TKviet_INtro_Enhanced Crashworthiness Parameters of Nested Thin-Walled Carbon Fiber-Reinforced Polymer and Al Structures.pdf

Citation: Yalçın, M.M.; Özsoy, M.İ.
Enhanced Crashworthiness
Parameters of Nested Thin-Walled
Carbon Fiber-Reinforced Polymer and
Al Structures: Effect of Using
Expanded Polypropylene Foam. Appl.
Sci. 2024, 14, 9635. https://doi.org/
10.3390/app14219635
Academic Editor: Ana Martins Amaro
Received: 14 August 2024
Revised: 3 October 2024
Accepted: 18 October 2024
Published: 22 October 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
applied
sciences
Article
Enhanced Crashworthiness Parameters of Nested Thin-Walled
Carbon Fiber-Reinforced Polymer and Al Structures: Effect of
Using Expanded Polypropylene Foam
Muhammet Muaz Yalçın * and Mehmet İskender Özsoy
Department of Mechanical Engineering, Sakarya University, Sakarya 54050, Turkey; iozsoy@sakarya.edu.tr
* Correspondence: myalcin@sakarya.edu.tr; Tel.: +90-264-2955858
Abstract: The in-plane loading conditions of carbon fiber/epoxy composite (CFRP) and aluminum
nested-tube-reinforced expanded polypropylene (EPP) blocks were empirically examined. This study
used crashworthiness metrics to estimate the best design configuration under quasi-static loading
rates. The experimental phase began with lateral loading testing of single and nested aluminum
and CFRP specimen. In-plane crushing experiments were performed on EPP foam blocks reinforced
with nested tubes. Both single and nested aluminum tubes had comparable force–response curves
and maintained their load-bearing capacity throughout testing. Despite a load-carrying capacity
drop above a particular displacement threshold, the CFRP specimens had superior specific energy
absorption (SEA) values due to their lightweight nature. The triple-tube nested specimens with two
smaller tubes exhibited the best SEA results (1.72 and 1.88 J/g, respectively, for the aluminum and
CFRP nested samples). During concurrent tube deformation, the nested samples showed a synergistic
connection that increased energy absorption, especially in the EPP foam blocks with reinforced tubes.
The study also examined the effects of building nested specimens with aluminum exterior tubes and
CFRP inner tubes, and vice versa. This method showed that CFRP tubes within aluminum outer
tubes lowered specimen weight (from 93.1 g to 67.7 g) and energy absorption (from 160.2 J to 153.3 J).
However, the weight reduction outweighed the energy absorption, increasing SEA values for certain
composite material configurations (from 1.72 J/g to 2.26 J/g).
Keywords: crashworthiness; CFRP; nested tubular structures; EPP foam; in-plane loading; lateral
crushing
1. Introduction
Energy absorbers represent a critical aspect of passive safety mechanisms within
vehicular systems, functioning to mitigate the impact force during collisions. Their pri-
mary objective is to minimize vehicular damage and, by extension, enhance occupant
protection [1–3]. Within this context, thin-walled metallic structures emerge as pivotal
components, particularly in the automotive and aerospace sectors. These structures are dis-
tinguished by their lightweight nature, cost-effectiveness, and superior energy absorption
capabilities [4–6]. Predominantly, steel and aluminum are the materials of choice in these
applications [7], owing to their optimal balance of strength and ductility. Moreover, the
energy absorption process in metallic tube structures is achieved through plastic deforma-
tion, which effectively dissipates collision energy. This deformation is influenced by the
direction of load application, whether axial or lateral [8,9], underscoring the importance of
design considerations in the development of effective energy absorbers.
While examining the energy absorption characteristics of tubes under axial and lateral
loads, it was observed that tubes with circular cross-sections exhibit superior energy
absorption capabilities when subjected to axial loading as compared to lateral loading.
However, this advantage is mitigated by the presence of significant fluctuations during
Appl. Sci. 2024, 14, 9635. https://doi.org/10.3390/app14219635 https://www.mdpi.com/journal/applsci

Appl. Sci. 2024, 14, 9635 2 of 23
loading, the manifestation of global bending, and the emergence of unstable deformation
modes when subjected to off-axis loading [10]. Conversely, when tubes are exposed to
lateral loading, they are characterized by the absence of unstable deformations in off-axis
scenarios, alongside the observation of large displacements and a force curve that delineates
a more consistent trend. This discrepancy underscores the distinct mechanical behaviors
inherent to loading directions and serves as a basis for the utilization of nested tubular
structures as an efficacious strategy for augmenting the energy dissipation behavior of tubes,
particularly in contexts where the stroke distance is constrained [11]. Nested tubes, typically
incorporating circular or rectangular cross-sections, are configured by placing multiple
tubes within each other, thus forming at least a dual-tube arrangement [12]. The application
of nested tubes as energy absorbing components culminates in enhanced performance
against lateral loads, primarily attributed to the expansion of plastic deformation zones
facilitated by the constraining effect of the nested configuration [13].
This paper delves into the exploration of various determinants influencing the en-
ergy absorption capabilities of nested metal tubes when subjected to both quasi-static and
dynamic loading conditions. Specifically, the research elucidates the impact of material
composition, tube diameter, wall thickness, and the spatial arrangement of these tubes on
their capacity to mitigate energy [14–17]. Steel, owing to its commendable strength, duc-
tility, and exceptional collision energy absorption properties, is predominantly employed
within the automotive sector [18–20]. The investigation conducted by Shabani et al. [21]
casts light on how the wall thickness and the strategic arrangement of single and nested
steel tubes, varying in diameter, under lateral impact loading, culminate in a markedly
enhanced energy dissipation efficacy in nested-tube configurations. Furthermore, research
by Olabi et al. [22] into the lateral crushing behavior of nested steel tubes under impact
tests, and Baroutaji et al.’s [23] experimental and parametric analysis using a finite element
methodology on the array of behaviors of nested steel tubes underscore the superior energy
absorption capacity facilitated by specific arrangements and dimensional characteristics
of these tubes. Additionally, Kahraman and Akdikmen’s study [24] on the lateral crush-
ing behavior of nested steel tubes presents a comparative analysis based on diameters,
combinations, and uniform wall thicknesses under compression tests. In parallel, the
application of aluminum alloys is extensively recognized in the automotive and aerospace
industries, and is attributed to their high specific strength, ductility, corrosion resistance,
and cost-effectiveness [25,26]. Research by Xu et al. [11] on the lateral deformation behav-
iors under quasi-static and impact loading of nested-tube systems employing aluminum
and steel elucidates the significant effects of material choice and tube combination on
deformation behavior. Lastly, Wu et al.’s study [27] on the deformation behavior of nested
structures comprising elliptical tubes within corrugated tubes under lateral compression
tests highlights the critical interaction between the corrugation and the internal tube, signif-
icantly impacting the energy dissipation behavior. This comprehensive body of research
significantly contributes to the ongoing advancements in the field of materials science, par-
ticularly in the optimization of the energy absorption capacities of nested-tube structures
for enhanced safety and efficiency in automotive and aerospace applications.
Nested tubular configurations have been increasingly recognized for their potential as
energy dissipation mechanisms in the face of impacts and explosive forces. In the realm of
material science and engineering, Wang et al. [12] investigated the incorporation of steel
triangular structures within circular tubes as a method to counteract the effects of impact
and explosion energies. Their research primarily focused on examining how variations in
the circular tube’s thickness, along with the geometric alterations in the triangular shape,
influenced the overall energy absorption capacity during lateral compression tests. The
results showed that nested structures are effective in absorbing energy. Nested-tube energy
absorbers tested under quasi-static loads were found to exhibit successful energy absorption
performance during plastic deformation stages. In addition, numerical analyses indicated
that these energy absorbers reduced blast loads by 50.1% to 74.3%. Complementing this
study, Yang et al. [28] explored the integration of nested structures by inserting elliptical

