugated compo-
the longitudinal main rails. It is also known as Crash site tube, consisting of inner and outer cylindrical and
Management System (CMS)2 to absorb the energy and conical tubes is considered and studied numerically in
limit the force acting on the rail during low speed axial and oblique crushing in order to achieve favorable
impacts and is adopted in most of passenger cars simi- crashworthiness parameters.18 The crushing behavior
lar to Figure 1. of hybrid metal-composite conical tube under dynamic
On the other sides, through engineering and aca- loading is studied by Shiravand and Asgari19 and a the-
demic researches, different energy absorbers are evalu- oretical solution for laminated composite conical tubes
ated according to their crashworthiness level. is developed.
Crashworthiness is defined as the ability of a structure In some other cases the researches focused on energy
to resist under certain level of loading and to reduce the absorption issue from a vehicle perspective with special
damage caused in those cases involving ultra-dynamic attention on crash box design. The optimization studies
loads.3 In terms of vehicle engineering, crashworthiness have been carried out to find a compromise settlement
is the capability of a vehicle to protect the passengers between lightweight and crashworthiness as the contra-
from severe injuries or even death in case of an accident dictory design targets. In order to solve the problem,
which is somehow survivable.4 Nowadays, the interest surrogate model is generally used. As an example, Lee
of using energy absorber structures with higher crash- et al.20 provided a design route to define the dimensions
worthiness capability has been increased.5 These ele- of the crash box cross-section in addition to its shape
ments convert the kinetic energy of crash into strain of by topology optimization in order to enhance an
energy through structural deformation.6 Thin-walled optimum design. They suggested detailed shapes of
structures have gained a lot of interests among different three new types of crash box based on their proposed
energy absorbers over time due to their much higher design procedure. Wang et al.21 proposed a crash box
efficiency and less weight compared to other peers.7 filled with a three dimensional negative Poisson’s ratio
One of the first pioneers of the thin-walled structures (NPR) inner core based on an inner hexagonal cellular
was Alexander.8 He studied the concertina deformation structure. And resulted the NPR structure can generate
mode of steel circular tubes under crushing forces and smooth and controllable deformation to absorb energy
derived an approximate theoretical model. Later on, as car crash box. Few researches considered crash box
Abramowicz and Jones9 and Wierzbicki et al.10 before and after components in loading process. For
improved the solution. Azimi and Asgari11 have studied example, Li et al.22 used surrogate model to optimize
crushing characteristics of small-sized conical tubes the crashworthiness for functionally graded foam-filled
called miniature frusta under axial loading using Finite- thin-walled structures. They focused the study on struc-
element models. Through another research, surface tural optimization and material replacements to per-
indentations are studied on thin-walled conical tubes form the crashworthiness optimization of the bumper,
under axial impact using surrogate models called meta- crash box and rails as an assembly. And the results
models.12 In a more generic survey by Malekshahia showed that the functionally graded foam-filled struc-
et al.13 a new theoretical approach proposed based on ture is more valuable than the uniform foam-filled
previously offered Super Folding Element (SFE) theory structure. In one of the latest surveys, Boreanaz et al.23
and the progressive collapse damage of prismatic thin have introduced origami geometry to shape the vehicle
walled metal columns with different regular cross sec- front crash box. They implemented numerical and
tions, under the action of axial quasi-static and impact experimental analysis of the structure under axial quasi
loads has been investigated both analytically and by static load. According to Mari study, the origami-
computer simulations. Through more recent studies inspired crash box design compared to a traditional
some innovative structural elements is also considered crash box would enhance the energy absorption capac-
as energy absorbers. Mahbod and Asgari14 have stud- ity in low speed axial crush. In parallel to the above
ied foam-filled corrugated composite tubes and under researches, some attempts have intended to find the
Mortazavi Moghaddam et al. 1837