Appl. Sci. 2024, 14, 9635 3 of 23
tubes inside circular tubes, specifically targeting applications in aviation components. Their
analysis delved into the lateral crushing behavior of these composite structures, concluding
that the force–response curves of the circular and elliptical nested configurations exhibited
greater stability compared to those composed solely of circular or elliptical tubes. This body
of work underscores the significance of geometric optimization in enhancing the energy
absorption efficiency of tubular structures under extreme loading conditions. Additionally,
the combination of circular and elliptical shapes provides a structural advantage by im-
proving stability and resistance to local buckling. The elliptical tube, in particular, enhances
resistance to bending, while the circular tube offers radial strength.
Tubular structures, when augmented with foam fillings, exhibit a significantly en-
hanced capacity for energy absorption. The integration of foams as hybrid components
alongside thin-walled tubes capitalizes on their inherent low density, ease of production,
and superior specific energy absorption characteristics, as indicated in the literature [29]. In
these studies, the foam filling significantly improves the crashworthiness of these structures
by distributing crushing forces more efficiently, stabilizing the column walls, and prevent-
ing local buckling. These characteristics result in higher energy absorption and better
structural integrity during collisions. The foam’s presence enhances both the load-carrying
capacity and the overall stability of the columns, making them more effective in crash
scenarios. Overall, the foam acts as a crucial component in improving crashworthiness
by distributing forces more effectively and enabling the structure to handle high-energy
impacts more efficiently. In hybrid structures combining both foam and tubular elements,
there is a notable increase in load bearing and energy dissipation capacities. This enhance-
ment can be attributed to the synergistic interaction between the foam material and the
walls of the tubes [30,31]. Moreover, foam-filled hybrid structures have been the subject of
investigations within the context of nested tubes. In this realm, Xu et al. [32] conducted
a comprehensive study on the behaviors of energy dissipation and lateral crushing for
aluminum foam filled within nested aluminum tubes, specifically focusing on configura-
tions comprising three and four tubes under compression testing scenarios. Additionally,
Wang et al. [33] explored the crushing behavior of aluminum foam-filled steel circular
and triangular nested tubes when subjected to lateral impacts. Their findings suggest that
the incorporation of aluminum foam significantly bolsters the energy absorption capacity,
mean crushing force, and collision force efficiency of the tubes, a phenomenon largely due
to the interactive dynamics between the tube structure and the foam.
In contemporary vehicular engineering, growing emphasis is placed on the aug-
mentation of component efficiency to mitigate fuel consumption and emission ratios [34].
Concurrently, the objective remains to preserve, if not enhance, the mechanical perfor-
mance expected of these components. Given these ambitions, the prioritization of materials
that exhibit both low density and high strength is paramount. In this context, composite
materials have emerged as formidable contenders versus traditional metals such as steel
and aluminum. This is attributed to their superior specific strength, reduced density, en-
hanced corrosion resistance, and the simplicity of their manufacturing processes [35,36].
However, the inherently brittle nature of composite materials introduces certain drawbacks.
Specifically, their mode of energy absorption during collisions—through matrix cracking,
fiber breakage, and delamination—precipitates abrupt reductions in their load-bearing
capacity [36,37]. To counteract these vulnerabilities, strategies such as the development
of hybrid composites incorporating metal structures and the reinforcement of composite
tubes with cellular formations, including honeycomb and foams, are being explored. These
innovations aim to imbue composite structures with a more resilient response to mechanical
stresses [38].
As delineated in scholarly discourse, extensive research efforts have been dedicated
to the development of metallic energy absorbers. Yet, the exploration of composite nested
tubes as energy absorbers under lateral loading remains conspicuously absent in the
existing literature. It has been observed that tubes with circular cross-sections deform into
elliptical shapes upon lateral compression [39,40]. While metallic tubes dissipate energy at

Appl. Sci. 2024, 14, 9635 4 of 23
the hinge points during lateral deformation, composite tubes exhibit fiber breakage and
ruptures at their quarter points when subjected to lateral stress, thereby compromising
their load-bearing capacity and diminishing their efficacy in energy absorption [41,42]. This
phenomenon is similarly observed in foam-filled composite tubes, where the reduction
in foam height—attributable to its transformation into an elliptical shape due to lateral
compression—impedes the tube’s contribution to load-bearing capacity [43]. To mitigate
these adverse effects, a strategy has been proposed to delay the onset of fiber breakage and
ruptures by encasing the composite tubes within expanded Polypropylene (EPP) blocks to
restrict lateral deformation.
This study examines the energy efficiency and deformation behavior of EPP foam
blocks reinforced with nested-tube reinforcements under quasi-static lateral loads. Previous
discussions emphasize that foam is not a suitable filler material because of its poor energy
efficiency, which is a result of the tubes’ lateral expansion under these loading scenarios. In
order to address this constraint, the current work creatively integrates CFRP and aluminum
nested tubes into the EPP blocks. By severely limiting the tubes’ lateral expansion under
lateral pressure, this deliberate positioning is intended to improve the specimens’ ability to
absorb energy. It is evident from empirical findings that EPP foam specimens supplemented
with nested-tube configurations perform significantly better in terms of crash efficiency
than configurations in which nested tubes are used but EPP foam is not integrated. In
particular, very good outcomes were obtained by combining lightweight nested CFRP
tubes with EPP foam blocks. This study highlights the potential of lightweight composite
materials in applications requiring high energy absorption and efficiency, while also adding
to the body of knowledge by demonstrating the efficacy of nested-tube reinforcements in
enhancing the energy absorption characteristics of EPP foam blocks.
2. Materials and Experimental Studies
In the fabrication of composite tubes, an epoxy resin known as “Sika CR 80” alongside
a hardening agent, Sika CH 80-2, was employed, both of which were supplied by Dost
Kimya Company, Istanbul, Turkey. This was complemented by the use of carbon fiber
woven fabrics possessing an area density of 200 g/m2. For the creation of metal tubes
within the study, Al 6063-T4 alloys were selected due to their specific material properties.
Additionally, EPP foam, characterized by a density of 30 kg/m3 and provided by Atermit
Company, Sakarya, Turkey, was utilized in the construction process. The experimental setup
involved the use of three distinct tube diameters to facilitate nested-tube combinations.
These diameters were categorized as large (77 mm), medium (60 mm), and small (37 mm),
respectively. The composite tubes themselves were meticulously crafted utilizing the hand
lay-up technique. This method was performed on mandrels, employing brushes and rollers
to ensure the uniform application and distribution of the resin and hardener components
across the carbon fiber fabrics.
The fabrication of large-diameter tubes involved a process wherein the tubes were
constructed by winding them around a two-piece polymer mold featuring a bolt–nut
connection mechanism. Conversely, the production of medium- and small-diameter tubes
was achieved by winding fibers around cylindrical cardboard tubes. To ensure that no
adhesion occurred between the resin and the cardboard tubes, the latter were meticulously
covered with tape. Following the initial construction phase, the composites were kept at
room temperature for a duration of 24 h, subsequent to which a post-curing process was
conducted in an oven maintained at a temperature of 60 ◦C for 4 h. For the purpose of
performing lateral crushing tests, the tubes were uniformly trimmed to a height 50 mm.
A wetting process was employed to facilitate the separation of the cardboard from the
composites, thus allowing for the isolation of medium- and small-diameter composites
from their cardboard encasements. The adhesion of the tubes to one another was achieved
through the application of an epoxy-based two-component adhesive, specifically Araldite
2011. In order to construct the nested-tube structures, these were installed within foam
blocks measuring 130 mm by 115 mm. The configurations of these nested structures were

Appl. Sci. 2024, 14, 9635 5 of 23
varied, encompassing both double- and triple-tube combinations along with their foamed
variants, as illustrated in Figure 1. To elucidate the crushing behavior of these nested
structures, compression tests were conducted utilizing an MTS 809 (Istanbul, Turkey) brand
universal testing device, with the tests being performed at a velocity of 6 mm/min.
Appl. Sci. 2024, 14, x FOR PEER REVIEW 5 of 23
from their cardboard encasements. The adhesion of the tubes to one another was achieved
through the application of an epoxy-based two-component adhesive, specifically Araldite
2011. In order to construct the nested-tube structures, these were installed within foam
blocks measuring 130 mm by 115 mm. The configurations of these nested structures were
varied, encompassing both double- and triple-tube combinations along with their foamed
variants, as illustrated in Figure 1. To elucidate the crushing behavior of these nested
structures, compression tests were conducted utilizing an MTS 809 (Istanbul, Turkey)
brand universal testing device, with the tests being performed at a velocity of 6 mm/min.
Figure 1. Arrangement of (a) nested tube-only and (b) nested-tube-reinforced EPP foam block
specimens.
Figure 1. Arrangement of (a) nested tube-only and (b) nested-tube-reinforced EPP foam block specimens.
3. Crashworthiness Parameters
Energy absorbing structures are assessed based on their performance efficiency, em-
ploying multiple criteria including specific energy absorption capability, crush force effi-
ciency, and overall energy efficiency [44,45]. Among these criteria, specific energy absorp-
tion (SEA) capability emerges as the paramount evaluation metric for energy absorbing

Appl. Sci. 2024, 14, 9635 6 of 23
structures. SEA, which is defined as the amount of energy absorbed per unit weight, is
articulated as illustrated in Equation (1).
SEA =
EA
m
(1)
where m denotes the aggregate mass of the energy absorbing structure. Furthermore, EA
represents the cumulative energy absorbed, which can be determined by calculating the
area under the force–displacement curve of the structure. This calculation is facilitated
through the utilization of the formula presented in Equation (2).
EA =
δ
Z
0
F(δ)·dδ (2)
The parameters δ and F represent displacement and force, respectively. The concept of
the crushability ratio is elucidated as the quotient obtained by dividing the displacement
value, recorded at the conclusion of the experimental procedure, by the initial diameter of
the structure under investigation. This is formally expressed in Equation (3).
eg =
l
d
(3)
The parameters of l and d, denoting the crushed and original length of the absorber,
are critical in this evaluation. The concept of work effectiveness (Weff) encompasses both
the specific energy absorption capacity and the crush efficiency indicator. This parameter is
essential in evaluating the performance of energy absorbers, offering a comprehensive measure
that combines both energy absorption efficiency and structural integrity post deformation.
We f f = SEA × eg (4)
4. Results and Discussion
The study conducted experiments on both single tubes and nested specimens to test
their lateral crushing capabilities. Each sample group underwent three separate tests to
ensure accurate and reliable results. To minimize visual confusion, the average degree
curve was used as the final result for each sample group. Additionally, experiments for
each specimen group were stopped at a displacement value equal to 85% of the maximum
crushing capacity, preventing any damage to the equipment or specimens.
4.1. Single Tubes
The force–displacement profiles and the progressive deformation stages derived from
lateral crush testing of aluminum and carbon fiber-reinforced polymer (CFRP) single tubes
are illustrated in Figure 2. It is imperative to underscore that the force profiles for both alu-
minum and CFRP tubes exhibit congruence with prior studies documented in the literature,
notwithstanding the observation that each material’s force profile presents distinct charac-
teristics, albeit homogeneity within their respective groups is observed. A notable aspect is
the rapid increase in force profiles at the onset of the experiments, characterized by a steep
slope. This rate of force escalation at the experiment’s commencement inversely correlates
with the diameter of the tubes, irrespective of the material composition. Consequently, the
initiation of deformation in the specimens was observed at the lowest force value in the tube
possessing the largest diameter, similar to results in the literature [46]. This phenomenon,
where a higher moment—and therefore force—is necessitated to initiate deformation in
tubes of diminishing diameters, accounts for the aforementioned force variation. In contrast
to CFRP tubes, aluminum tubes maintained their load-bearing capacity post the initial de-
formation. The diminished load-bearing capability observed in CFRP tubes can be ascribed
to the inherent layered structure of composite materials and their comparative brittleness

Appl. Sci. 2024, 14, 9635 7 of 23
compared to metal counterparts. Indeed, while brittle composite tubes exhibiting lower
deformability commenced deformation at elevated force values relative to their metallic
counterparts, they subsequently underwent a near-complete loss of load-carrying capacity
within a brief duration. This phenomenon markedly influenced the energy absorption
metrics of the tubes, with absorbed energy values in aluminum tubes delineating a decrease
from 56.4 J, 55.7 J, and 51.1 J across specimens of increasing diameters (TS-TM-TB), to 22.1 J,
29.4 J, and 32.4 J in CFRP tubes. This attenuation in load-carrying capacity engendered a
reversal in the trend in energy absorption behavior, which in aluminum tubes escalated
with decreasing diameter, a trend that was inverted in CFRP tubes. If the characteristics of
metal and composite curves are examined, aluminum tube structures absorb energy due to
the high ductility behaviors and superior plastic deformation capabilities of metals, while
the curves are formed in a smooth form. However, composite materials absorb crushing
energy with damage mechanisms such as matrix cracking, local buckling of fibers, fiber
breakage, and delamination. Due to these fiber breaks, oscillations occur in the curves of
composite structures [47,48].
literature [46]. This phenomenon, where a higher moment—and therefore force—is neces-
sitated to initiate deformation in tubes of diminishing diameters, accounts for the afore-
mentioned force variation. In contrast to CFRP tubes, aluminum tubes maintained their
load-bearing capacity post the initial deformation. The diminished load-bearing capabil-
ity observed in CFRP tubes can be ascribed to the inherent layered structure of composite
materials and their comparative brittleness compared to metal counterparts. Indeed, while
brittle composite tubes exhibiting lower deformability commenced deformation at ele-
vated force values relative to their metallic counterparts, they subsequently underwent a
near-complete loss of load-carrying capacity within a brief duration. This phenomenon
markedly influenced the energy absorption metrics of the tubes, with absorbed energy
values in aluminum tubes delineating a decrease from 56.4 J, 55.7 J, and 51.1 J across spec-
imens of increasing diameters (TS-TM-TB), to 22.1 J, 29.4 J, and 32.4 J in CFRP tubes. This
attenuation in load-carrying capacity engendered a reversal in the trend in energy absorp-
tion behavior, which in aluminum tubes escalated with decreasing diameter, a trend that
was inverted in CFRP tubes. If the characteristics of metal and composite curves are ex-
amined, aluminum tube structures absorb energy due to the high ductility behaviors and
superior plastic deformation capabilities of metals, while the curves are formed in a
smooth form. However, composite materials absorb crushing energy with damage mech-
anisms such as matrix cracking, local buckling of fibers, fiber breakage, and delamination.
Due to these fiber breaks, oscillations occur in the curves of composite structures [47,48].
Figure 2. The force–displacement curves of single (a) aluminum and (b) CFRP tubes under a lateral
crushing load.
Figure 2. The force–displacement curves of single (a) aluminum and (b) CFRP tubes under a lateral
crushing load.
4.2. Nested Tubes
The findings from the lateral compression examinations of composite samples, con-
sisting of dual and triple aluminum tubing configurations, are delineated in Figure 3. The