proper targets and criteria for crashworthiness perfor- published basic definitions are introduced here bellow
mance evaluations. Leimbach and Kiebach1 performed which will be helpful to validate the crashworthiness
a review to address the history of low speed repair efficiency of different thin-walled structures under
crash tests and the relevance of crash repair tests in the crushing loads through finite-element simulations.
calculation of insurance premiums for fully comprehen- Initial peak crushing force (IPCF), is the maximum
sive cover. They studied various standards and crash buckling resistance force which rise usually at the start
tests and concluded the RCAR (Research Council for of compressing of the structure. The greater IPCFs
Automobile Repairs) as a common test for low speed indicate higher initial resistance of the structure for
crashes. buckling and as results, higher damages and worst
However, the numerous above mentioned researches injuries.
on a variety of geometries for crashworthiness and Total energy absorbed (EA), is the total work done
energy absorptions, lead to many achievements of on the structure to cause deformation as results of
developing the specific crashworthy models and materi- impacting by an object. In terms of mathematics, it can
als, still most of these investigations have been limited be formulated as the following:
on the analyzing of individual elements or structures ð Lc
under ideal loading situations and the needs for real EA = Fdx ð1Þ
case simulations are strongly sensible. On the other 0
hands, new proposals for crash box robust design by Where Lc is the crushing length and F denotes the resul-
considering both the individual structural crushing tant impact force.
effects and besides implementing the structure in real Specific energy absorbed (SEA) is used in order to
vehicle conditions and performing the vehicle level characterize the structure independent from the mass
analysis seems to be more practical and need more as the absorbed energy per unit mass of material:
attentions.
In this paper, a methodology for vehicle crash box EA
SEA = ð2Þ
design has been presented by implementing three main m
vehicle frontal crash simulations (i.e. AZT (Allianz Where m is the mass of the energy absorber.
Zentrum für Technik) test as per RCAR, full frontal Undulation of load carrying-capacity (ULC) was
crash against rigid barrier according to FMVSS 208 introduced by Wang et al.21 evaluate the stability of the
and oblique 30 degree crash selected from general vehi- structure under crushing. Lower ULCs indicate that
cle crash test scenarios). To reach the goal, the problem the fluctuations of the load–displacement curve are
is undergone through three main steps. First of all the close to each other which indicate a more stable struc-
specific crashworthy parameters (i.e. SEA, CFE, ULC ture under crushing. It can be calculated as:
and IPCF) related to frontal crash and structural
Ð Lc
energy absorption have been introduced. In addition, jF(x)  Fm jdx
the theoretical formulation for the rectangular and con- ULC = 0 ð3Þ
EA
ical tubes collapse under axial loading is also presented.
Then according to these characteristics, through step 1, Where Fm is the mean crushing force and is calculated
the conceptual idea of special conical corrugated tubes as follows:
as an optimum mini-structure for the crash box struc- EA
ture is picked up from different investigated alterna- Fm = ð4Þ
Lc
tives. In step 2, the geometrical parameters of the
selected crash box thin-walled conical tube is designed Crushing Force Efficiency (CFE); peak resistance force
during quasi-static axial loading in comparison to ori- (which usually happens at the initial loading phase) and
gami and conventional rectangular structures. An ana- the mean force are extremely important parameters that
lytical calculation is also performed at this step for directly influence the deceleration of the passengers in
simulation evaluation. At the 3rd and final step, the the vehicle. Bellow formula takes both of these para-
new proposed crash box is packaged in a benched vehi- meters into consideration very well. So an ideal absor-
cle and its efficiency is proved through dynamic crash ber can exhibit a crush force efficiency of unity with a
simulations in comparison to the general rectangular rectangular-shaped of force versus crushing distance
crash box. curve:
Fm
CFE = ð5Þ
Problem formulations and definitions Fmax

Energy absorption characteristics of thin-walled Pcrashbox and Prail; Crash box and rail reaction force lim-
its are defined through design process in order to have
structures an optimum crash box and safe detached longitudinal
To date, many characteristics have been defined to esti- rails from permanent deformations (in low speed
mate the crashworthiness competency.24,25 The most crashes) as bellow:
1838 Proc IMechE Part D: J Automobile Engineering 235(7)

Pmax Crashbox \ Pmax Rail ð6:1Þ

Pmax Crashbox 4PmeanRail ð6:2Þ

In the case of low speed impact made on the left side of
vehicle (e.g. AZT), the crash box that is subjected to the
impact is almost completely deformed axially, while the
two front rails do not exhibit relevant deformation26
and the adequate safety margin for equation (6) would
clearly dependent on manufacturing scatter. So here by
considering 15% of safety margin, the corrected crush-
ing force limits is defined as bellow:

Pmax Crashbox = 0:85Pmax Rail ð7Þ

Figure 2. Geometrical parameters of corrugation model in

Analytical formulations of tubes under axial crushing rectangular crash box.

The energy absorption of the conical corrugated tube based on the external work done by compression of the
under axial static loading was formulated by Asgari box through the rotational plastic deformation in bend-
et al.12 based on the work have been done during defor- ing and extensional/compressional deformation of the
mation (bending at the plastic hinges and energy dissi- membrane walls. So the mean crushing force Fm was
pated by the circumferential stretching between obtained as bellow:
corrugations) and it was reported as bellow:
" "   p s 0 H2 s0 HlNc
XN
1 L kFm = (Lc1 + Lc2 ) + ð10Þ
EA = 2
pffiffiffisy t p r0  (2i  1) 4 l 4
3 2
1
# # Where LC1 and LC2 are the inner and outer circumfer-
(i + b) i+b A ence of the corrugation respectively
+ (  1) : tan (a):A 3 sin (a) + ( 1) : s0 is the flow stress (considering the strain hardening
cos (a)
  effect) and is obtained from:
2A p:t:sy :L2 :½1  sin (u0 ) cos (a)
3 p  2tan1 + s y + su
L cos2 (a) s0 = ð11Þ
ð8Þ 2
Where sy and su are yield stress, and ultimate tensile
In which:
strength of the box material, respectively.
a is the conic semi-epical angle
And factor k4 1 is a correction factor for effective
i is counted from the base of the tube
crush distance is defined as bellow
b is 0 for even and 1 for odd number of corrugations
respectively k = 5:3l + 0:52 ð12Þ
N is the total number of engaged corrugations
through the deformation Nc, H and l are the geometrical of the corrugation (see
sy denotes the Von-Mises criterion resulting from Figure 2).
plastic moment
t, r0, A and L are conic geometrical parameters Crash box design criteria in AZT simulation
and u0 is derived from bellow relation: According to the Research council for automobile
repairs (RCAR), an important test to evaluate the vehi-
2A
u0 = tan1 ð9Þ cle damageability and reparability is the so called AZT
L
test. The test includes a car (by 40% offset) collide with
The mean reaction force could be calculated by putting a rigid barrier with special setting parameters as indi-
equation (8) into equation (4). Further on, the above cated in Figure 3 with a low speed impact of 15 km/h.
formulation is used as analytical solution for evaluation Therefore, the effectiveness of the crash box counter-
of the computational simulation results as well. measure is usually assessed also by the AZT.
Regarding the rectangular corrugated tube, In this article a car weighing 1500 kg is desired as a
Ghasemnejad et al.27 used a theoretical solution sample passenger car for AZT simulation. The total
method (the so called Super Folding Element method energy (here the kinetic energy of the car) that has to be
which was developed by Wierzbicki and Abramowicz28 absorbed during crash is almost 15 kJ. However, usu-
for obtaining the mean dynamic crush force in the axial ally based on vehicle design experience, the crash box
progressive crushing of thin-walled square columns) has to absorb a lower amount of energy, approximately
and extended this approach to the corrugated crash 70% (desired efficiency of collapse of a well-designed
boxes. Again the phenomenon for this formulation is crash box) of the initial kinetic energy. So the crash box
Mortazavi Moghaddam et al. 1839

Figure 3. AZT set up according to RCAR.