Appl. Sci. 2024, 14, 9635 8 of 23
bi-tubular samples were fabricated by inserting tubes of small (TS) and medium (TM)
dimensions into a larger tube, whereas the tri-tubular specimens were constructed by
incorporating either two small tubes or one small and one medium tube within a large
tube. An epoxy-based adhesive was employed to preserve the original positioning of the
tubes during the lateral compression test. In the case of the bi-tubular specimens, the
spatial separation between the outer surface of the TS and TM tubes and the inner surface
of the large tube measured at 37 mm and 14 mm, respectively. Additionally, a 20 mm
gap was observed between the TS and TM tubes. The dimensional selection of the tubes,
allowing for the accommodation of two smaller tubes within the larger tube, was a critical
consideration. Upon analysis of the force–displacement graphs presented in Figure 3a,
it is observed that the force profiles initially align with those of the TB tube. However,
post a specific displacement threshold, the nature of the force curve alters. This suggests
that deformation initially occurs solely within the TB tube, and subsequently, as the TB
tube comes into contact with the inner tube(s), the combined deformation of these tubes
results in the modification of the force curve. Utilizing the TM tube internally results in
a rapid escalation in the force curve at approximately 14 mm of displacement, akin to
the initial response observed in the TM single-tube experiment. Conversely, when a TS
tube is incorporated (in the NT2-TS sample), this escalation is noted at a displacement
of roughly 37 mm. The emergence of a stepped force curve through the integration of
tubes of varying diameters is significantly noteworthy as it demonstrates the potential for
deliberate manipulation of the force curve. Given that the NT2-TM specimen exhibits an
energy absorption capacity approximately 16% higher than that of the NT2-TS specimen, it
is inferred that an earlier onset of the stepped force curve phenomenon is preferable.
The stepped structure of the force curve, previously mentioned, exhibits a more
pronounced character in the NT3-TS+TM specimen, as delineated in Figure 3b. Initially,
deformation occurs in the larger tube, succeeded by the TM tube’s deformation at ap-
proximately 14 mm, culminating in the emergence of the initial step; the subsequent step
materializes with the TS tube’s deformation at around 34 mm. In juxtaposition, the NT2-TS
specimen evidences an escalation in the force curve at a displacement value of 37 mm.
However, this value markedly diminishes to 14 mm in the NT3-TS+TM specimen, a phe-
nomenon likely attributable to the concurrent deployment of the TS and TM tubes within
the triply nested specimen. Conversely, the NT3-TS+TS specimen, employing two TS tubes,
does not exhibit a stepped force curve, maintaining uniformity akin to the force curves
observed in single-tube specimens, as illustrated in Figure 3b. This uniformity arises from
the inner tubes’ interaction with the TB tube, facilitating a more consistent force curve and
enabling a 12% enhancement in energy absorption at the experiment’s inception. Given
the dual incorporation of smaller tubes in the NT3-TS+TS specimen, it is anticipated that a
higher specific energy value will be achieved, correlating with a reduced sample weight
compared to the NT3-TS+TM specimen.
The preceding text outlines the results from lateral crushing tests performed on nested
CFRP composite specimens, as seen in the cited pictures (Figure 4). The experimental data
primarily examine the force–displacement characteristics of both two-tube and three-tube
CFRP composite specimens, with a comparison versus their aluminum counterparts. The
early deformation phase is notably comparable across different specimens, due to the
primary deformation of the TB specimen, which reflects the behavior seen in aluminum
tubes. The differences in the force curves resulting from initial contact versus non-contact
with the main tube are distinctly seen in the graphs. This phenomenon is particularly
pronounced in specimens featuring three tubes; nonetheless, the initial congruence of the
force curves in the absence of contact (Figure 4a) is also significant as it demonstrates the
efficient manufacturing of the CFRP tubes. The story clarifies the specimens’ dynamic
response to a load, emphasizing the cyclical adaptation of force due to gradual structural
compromise and the consequent involvement of the smaller tube in the deformation
process. The discussion highlights a unique energy absorption pattern between the two-
tube and three-tube specimens, with the latter exhibiting a more stable force curve, despite

Appl. Sci. 2024, 14, 9635 9 of 23
closely comparable energy absorption levels, differing from the behavior seen in the
aluminum tubes. This exposition emphasizes the intricate behavioral characteristics of
CFRP composite tubes during lateral crushing and contributes to the wider discussion on
the structural integrity and durability of composite materials in load-bearing applications.
Figure 3. The force–displacement curves of nested aluminum (a) two-tube and (b) three-tube sam-
ples under a lateral crushing load.
The preceding text outlines the results from lateral crushing tests performed on
nested CFRP composite specimens, as seen in the cited pictures (Figure 4). The experi-
mental data primarily examine the force–displacement characteristics of both two-tube
and three-tube CFRP composite specimens, with a comparison versus their aluminum
counterparts. The early deformation phase is notably comparable across different speci-
mens, due to the primary deformation of the TB specimen, which reflects the behavior seen
in aluminum tubes. The differences in the force curves resulting from initial contact versus
non-contact with the main tube are distinctly seen in the graphs. This phenomenon is par-
ticularly pronounced in specimens featuring three tubes; nonetheless, the initial congru-
ence of the force curves in the absence of contact (Figure 4a) is also significant as it demon-
strates the efficient manufacturing of the CFRP tubes. The story clarifies the specimens’
dynamic response to a load, emphasizing the cyclical adaptation of force due to gradual
Figure 3. The force–displacement curves of nested aluminum (a) two-tube and (b) three-tube samples
under a lateral crushing load.

Appl. Sci. 2024, 14, 9635 10 of 23
tween the two-tube and three-tube specimens, with the latter exhibiting a more stable
force curve, despite closely comparable energy absorption levels, diﬀering from the be-
havior seen in the aluminum tubes. This exposition emphasizes the intricate behavioral
characteristics of CFRP composite tubes during lateral crushing and contributes to the
wider discussion on the structural integrity and durability of composite materials in load-
bearing applications.
Figure 4. The force–displacement curves of nested CFRP (a) two-tube and (b) three-tube samples
The progressive deformation stages of the nested aluminum samples, comprising
configurations with two and three tubes, are detailed in Table 1. Initially, deformation
begins in the largest aluminum tube for all samples, except for the nested sample
Figure 4. The force–displacement curves of nested CFRP (a) two-tube and (b) three-tube samples
The progressive deformation stages of the nested aluminum samples, comprising
configurations with two and three tubes, are detailed in Table 1. Initially, deformation
begins in the largest aluminum tube for all samples, except for the nested sample containing
two smaller tubes. The outermost tube starts to deform under the applied load until it
contacts the inner tube. Once contact is made, the deformation propagates to the inner
tube, causing it to deform as well. This sequential deformation pattern creates force curves
characterized by distinct steps, each corresponding to the different stages of deformation
in the nested structure. Similarly, the nested samples made from carbon fiber-reinforced
polymer (CFRP) exhibit a progressive deformation pattern. However, due to the brittle
nature of CFRP, these tubes experience cracking as deformation progresses. The cracks

Appl. Sci. 2024, 14, 9635 11 of 23
appear on the tube walls once the deformation reaches a certain threshold. Notably, the
sequence of cracking is consistent across all CFRP tubes, irrespective of their diameter.
Cracks first develop at the upper and lower sections of the tube and subsequently at the
right and left sides. This cracking sequence significantly impacts the load-bearing capacity
of the nested CFRP samples, leading to abrupt reductions in force. These sudden drops are
evident in the force–displacement curves of the CFRP samples, as illustrated in Figure 4.
The contrasting behavior between aluminum and CFRP tubes is further highlighted in the
smooth force curves observed for the aluminum samples (Figure 3). The absence of cracking
in the aluminum tubes is attributed to their ductile behavior, which allows them to undergo
significant deformation without sudden failure. This ductility ensures a more gradual and
continuous absorption of energy, resulting in smoother force–displacement curves com-
pared to the CFRP samples. In conclusion, the progressive deformation behavior of nested
aluminum and CFRP tubes demonstrates distinct characteristics influenced by the material
properties. The stepped force curves of the aluminum samples are indicative of a sequential
deformation process without sudden failure, while the force–displacement curves of the
CFRP samples reflect the brittle nature of the material, marked by sudden drops due to
cracking. Understanding these deformation mechanisms is crucial for optimizing the
design and performance of nested tubular structures in various engineering applications.
Table 1. Deformation stages of nested aluminum and CFRP samples.
NT2-TS
until it contacts the inner tube. Once contact is made, the deformation propagates to the
inner tube, causing it to deform as well. This sequential deformation pattern creates force
curves characterized by distinct steps, each corresponding to the diﬀerent stages of defor-
mation in the nested structure. Similarly, the nested samples made from carbon fiber-re-
inforced polymer (CFRP) exhibit a progressive deformation pattern. However, due to the
brittle nature of CFRP, these tubes experience cracking as deformation progresses. The
cracks appear on the tube walls once the deformation reaches a certain threshold. Notably,
the sequence of cracking is consistent across all CFRP tubes, irrespective of their diameter.
of the nested CFRP samples, leading to abrupt reductions in force. These sudden drops
are evident in the force–displacement curves of the CFRP samples, as illustrated in Figure
4. The contrasting behavior between aluminum and CFRP tubes is further highlighted in
the smooth force curves observed for the aluminum samples (Figure 3). The absence of
cracking in the aluminum tubes is attributed to their ductile behavior, which allows them
to undergo significant deformation without sudden failure. This ductility ensures a more
gradual and continuous absorption of energy, resulting in smoother force–displacement
curves compared to the CFRP samples. In conclusion, the progressive deformation behav-
ior of nested aluminum and CFRP tubes demonstrates distinct characteristics influenced
by the material properties. The stepped force curves of the aluminum samples are indica-
tive of a sequential deformation process without sudden failure, while the force–displace-
ment curves of the CFRP samples reflect the brittle nature of the material, marked by sud-
den drops due to cracking. Understanding these deformation mechanisms is crucial for
optimizing the design and performance of nested tubular structures in various engineer-
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TM
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT3-TS+TS
containing two smaller tubes. The outermost tube starts to deform under the applied load
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
ing applications.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT2-TS
NT2-TM
NT2-TS
NT2-TM
NT2-TS
NT2-TM

Appl. Sci. 2024, 14, 9635 12 of 23
Table 1. Cont.
NT2-TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
4.3. The Interaction Occurred in the Nested Sample
The deformation of tubes arranged in nested configurations leads to interactive phe-
nomena that substantially affect the energy absorption properties of these structures. In
this context, the force–displacement characteristics of the NT3-TS+TM specimen, along
with the force curves corresponding to the individual tubes that constitute this specimen,
are collectively illustrated in Figure 5. The force curve associated with the NT3-TS+TM sam-
ple is clearly represented in a maroon color within the figure, contrasting with the force
curves of the individual tubes, which are depicted in different shades of blue (specifically
blue, dodger blue, and cyan) to enhance differentiation. The segmentation of the force
curve into three distinct parts clarifies the sequential deformation processes encountered
by tubes of different dimensions. The initial segment specifically illustrates the defor-
mation occurring in the largest tube alone, while the following segments indicate the grad-
ual involvement of the medium and smallest tubes in the deformation process, respec-
tively. The force curve for each individual tube was derived by algebraically summing the
initial force values associated with each tube, starting from the force value recorded in the
previous section. The NT3-TS+TM specimen demonstrated a significant increase in energy
absorption, amounting to 19.9 J, when compared to the total energy absorbed by the indi-
vidual tubes at the same displacement threshold. Additionally, the assessment of the max-
imum crush displacement metric was based on the highest crush displacement recorded
in the tri-tubular specimen configuration.
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TM
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT3-TS+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
NT2-TS
NT2-TM
NT3-TS+TS
NT3-TM+TS
nomena that substantially affect the energy absorption properties of these structures. In
this context, the force–displacement characteristics of the NT3-TS+TM specimen, along with
the force curves corresponding to the individual tubes that constitute this specimen, are
collectively illustrated in Figure 5. The force curve associated with the NT3-TS+TM sample
is clearly represented in a maroon color within the figure, contrasting with the force curves
of the individual tubes, which are depicted in different shades of blue (specifically blue,
dodger blue, and cyan) to enhance differentiation. The segmentation of the force curve into
three distinct parts clarifies the sequential deformation processes encountered by tubes of
different dimensions. The initial segment specifically illustrates the deformation occurring
in the largest tube alone, while the following segments indicate the gradual involvement
of the medium and smallest tubes in the deformation process, respectively. The force
curve for each individual tube was derived by algebraically summing the initial force
values associated with each tube, starting from the force value recorded in the previous
section. The NT3-TS+TM specimen demonstrated a significant increase in energy absorp-
tion, amounting to 19.9 J, when compared to the total energy absorbed by the individual
tubes at the same displacement threshold. Additionally, the assessment of the maximum
crush displacement metric was based on the highest crush displacement recorded in the
tri-tubular specimen configuration.

Appl. Sci. 2024, 14, 9635 13 of 23
Figure 5. The interaction between the single tubes when deforming together in the nested sample
NT3-TS+TS.
In the context of three-tube nested specimens, the investigation extends to configura-
tions wherein tubes are fabricated from dissimilar materials, scrutinizing the resultant in-
teractions as previously delineated. The subsequent figures (referenced as Figure 6) delin-
eate the force–displacement trajectories for specimens characterized by the employment
of TB and TS tubes composed of heterogeneous materials. Specifically, Figure 6a illus-
trates a composite of aluminum TB and CFRP TS tubes, whereas Figure 6b depicts the
inverse material configuration. Notably, Figure 6a reveals a precipitous decline in the
force curve at approximately 25 mm of displacement when CFRP tubes are utilized inter-
nally—a phenomenon absent in specimens comprising aluminum analogs. This decline is
attributable to fractures manifesting on the lateral aspects of the CFRP TS tubes, engen-
dering a 4% reduction in energy absorption capacity of the specimen. Furthermore, the
incorporation of CFRP TS tubes results in a substantial mass reduction exceeding 27%,
enhancing the specimen’s overall efficiency. Conversely, the specimen illustrated in Fig-
ure 6b, despite the decrement in absorbed energy due to the substitution of aluminum TS
tubes with CFRP, experiences a compensatory reduction in mass that ostensibly mitigates
the impact of reduced energy absorption. The juxtaposition of different material tubes not
only influences the absolute energy absorption but also significantly affects the energy
absorption efficiency. Intriguingly, specimens evidencing a decline in absorbed energy
exhibit enhanced specific energy absorption capabilities relative to their original configu-
ration. Conversely, an augmentation in absorbed energy correlates with a diminution in
specific energy values. Consequently, this suggests that the pivotal metric in evaluating
energy absorbing structures is not merely the quantum of energy absorbed but rather the
efficiency with which this energy is assimilated.
Figure 5. The interaction between the single tubes when deforming together in the nested sample
NT3-TS+TS.
In the context of three-tube nested specimens, the investigation extends to configu-
rations wherein tubes are fabricated from dissimilar materials, scrutinizing the resultant
interactions as previously delineated. The subsequent figures (referenced as Figure 6) de-
lineate the force–displacement trajectories for specimens characterized by the employment
of TB and TS tubes composed of heterogeneous materials. Specifically, Figure 6a illustrates
a composite of aluminum TB and CFRP TS tubes, whereas Figure 6b depicts the inverse
material configuration. Notably, Figure 6a reveals a precipitous decline in the force curve
at approximately 25 mm of displacement when CFRP tubes are utilized internally—a phe-
nomenon absent in specimens comprising aluminum analogs. This decline is attributable to
fractures manifesting on the lateral aspects of the CFRP TS tubes, engendering a 4% reduc-
tion in energy absorption capacity of the specimen. Furthermore, the incorporation of CFRP
TS tubes results in a substantial mass reduction exceeding 27%, enhancing the specimen’s
overall efficiency. Conversely, the specimen illustrated in Figure 6b, despite the decrement
in absorbed energy due to the substitution of aluminum TS tubes with CFRP, experiences a
compensatory reduction in mass that ostensibly mitigates the impact of reduced energy
absorption. The juxtaposition of different material tubes not only influences the absolute en-
ergy absorption but also significantly affects the energy absorption efficiency. Intriguingly,
specimens evidencing a decline in absorbed energy exhibit enhanced specific energy ab-
sorption capabilities relative to their original configuration. Conversely, an augmentation in
absorbed energy correlates with a diminution in specific energy values. Consequently, this
suggests that the pivotal metric in evaluating energy absorbing structures is not merely the
quantum of energy absorbed but rather the efficiency with which this energy is assimilated.