Figure 4. Conical corrugated tube and geometrical parameters

role would be reduced to 10 kJ, and the missing 5 kJ (i.e. A, t, Li, D, L, and a).15
energy could mainly be damped by elastic deformation
of the body shell, damage to bumper, grille, fender,
bonnet etc. and by oscillations of the elements not that lessen the maximum force while keeping the energy
rigidly fixed to the body like vehicle suspensions, absorption level intact. On the other hands, the mean
powertrain, dummy and fuel. As a consequence: crushing force doesn’t decrease too much. Recently,
these elements are desired for their more constant load-
EACrashbox ffi 0:7Kecrash@AZT ð13Þ displacement curve compared to straight tubes besides
their ability to withstand oblique impact loadings.
In which Ke denotes the total vehicle kinetic energy just Figure 4 shows a sample conical corrugated tube stud-
before crash. ied by Ahmadi and Asgari.15
As results, the conical corrugated concept is selected
Results and Discussion as it seems to closely satisfy bellow performance guide
lines and somehow more flexible to being modified
Step 1, selection of crash box structure insight into an ideal crash box model.
In this section, some structural configurations have
 Low IPCF comparable to the average deformation
been reviewed and the conceptual crashworthy element
is selected based on the above mentioned characteris- force
 Lower fluctuation amplitudes through force – dis-
tics. The crashworthiness and energy abortion effi-
ciency of those structures depend on several factors, placement curve
 Higher swapped area under force-displacement
like as geometry and constituent material. However,
when a specific material is selected, then one should curve
 Not influenced by load direction
concentrate the attention on the geometrical factors
 Gradual and regular folding
like as thickness, cross section, corrugations, extrude
 Ease of fabrication and lowest weight escalation
angle, etc. The first considered structure is cylindrical
 No global buckling and better energy management
tube with and without corrugations as it was studied
by Mahbod and Asgari.14 The straight cylindrical tube capability as results of special corrugations.
impose very high initial force and unstable deformation
while creating corrugations decreases the IPCF and in Step 2, Crash box parametric design
some cases improves the CFE criterion while keeping
the SEA intact. The second structure is small-sized con- Based on the Mario study23 the sample conventional
ical tubes called miniature frusta.11 It was stated that and origami crash box is modeled with similar dimen-
increasing the thickness leads to larger amplitudes in sions as in Figure 5. General crash boxes are made of
load oscillation and so EA while, higher ULC and so square tubes, instead of origami type that has a series
lower structural stability, which is not in favor of crash- of pre-folded surfaces. These tubes generally shaped a
worthiness element. In addition, having semi-epical rectangular cross section with a smaller side of 68 mm,
angles decreases the IPCF as results of creating dia- a larger side of 110 mm. The tubes height is considered
250 mm and the shell thickness is desired 1.6 mm.
mond folding. Semi epical angle of 5°–15° was finally
recommended for generalized energy absorption appli-
cation. The Corrugated conical tubes was another New crash box 3D and FE model developments. In order to
investigated election which seems to as a combination have fairly comparison with general and origami
of corrugated cylinder and miniature frusta. This design, the most possible similarities (i.e. the overall
tapered thin-walled introduce a new corrugation form dimensions, material and weight) have been considered
1840 Proc IMechE Part D: J Automobile Engineering 235(7)

other general parameters are the same according to

Table 1.
The other corrugated parameters (i.e. A and L) are
derived by some simulation iteration of quasi static
axial loadings on FEM model. Table 2 and Figure 6
show the 6 cases generated on corrugated conic con-
cept. The conic was situated vertically between two
rigid plates as indicated in Figure 7. General contact
algorithm was used and the coefficient of friction is
considered 0.2 to account for the friction between tubes
and rigid bodies as well as tube surface itself. The base
Figure 5. General (left) versus origami (right) crash box. of the tube was connected to the rigid plate via ‘‘Tied
node to surface’’ interaction during impact. The bot-
tom plate was fixed and the top plate was limited to
move only in the axial direction. The upper plate was
Table 1. Crash box desired basic material properties. moving with constant velocity (42 mm/s to guarantee a
true quasi static simulation) in conic axial direction.
Material properties And the mass scaling technique was implemented (in
Density 7800 kg/m3 parallel the ratio of total kinetic energy to the total
Young’s modulus 210 Gpa internal energy was monitored during the simulation to
Poisson’s ratio 0.3 be below 5%) for speeding up the job. Linear S4R shell
elements are used for meshing. Then, a mesh sensitivity
analysis has been carried out for defining appropriate
element size. According to Figure 8, it can be seen that
Table 2. Case study parameters. decreasing the element length lower than 2.5 mm has
minor effects on the results while it will cause more
L (mm) A (mm) simulation time. So, the conic is meshed with element
size 2.5 which seems acceptable to validate the model
Case_01 10 2
Case_02 20 2 with a proper accuracy besides a reasonable time step.
Case_03 10 1.5
Case_04 10 1.25
Case_05 10 1 Results analysis of the case studies. Figure 9 shows the
quasi-static force versus deformed length of sample
cases along with the Origami and general23 crash box
results. According to the curves trajectory, one can see
among the provided FEM models and Mario study. that the resistance force of the Origami structure
Hence, the base circle of the conic has the same peri- crosses the ‘‘rail buckling force’’ border (which is
meter as the general crash box. So, the new crash box desired ;80kN as generic idea of 20% safety margin
would have a base diameter equal to 113mm and over- related to simulation results and Fr in Table 4) in the
all height of 250 mm. Dual phases steel is desired as the initial and also during deformation process. On the
crash box material with the yield strength equal to other side, the traditional curve starts with a reasonable
410 MPa, the tensile strength equal to 600 MPa and the pick force but fall down very soon. The conics

Figure 6. Case study models, new crash box design.