Appl. Sci. 2024, 14, 9635 14 of 23
Figure 6. The force-displacement curves of three tube nested samples (a) small tubes of CFRP and
Al placed in Al outer tube, (b) small CFRP and Al tubes placed in CFRP outer tube.
4.4. Nested Tube-Reinforced EPP Foams
This section presents the findings of testing EPP foam blocks reinforced with alumi-
num and CFRP composite nested tubes under in-plane crushing stresses. The EPP foam
blocks employed in this investigation are consistent in terms of dimensions, each measur-
ing 130 mm by 115 mm, with a density of 30 kg/m3. Only the tubes with a larger diameter
were chosen to reinforce the EPP foam. Due to the considerably greater strength of both
aluminum and CFRP composite tubes relative to EPP foam, no appreciable deformation
of the tubes was detected until a displacement of about 35 mm was attained from the com-
mencement of the testing procedure. Following this displacement threshold, a progressive
increase in the force curve was recorded, as illustrated in Figures 7 and 8. Furthermore, it
Figure 6. The force-displacement curves of three tube nested samples (a) small tubes of CFRP and Al
placed in Al outer tube, (b) small CFRP and Al tubes placed in CFRP outer tube.
4.4. Nested Tube-Reinforced EPP Foams
This section presents the findings of testing EPP foam blocks reinforced with alu-
minum and CFRP composite nested tubes under in-plane crushing stresses. The EPP
foam blocks employed in this investigation are consistent in terms of dimensions, each
measuring 130 mm by 115 mm, with a density of 30 kg/m3. Only the tubes with a larger
diameter were chosen to reinforce the EPP foam. Due to the considerably greater strength
of both aluminum and CFRP composite tubes relative to EPP foam, no appreciable de-
formation of the tubes was detected until a displacement of about 35 mm was attained
from the commencement of the testing procedure. Following this displacement threshold,
a progressive increase in the force curve was recorded, as illustrated in Figures 7 and 8.

Appl. Sci. 2024, 14, 9635 15 of 23
Furthermore, it is noteworthy that above this displacement threshold, the force curves
increase at a reduced gradient compared to those observed for both aluminum and CFRP
composite tubes without EPP foam reinforcement. The deformation curves for the double
and triple nested tubes, depicted in Figure 7, demonstrate the emergence of distinctive
force curves for the nested specimens, similar to those shown in Figures 3 and 4, after an
average displacement of 40 mm. A consistent trend is evident in the force curves of the
CFRP tubes, as illustrated in Figure 8. The force values for both aluminum and CFRP
composite tubes increase by an average of 1000 N with the addition of EPP foam. Analysis
of the energy absorption values of the specimens revealed a significant increase in EPP
foam, exceeding the total energy values of both the specimen and the foam. This result
is notably significant, reflecting the interaction effect seen when individual tubes are em-
ployed together. The single TB tube and EPP foam exhibited energy absorption values
of 51.1 J and 35.2 J, respectively, totaling 86.3 J, whereas the FF_TB sample showed a 20%
enhancement in energy absorption, as illustrated in Figures 2a and 7a. The increase was
particularly significant in the CFRP composite TB tube, reaching approximately 39%, as
illustrated in Figures 2b and 8a. The maximum and minimum improvements in energy
absorption from interactions in the nested-tube-reinforced EPP foam specimens were ob-
served in the FF_NT2-TM and FF_NT3-TS+TS samples, with enhancements of 35% and
5% for aluminum and 25% and 52% for CFRP composite, respectively. Furthermore, the
increase in energy absorption for all nested CFRP composite tube-reinforced specimens
surpassed that recorded in specimens reinforced with nested aluminum tubes.
Following the completion of experiments on the nested samples, the EPP foam blocks
were reinforced with nested aluminum and CFRP tubes and underwent compression
testing. The main aim of this reinforcing method was to restrict the lateral expansion of the
aluminum and CFRP tubes, thus improving the energy absorption capacity of the samples.
The compressive deformation behavior of the EPP foam blocks was meticulously examined.
The findings in Table 2 demonstrate that the EPP foam blocks underwent considerable
expansion when exposed to compressive stresses. This deformation was directly linked to
the lateral expansion of the outer tube. The strengthening of EPP foam sought to limit lateral
expansion, thus enhancing the structural integrity and energy absorption capabilities of the
nested tubes. A comprehensive comparison of the force–displacement curves between the
nested samples and the nested-tube-reinforced EPP foam samples demonstrated significant
differences. The use of EPP foam led to an increase in the crushing displacement of the
samples by roughly 30 mm. This research demonstrates that the EPP foam permitted more
deformation prior to failure, which is essential for applications necessitating high energy
absorption. Moreover, the examination of the force–displacement curves indicated that
the plateau and maximum force values of the nested samples were markedly increased
with the inclusion of EPP foam. The plateau force, indicative of the sustained force level
during deformation, was elevated, signifying an improved capacity to absorb energy over
an extended displacement. Correspondingly, the maximum force value, indicative of the
peak load the sample can endure prior to failure, was elevated, illustrating the enhanced
strength of the reinforced samples. The results highlight the substantial role of EPP foam
in enhancing the energy absorption capacity of the nested samples. The augmented
crushing displacement and heightened force values indicate that EPP foam significantly
improves the mechanical properties of the nested-tube constructions. The enhancement in
energy absorption capability has significant implications for the design and development of
sophisticated materials and structures across numerous engineering applications, especially
in domains where impact resistance and energy dissipation are crucial. The reinforcement
of nested aluminum and CFRP tubes with EPP foam blocks greatly improves the energy
absorption capacity of the samples. The experimental findings indicate that EPP foam
can enhance the mechanical performance of nested-tube constructions, positioning it as
a promising material for applications necessitating high impact resistance and energy
absorption. Future research should investigate the optimization of EPP foam characteristics

Appl. Sci. 2024, 14, 9635 16 of 23
and reinforcement combinations to further improve the performance of these composite
structures.
the optimization of EPP foam characteristics and reinforcement combinations to further
improve the performance of these composite structures.
Figure 7. Force–displacement curves of nested aluminum (a) two-tube- and (b) three-tube-rein-
forced EPP foam blocks under in-plane loading.
Figure 7. Force–displacement curves of nested aluminum (a) two-tube- and (b) three-tube-reinforced
EPP foam blocks under in-plane loading.

Appl. Sci. 2024, 14, 9635 17 of 23
Figure 8. Force–displacement curves of nested CFRP (a) two-tube- and (b) three-tube- reinforced
EPP foam blocks under in-plane loading.
Figure 8. Force–displacement curves of nested CFRP (a) two-tube- and (b) three-tube- reinforced EPP
foam blocks under in-plane loading.
Table 2. Deformation stages of nested aluminum and CFRP tube-reinforced EPP foam blocks.
FF_NT2-TS
FF_NT2-TS
FF_NT2-TM
FF_NT2-TS
FF_NT2-TM
FF_NT2-TS
FF_NT2-TM
FF_NT2-TS
FF_NT2-TM
FF_NT2-TS
FF_NT2-TM

Appl. Sci. 2024, 14, 9635 18 of 23
Table 2. Cont.
FF_NT2-TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT3-TS+TS
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT3-TS+TS
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM
FF_NT2-TS
FF_NT2-TM
FF_NT3-TS+TS
FF_NT3-TS+TM