Mortazavi Moghaddam et al. 1841

120
110 Rail buckling
100 limit force
90 Case_01
80
Case_02

Force (kN)
70
60 Case_03
50 Case_04
40
30 Case_05
20 General
10
Origami
0
0 50 100 150 200
Deformaon (mm)

Figure 9. Quasi-static force – displacement of the new crash

box cases versus origami and general models.
Figure 7. Mesh and FE models of new crash box.

0.5 1 1.5 2 2.5 3 3.5 4 EA (kJ) ULCx10

-62000
12

10
-67000
IPCF (N)

-72000 6

4
-77000
Element Size (mm) 2
(a)
13 0
Case_01 Case_02 Case_03 Case_04 Case_05 General Origami

12
Figure 10. EA and ULC (scaled by 10) for five case studies
besides origami and general samples.
EA (kJ)

11

10
instead. According to the results, the IPCF raise by
implementing lower ‘‘A’’ parameters. However, this
parameter in Case 03 is still lower than traditional one.
9
0.5 1 1.5 2 2.5 3 3.5 4 While, in case_04 and 05 the IPFC reaches the reason-
Element size (mm)
able value higher than general pick force. Comparing
(b) the case_04 and 05 leads to the idea that by decreasing
the A value lower than 1; no considerable increase
Figure 8. Mesh sensitivity analysis results for IPCF (a) and EA would be achieved in IPCF while higher fluctuation
(b) through Case_04. amplitudes would be expected as results of semi-
straight tube.
In order to finalize the problem and find the best
geometrical parameters were desired with reference to case, two another crashworthy parameters (i.e. EA
the guide lines which were described before insight into and ULC) is also compared among the case studies
having an optimal crash box and considering the ease (see Figure 10). It is worth mentioning that here the
of fabrications. So L5, 30, 40 and A0.25, 0.5 were EA could also represent the SEA, as to some extents,
excluded from the selections. all the tubes have similar weight. According to Figure
Starting with Case_01, it experience a moderate 10, the value of the energy absorbed by case_05 is
IPCF (;45 kN) and increases gradually to higher val- closer to the Origami design and higher than the other
ues, however, the swapped area under the curve (i.e. samples. This advantage beside the moderate ULC
energy absorbed) is rather low. By increasing the corru- value of Case_05 in comparison to the cases 01, 03,
gation period (L value) from 10 to 20 mm, In Case_02 and 04 and its lower value compare to case_02, ori-
the pick loads also increases whilst the load fluctua- gami and general samples, leads to the result that
tions denote an unstable structure. As results, we fol- Case_05 is a proper and optimum structure to be used
low the study with L10 and decreasing the A value as vehicle crash box.
1842 Proc IMechE Part D: J Automobile Engineering 235(7)

Table 3. Crashworthy characteristics. The computer simulation is conducted by explicit,