Appl. Sci. 2024, 14, 9635 19 of 23
Table 2. Cont.
FF_NT3-TS+TM
4.5. Crashworthiness
The findings of the experimental study, inclusive of all utilized specimens and spe-
cific crashworthiness parameters, are comprehensively delineated in Table 3. This table
elucidates a discernible variance in the force exerted by specimens contingent upon the
material composition. It is observed that both the mean and peak force metrics for the
single and nested CFRP composite tubes are markedly inferior to those of their aluminum
counterparts across all specimen configurations. This discrepancy is attributed to the brit-
tle nature of carbon fiber composites, which detrimentally impacts the specimens’ capac-
ity to bear loads. Furthermore, the crushability indices of the samples exhibited variability
correlating to the quantity of tubes employed. For singular tubes, the crushability index
was ascertained through the calculation of the ratio of 85% of the tube’s inner diameter to
its outer diameter. The method for determining the crushability of nested samples ad-
hered to a similar paradigm. Nonetheless, a distinct approach was employed for nested
samples wherein 85% of the value derived from subtracting the cumulative wall thickness
of the interior tubes from the inner diameter of the TB tube was established as the sample’s
crushability ratio. Consequently, an inverse relationship between the crushability ratio
and the number of tubes in the nested samples is anticipated. Independent of material
composition, it was noted that tubes of smaller diameter exhibited superior maximum
force values relative to their larger counterparts. This phenomenon aligns with the prem-
ise that the force requisite to deform a specimen should escalate inversely with its diame-
ter. Evidently, the maximum force values recorded for the nested specimens utilizing the
TS tube significantly surpassed those of specimens employing the TM tube, a trend that
was consistent among specimens integrated with EPP foam.
Table 3. The crashworthiness results of samples used in the experimental study.
Sample Combination
Crushability
Ratio,
eg,
(mm/mm)
Sample
Weight
(g)
Fmean
(N)
Fmax
(N)
Absorbed
Energy,
EA, (J)
Specific
Energy
Absorp-
tion,
SEA, (J/g)
Crush
force
Effi-
ciency,
CFE, (%)
Work
Effective-
ness,
Weff, (J/g)
Aluminum
based
samples
Single
rings
TB 0.82 46.5 812 1491 51.1 1.10 54 0.90
TM 0.81 39.2 1150 1640 55.7 1.42 70 1.15
TS 0.78 23.3 1952 4141 56.4 2.42 47 1.89
Nested
tube
samples
NT2-TS 0.78 69.8 1420 3865 85.7 1.23 37 0.96
NT2-TM 0.78 85.7 1649 2884 99.5 1.16 57 0.91
NT3-TS+TS 0.75 93.1 2772 5219 160.2 1.72 53 1.29
NT3-TS+TM 0.75 109 2484 5799 143.6 1.32 43 0.99
Nested
tube
reinforced
EPP
foam
FF_TB 0.82 59.2 1105 2550 103.8 1.75 43 1.43
FF_NT2-TS 0.78 82.5 1692 4781 154.6 1.87 35 1.47
FF_NT2-TM 0.78 98.4 1990 4058 181.8 1.85 49 1.45
FF_NT3-TS+TS 0.75 105.8 2292 4774 203.5 1.92 48 1.44
FF_NT3-TS+TM 0.75 121.8 2427 7148 215.5 1.77 34 1.33
CFRP
based
Single
rings
TB 0.82 25.3 515 1367 32.4 1.28 38 1.05
TM 0.81 20.5 607 1544 29.4 1.43 39 1.16
TS 0.78 10.6 765 1858 22.1 2.08 41 1.63
Sample Combination
Crushability
Ratio,
eg,
(mm/mm)
Sample
Weight
(g)
Fmean
(N)
Fmax
(N)
Absorbed
Energy,
EA, (J)
Specific
Energy
Absorp-
tion,
SEA, (J/g)
Crush
force
Effi-
ciency,
CFE, (%)
Work
Effective-
ness,
Weff, (J/g)
Aluminum
based
samples
Single
rings
TB 0.82 46.5 812 1491 51.1 1.10 54 0.90
TM 0.81 39.2 1150 1640 55.7 1.42 70 1.15
TS 0.78 23.3 1952 4141 56.4 2.42 47 1.89
Nested
tube
samples
NT2-TS 0.78 69.8 1420 3865 85.7 1.23 37 0.96
NT2-TM 0.78 85.7 1649 2884 99.5 1.16 57 0.91
NT3-TS+TS 0.75 93.1 2772 5219 160.2 1.72 53 1.29
NT3-TS+TM 0.75 109 2484 5799 143.6 1.32 43 0.99
Nested
tube
reinforced
EPP
foam
FF_TB 0.82 59.2 1105 2550 103.8 1.75 43 1.43
FF_NT2-TS 0.78 82.5 1692 4781 154.6 1.87 35 1.47
FF_NT2-TM 0.78 98.4 1990 4058 181.8 1.85 49 1.45
FF_NT3-TS+TS 0.75 105.8 2292 4774 203.5 1.92 48 1.44
FF_NT3-TS+TM 0.75 121.8 2427 7148 215.5 1.77 34 1.33
CFRP
based
Single
rings
TB 0.82 25.3 515 1367 32.4 1.28 38 1.05
TM 0.81 20.5 607 1544 29.4 1.43 39 1.16
TS 0.78 10.6 765 1858 22.1 2.08 41 1.63
Sample Combination
Crushability
Ratio,
eg,
(mm/mm)
Sample
Weight
(g)
Fmean
(N)
Fmax
(N)
Absorbed
Energy,
EA, (J)
Specific
Energy
Absorp-
tion,
SEA, (J/g)
Crush
force
Effi-
ciency,
CFE, (%)
Work
Effective-
ness,
Weff, (J/g)
Aluminum
based
samples
Single
rings
TB 0.82 46.5 812 1491 51.1 1.10 54 0.90
TM 0.81 39.2 1150 1640 55.7 1.42 70 1.15
TS 0.78 23.3 1952 4141 56.4 2.42 47 1.89
Nested
tube
samples
NT2-TS 0.78 69.8 1420 3865 85.7 1.23 37 0.96
NT2-TM 0.78 85.7 1649 2884 99.5 1.16 57 0.91
NT3-TS+TS 0.75 93.1 2772 5219 160.2 1.72 53 1.29
NT3-TS+TM 0.75 109 2484 5799 143.6 1.32 43 0.99
Nested
tube
reinforced
EPP
foam
FF_TB 0.82 59.2 1105 2550 103.8 1.75 43 1.43
FF_NT2-TS 0.78 82.5 1692 4781 154.6 1.87 35 1.47
FF_NT2-TM 0.78 98.4 1990 4058 181.8 1.85 49 1.45
FF_NT3-TS+TS 0.75 105.8 2292 4774 203.5 1.92 48 1.44
FF_NT3-TS+TM 0.75 121.8 2427 7148 215.5 1.77 34 1.33
CFRP
based
Single
rings
TB 0.82 25.3 515 1367 32.4 1.28 38 1.05
TM 0.81 20.5 607 1544 29.4 1.43 39 1.16
TS 0.78 10.6 765 1858 22.1 2.08 41 1.63
Sample Combination
Crushability
Ratio,
eg,
(mm/mm)
Sample
Weight
(g)
Fmean
(N)
Fmax
(N)
Absorbed
Energy,
EA, (J)
Specific
Energy
Absorp-
tion,
SEA, (J/g)
Crush
force
Effi-
ciency,
CFE, (%)
Work
Effective-
ness,
Weff, (J/g)
Aluminum
based
samples
Single
rings
TB 0.82 46.5 812 1491 51.1 1.10 54 0.90
TM 0.81 39.2 1150 1640 55.7 1.42 70 1.15
TS 0.78 23.3 1952 4141 56.4 2.42 47 1.89
Nested
tube
samples
NT2-TS 0.78 69.8 1420 3865 85.7 1.23 37 0.96
NT2-TM 0.78 85.7 1649 2884 99.5 1.16 57 0.91
NT3-TS+TS 0.75 93.1 2772 5219 160.2 1.72 53 1.29
NT3-TS+TM 0.75 109 2484 5799 143.6 1.32 43 0.99
Nested
tube
reinforced
EPP
foam
FF_TB 0.82 59.2 1105 2550 103.8 1.75 43 1.43
FF_NT2-TS 0.78 82.5 1692 4781 154.6 1.87 35 1.47
FF_NT2-TM 0.78 98.4 1990 4058 181.8 1.85 49 1.45
FF_NT3-TS+TS 0.75 105.8 2292 4774 203.5 1.92 48 1.44
FF_NT3-TS+TM 0.75 121.8 2427 7148 215.5 1.77 34 1.33
CFRP
based
Single
rings
TB 0.82 25.3 515 1367 32.4 1.28 38 1.05
TM 0.81 20.5 607 1544 29.4 1.43 39 1.16
TS 0.78 10.6 765 1858 22.1 2.08 41 1.63
Sample Combination
Crushability
Ratio,
eg,
(mm/mm)
Sample
Weight
(g)
Fmean
(N)
Fmax
(N)
Absorbed
Energy,
EA, (J)
Specific
Energy
Absorp-
tion,
SEA, (J/g)
Crush
force
Effi-
ciency,
CFE, (%)
Work
Effective-
ness,
Weff, (J/g)
Aluminum
based
samples
Single
rings
TB 0.82 46.5 812 1491 51.1 1.10 54 0.90
TM 0.81 39.2 1150 1640 55.7 1.42 70 1.15
TS 0.78 23.3 1952 4141 56.4 2.42 47 1.89
Nested
tube
samples
NT2-TS 0.78 69.8 1420 3865 85.7 1.23 37 0.96
NT2-TM 0.78 85.7 1649 2884 99.5 1.16 57 0.91
NT3-TS+TS 0.75 93.1 2772 5219 160.2 1.72 53 1.29
NT3-TS+TM 0.75 109 2484 5799 143.6 1.32 43 0.99
Nested
tube
reinforced
EPP
foam
FF_TB 0.82 59.2 1105 2550 103.8 1.75 43 1.43
FF_NT2-TS 0.78 82.5 1692 4781 154.6 1.87 35 1.47
FF_NT2-TM 0.78 98.4 1990 4058 181.8 1.85 49 1.45
FF_NT3-TS+TS 0.75 105.8 2292 4774 203.5 1.92 48 1.44
FF_NT3-TS+TM 0.75 121.8 2427 7148 215.5 1.77 34 1.33
CFRP
based
Single
rings
TB 0.82 25.3 515 1367 32.4 1.28 38 1.05
TM 0.81 20.5 607 1544 29.4 1.43 39 1.16
TS 0.78 10.6 765 1858 22.1 2.08 41 1.63
counterparts across all specimen configurations. This discrepancy is attributed to the brittle
nature of carbon fiber composites, which detrimentally impacts the specimens’ capacity
to bear loads. Furthermore, the crushability indices of the samples exhibited variability
its outer diameter. The method for determining the crushability of nested samples adhered
to a similar paradigm. Nonetheless, a distinct approach was employed for nested samples
wherein 85% of the value derived from subtracting the cumulative wall thickness of the
interior tubes from the inner diameter of the TB tube was established as the sample’s
force values relative to their larger counterparts. This phenomenon aligns with the premise
that the force requisite to deform a specimen should escalate inversely with its diameter.
Evidently, the maximum force values recorded for the nested specimens utilizing the TS
tube significantly surpassed those of specimens employing the TM tube, a trend that was
consistent among specimens integrated with EPP foam.
The outcomes derived from the utilization of various specimens within the experi-
mental framework, alongside associated crashworthiness metrics, are systematically docu-
mented in Table 1. This tabulation elucidates a pronounced disparity in the force exerted by
specimens based on their material composition. Specifically, both average and maximum
force exertions by single and nested carbon fiber-reinforced polymer (CFRP) composite
tubes were observed to be inferior to those of their aluminum analogs across all specimen
configurations. This phenomenon can be attributed to the brittle character of the carbon
fiber composite, which negatively impacts the load-bearing efficacy of the specimen. Addi-
tionally, the crushability indices of the samples manifested variations contingent upon the
number of tubes employed. For individual tubes, the crushability index was derived by
calculating the ratio of 85% of the inner diameter to the outer diameter of the tube. The
computation of crushability for nested configurations adhered to a similar methodology.
However, for nested samples, 85% of the resultant value obtained by subtracting the ag-
gregate wall thickness of the internal tubes from the inner diameter of the TB tube was
designated as the crushability ratio for the sample. Consequently, an augmentation in the
number of tubes within nested configurations is anticipated to affect the crushability ratio
inversely. Irrespective of the material composition, the maximum force value associated
with tubes of smaller diameters surpassed those of larger diameters. This observation
corroborates the hypothesis that a decrease in diameter necessitates an increase in the force
required to deform the specimen. Indeed, the maximum force values for nested specimens