non-linear finite element code PAM-CRASH. The
EA (simulation) EA (analytic) Deviation (%) crash boxes are fixed together at rear end using rigid
Case_01 8500 8190 3.65 body boundary condition, and the vehicle mass (here
Case_02 9000 6541 27.32 1500 Kg) is added to middle node of rigid body. At the
Case_03 9900 8800 11.11 other ends the crash boxes are attached to the bumper
Case_04 10,500 9120 13.14 by two plates which are desired for better force distribu-
Case_05 11,400 9448 17.12
tion during crash events. The barrier is modeled as rigid
General 5000 – –
Origami 11,500 – – body and the vehicle model confined to move only in
X-axis. Conventional steel type (DP590) is defined for
crash box and less stiff one (440R) is used for the bum-
per beam. The mesh size is again considered 2.5 mm.
Specimens are modeled using Quad/Tria-1st order shell
with reduced integration algorithm. In order to elimi-
nate zero energy modes, the stiffness-type hourglass
control is implemented. ‘‘SURFACE TO SURFACE’’
and ‘‘‘SELF’’ contact type is adopted for contact simu-
lation between the crash box, bumper and barrier. All
DOF of vehicle model except X-direction movements is
constraint and an initial velocity INVEL condition is
imposed on the model. In all cases the static and
Figure 11. The mesh model of the crash box (left: new dynamic coefficient of friction is taken 0.2. Section
proposal; right: traditional). force plane is defined at the end of crash box to record
the force time history transferred through the structure.
The whole model is undergone through three test cases
Simulation validation based on theoretical formulation. In out of common vehicle manufacturer crash scenario.
order to validate the simulation results of case studies, The simulation begins with AZT as the basic test and
the energy absorbed from Equation 8 is calculated for continues with FFRB 50 Kph and Oblique 30 Kph
all five cases and the results compared with CAE out- crash tests for design robustness and validation.
puts. Table 3 compares the FEM and analytical energy
absorption characteristics. The resultant deviation is
almost in reasonable range and there is a good agree- AZT simulation model. The finite element models used
ment between analytical and FEM values. However, below include three main parts, which are the crash
for higher corrugation length (e.g. L = 20 as in boxes (left and right crash box that simulate the vehi-
Case_02) the number of corrugations is not equal to cle), the barrier and the front bumper beam, as shown
the number of occurred plastic hinges and the results in Figure 12.
could not be liable for CAE validation. In addition, Referring to the design criteria stated in part 2.1, the
decreasing the corrugation amplitude (A), will stimu- base and target resistance loads of both rail and crash
late the corrugated cone to behave like a simple cone box are defined in Table 4. It is worth mentioning that
with no corrugations and so the deviation between the chronologically, here the minimum resistance load of
analytical solution and FEM results increases. the rail (i.e. Fr in Table 4) is derived from crash box
desired efficiency. Whilst in a vehicle design process, it
Step 3, Crash box performance validation in real is also possible to use the rail collapse load as an input
for crash box design.
benched vehicle model Figure 13 shows the model before and after AZT
3D modeling and meshing. In this step a benched vehicle simulation. The energy balance of the problem is also
is selected with a relatively long crash box (so it is a presented in Figure 14. This graph indicates that the
good bench for buckling effects analysis). Then two total hourglass energy is negligible and the simulation
models are packaged, one with traditional (currently in was stable.
used) crash box and the other with new designed crash For better understanding of the crash box efficiency
box out from step 2. To simplify the problem and focus we compare the identical situations for both the new
on the crash box model independent from vehicle struc- and traditional crash box with each other as presented
ture, the whole vehicle assembly behind the crash box is here bellow in Figure 15. The buckling of traditional
omitted and is replaced with a mass body. 3D CAD model is executed considerably on two locations, while
DATA is provided by CATIA V5. The geometrical these deformations are very minor in new crash box.
parameters were kept the same with benched vehicle. On the other hands, the new crash box deforms more
The 3D assembly is imported to ANSA for mesh and regularly in comparison to the traditional one. Figure
FEM modeling. (Figure 11 shows the meshed 3D model 15 also shows that the overall deformation of the new
of the new and traditional crash box.) crash box is below 144 mm and comparing with the
Mortazavi Moghaddam et al. 1843

Figure 12. AZT FE model of the vehicle with new crash box.

Table 4. Dimensioning of the crash box and loading predictions for AZT.

Parameter name Formulation Unit Value

Vehicle curb weight – kg 1500

Vehicle velocity in AZT V mm/ms 4.16
Vehicle kinetic energy Ke kJ 12.98
Crash box desired efficiency H % 70
Kinetic energy dissipated by crash box EAcrashbox = Ke 3 h kJ 9.08
Initial crash box average length Li mm 205
Max crash box collapse Lc = Li 3 h mm 143.5
Average load of collapse of crash box + bumper beam Fm = EAcrashbox/Lc kN 63.28
Max load from crash box Fmax = Fm/h kN 90.4
Min compressive resistance load of the rail (considering 15% safety margin) Fr = 1.15Fm kN 104

Figure 14. New crash box energy transfer during AZT

Figure 13. Crash box deformation through AZT simulation. simulation.

target value of Lc (i.e. 143.5 mm as it was predicted in While, the traditional one should deform up to 162 mm
Table 4), the new model has been absorbed the kinetic (about 12.5% more than the target value) to absorb the
energy of the crash by 70% of initial length reduction. whole crash energy and as results its efficiency is lower.
1844 Proc IMechE Part D: J Automobile Engineering 235(7)

Figure 15. Left side crash box deformation through AZT simulation: (a, b) at 30 ms and (c, d) at 85 ms.

Figure 16. Left side crash box section force versus

Figure 17. Oblique crash FE model for new crash box.
displacement through AZT simulation.
rotation is restricted for convenience. Figure 18 is also
In addition, Figure 16, shows the force – displacement
related to crash sequences. Both structures experience
(F-D) curves for both models. The area under the curves
the first buckling at 8 ms. However, the full deforma-
replicate the amount of work done by the structure
tion happens after 18ms through which the new crash
through deformations which simulate the EA and the
box overall deformation is a bit less than that of tradi-
curve fluctuations are also a sign of structural stability
tional crash box (129.2 mm compare to 134.4 mm, see
(refer to ULC and CFE). In addition the average reaction
Figure 18).
force is also very important as it define the proper safety
Figure 19 provided the force-displacement curves
margin for the main rail buckling force. On the other
during oblique simulation. In a general view, the new
hands, bellow the maximum rail buckling force, the
crash box shows a stiffer energy absorber than tradi-
greater mean force the more optimum crash box design.
tional one as its curve is mostly above and the average
From Figure 16, it is obvious that the average load of
reaction force is bigger as well. The average reaction
new crash box is distinctly higher than that of traditional
force for new and traditional crash boxes are 70.38 kN
one (67.03 kN vs 57.69 kN respectively) and the total
and 62.36 kN respectively.
curve is more similar to an ideal rectangular curve.

Oblique simulation model. Oblique crash is simulated via Full frontal crash, simulation model. The full frontal crash
a 30° inclined rigid barrier (Figure 17) and the vehicle at speed of 50 Kph with rigid barrier is a high threshold
Mortazavi Moghaddam et al. 1845

Figure 18. Left side crash box deformation through oblique simulation: (a, b) at 8 ms and (c, d) at 18 ms.

Figure 19. Force-displacement curves during oblique

simulation.
Figure 20. Full frontal crash simulation model.

test in NCAP (New Car Assessment Programs) scenario buckling while this effect is moderate in new crash box.
and the energy absorption management of the vehicle is In addition, the corresponding new crash box model
of high importance cause the most of energy should be absorbs about 20% (10% each side) of the whole crash
dilapidated by crumple structure of the vehicle. On the energy through more regular folding (follow the kinetic
other side, the time to engage the restraint system (e.g. energy value in Figure 22).
airbags and pretensions,) are also very limited as the The force-displacement curves are shown in Figure
consequence of the crash severity and high and sharp 23. It is noteworthy that regular lobes in new crash box
acceleration increase. So, the crash box stiffness can deformations presented a stiffer and more reliable
drive the essential role of producing high and early structure with higher average reaction force (about
acceleration signal in order to waking up the safety sys- twice the average load of traditional crash box).
tem. The overall model during deformation is shown in
Figure 20.
In this case the bucking is seen extremely different
Conclusion
among the models. According to Figure 21 the tradi- In this paper a simulation methodology is presented in
tional crash box experience significant and obvious order to design an optimum crash box for passenger
1846 Proc IMechE Part D: J Automobile Engineering 235(7)

Figure 21. Left side crash box deformation through full frontal crash simulation: (a) at 12 ms, (b) at 1 ms, and (c, d) at 20 ms.

Figure 22. New crash box energy transfer during FF50Kph Figure 23. Reaction force versus crash box deformation in full
simulation. frontal crash simulation.

cars. To reach the goal, first the ideal crash box charac- respect to traditional rectangular design. Also in com-
teristics are defined based on previous investigations parison to Origami design, the proposed crash box
and with reference to the vehicle industry knowledge showed relatively similar energy absorption level while
and experiences. Then, a corrugated conical tube is with a better stability (i.e. the ULC of origami is twice
selected among a variety of previous publications as the new crash box). So, it seems that the corrugated
the conceptual design element for energy absorption. conical tube could be an appropriate choice for crush
Further on, the proper geometrical parameters of the energy absorption in passenger cars.
tube is derived according to quasi-static CAE simula- The first part of this study is performed by finite ele-
tions and in comparison to general rectangular tube ment explicit code Abaqus and the calculated data
and also with respect to Origami design. The results obtained from analytical formulation proved the accep-
emphasized that the conical corrugated tube with spe- table accuracy of CAE simulation. In the second phase
cial parameters as in Case-05 (Table 2) has relatively of this investigation, the selected concept is implemen-
moderate IPCF, lower ULC and higher SEA with ted in a vehicle model and some crash simulation is
Mortazavi Moghaddam et al. 1847

performed in order to evaluate the crash box deforma- 6. Acar E, Guler MA, Gerceker B, et al. Multi-objective
tion and energy absorption efficiency during real vehi- crashworthiness optimization of tapered thin-walled
cle situations. So, three crashes has been selected as the tubes with axisymmetric indentations. Thin-Walled Struct
reference test cases. AZT 15 Kph is desired as the basic 2011; 49: 94–105.
test and full frontal 50 Kph and oblique 35 Kph are also 7. Sadighi A, Eyvazian A, Asgari M, et al. A novel axially
half corrugated thin-walled tube for energy absorption
used as the high speed crash threshold test cases. The
under axial loading. Thin-Walled Struct 2019; 145:
latest part has been performed by nonlinear dynamic 106418.
simulation through PAM CRASH code. It is shown 8. Alexander JM. An approximate analysis of the collapse
that the proposed new crash box could reach the target of thin cylindrical shells under axial loading. Q J Mech
of 70% length reduction for the crash energy absorp- Appl Math 1960; 13: 10–15.
tion by regular and stable deformation in low speed 9. Abramowicz W and Jones N. Dynamic axial crushing of
AZT simulation while it can absorb almost 10% of the circular tubes. Int J Impact Eng 1984; 2: 263–281.
total crash energy with a stiff crash pulse through high 10. Wierzbicki T, Bhat SU, Abramowicz W, et al. Alexander
speed crashes. revisited—a two folding elements model of progressive
In this article, the crash box design is presented for a crushing of tubes. Compos Struct 2012; 94: 1959–1966.
typical passenger car and also with accordance to spe- 11. Azimi MB and Asgari M. Energy absorption characteris-
tics and a meta-model of miniature frusta under axial
cial packaging restrictions, and the main rail strength
impact. Int J Crashworth 2016; 21(3): 222–230.
limits is defined based on the crash box design targets. 12. Asgari M, Babaee A and Jamshidi M. Multi-objective opti-
In addition, the article has focused on theoretical for- mization of tapered tubes for crashworthiness by surrogate
mulations and the results presented are based on FEM methodologies. Steel Compos Struct 2018; 27(4): 427–438.
simulations. However, vise design routine (i.e. having 13. Malekshahia A, Shirazia KH and Shishesaza M. Static
finalized main rails and starting to design the crash and dynamic axial crushing of prismatic thin-walled
box) and related experimental investigation would be metal columns. J Comput Appl Mech 2019; 50(1): 27–40.
beneficial to be carried out in future studies. 14. Mahbod M and Asgari M. Energy absorption analysis of a
novel foam-filled corrugated composite tube under axial
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Declaration of conflicting interests 15. Ahmadi A and Asgari M. Efficient crushable corrugated
The author(s) declared no potential conflicts of interest conical tubes for energy absorption considering axial and
with respect to the research, authorship, and/or publi- oblique loading. Proc IMechE, Part C: J Mechanical
cation of this article. Engineering Science 2019; 233(11): 3917–3935.
16. Azimi MB, Asgari M and Salaripoor H. A new homo-
polygonal multi-cell structures under axial and oblique
Funding impacts; considers the effect of cell growth in crash-
The author(s) received no financial support for the worthiness. Int J Crashworth. Epub ahead of print June
research, authorship, and/or publication of this article. 2019. DOI: 10.1080/13588265.2019.1628461.
17. Azimi MB and Asgari M. A new bi-tubular conical–
circular structure for improving crushing behavior under
ORCID iD axial and oblique impacts. Int J Mech Sci 2016; 105: 253–
Masoud Asgari https://orcid.org/0000-0002-2063- 265.
18. Sadighi A, Mahbod M and Asgari M. Bi-tubular corru-
8699
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