Appl. Sci. 2024, 14, 9635 20 of 23
utilizing the TS tube significantly exceeded those involving the TM tube, a pattern that
remained consistent for specimens incorporating EPP foam.
Sample Combination
Crushability
Ratio,
e.g.,
(mm/mm)
Sample
Weight
(g)
Fmean
(N)
Fmax
(N)
Absorbed
Energy,
EA, (J)
Specific Energy
Absorption,
SEA, (J/g)
Crush Force
Efficiency,
CFE, (%)
Work
Effectiveness,
Weff, (J/g)
Aluminum
based
samples
Single
rings
TB 0.82 46.5 812 1491 51.1 1.10 54 0.90
TM 0.81 39.2 1150 1640 55.7 1.42 70 1.15
TS 0.78 23.3 1952 4141 56.4 2.42 47 1.89
Nested
tube
samples
NT2-TS 0.78 69.8 1420 3865 85.7 1.23 37 0.96
NT2-TM 0.78 85.7 1649 2884 99.5 1.16 57 0.91
NT3-TS+TS 0.75 93.1 2772 5219 160.2 1.72 53 1.29
NT3-TS+TM 0.75 109 2484 5799 143.6 1.32 43 0.99
Nested
tube
reinforced
EPP
foam
FF_TB 0.82 59.2 1105 2550 103.8 1.75 43 1.43
FF_NT2-TS 0.78 82.5 1692 4781 154.6 1.87 35 1.47
FF_NT2-TM 0.78 98.4 1990 4058 181.8 1.85 49 1.45
FF_NT3-TS+TS 0.75 105.8 2292 4774 203.5 1.92 48 1.44
FF_NT3-TS+TM 0.75 121.8 2427 7148 215.5 1.77 34 1.33
CFRP
based
samples
Single
rings
TB 0.82 25.3 515 1367 32.4 1.28 38 1.05
TM 0.81 20.5 607 1544 29.4 1.43 39 1.16
TS 0.78 10.6 765 1858 22.1 2.08 41 1.63
Nested
tube
samples
NT2-TS 0.78 35.9 931 2234 56.2 1.57 42 1.23
NT2-TM 0.78 45.8 958 2087 57.8 1.26 46 0.99
NT3-TS+TS 0.75 46.5 1514 2113 87.5 1.88 72 1.41
NT3-TS+TM 0.75 56.4 1521 3886 87.9 1.56 39 1.17
Nested
tube
reinforced
EPP
foam
FF_TB 0.82 38 1000 1925 93.9 2.47 52 2.02
FF_NT2-TS 0.78 48.6 1477 3295 134.9 2.78 45 2.18
FF_NT2-TM 0.78 58.5 1548 3233 141.4 2.42 48 1.89
FF_NT3-TS+TS 0.75 59.2 1727 3128 153.4 2.59 55 1.95
FF_NT3-TS+TM 0.75 69.1 1908 4718 169.4 2.45 40 1.84
5. Conclusions
The investigation into the progressive deformation and energy absorption character-
istics of aluminum and CFRP nested-tube specimens under quasi-static lateral loading
conditions has yielded significant insights. Notably, the force–displacement behavior of the
aluminum and CFRP tubes demonstrated distinct material-dependent characteristics, with
aluminum tubes maintaining load-bearing capacity post the initial deformation, whereas
CFRP tubes exhibited rapid force escalation followed by a sudden loss of load-carrying
capability due to their brittle nature. Aluminum tubes demonstrate a sequential defor-
mation process, with the larger tube deforming first, followed by the inner tube upon
contact. This progression results in smooth, stepped force curves characteristic of ductile
materials, allowing for efficient energy absorption without sudden failure. Specifically, the
energy absorption values for aluminum tubes were found to be 56.4 J, 55.7 J, and 51.1 J for
specimens of increasing diameters, showcasing a decreasing trend with larger diameters.
Comparative analysis revealed that the NT3-TS+TM sample, which included a combina-
tion of one small tube (TS) and one medium tube (TM) within a larger tube, exhibited
superior energy absorption performance. Specifically, this configuration enhanced energy
absorption by 19.9 J relative to the sum of the individual tubes’ energy absorption up to the
corresponding displacement threshold. Furthermore, this sample configuration showed
a stepped force curve, indicating progressive deformation stages, which is beneficial for
controlled energy dissipation during impact.
In contrast, CFRP nested samples, while demonstrating higher specific energy absorp-
tion due to their lightweight nature, experienced abrupt decreases in load-bearing capacity
upon a sequence of cracking occurring on the tube wall due to reaching higher deformation
levels. These cracks occur sequentially, first at the upper and lower parts of the tube,
followed by the right and left sides. This significantly impacts their load-bearing capacity
and results in lower energy absorption values of 22.1 J, 29.4 J, and 32.4 J for increasing
diameters. The NT3-TS+TS configuration, which involved two small CFRP tubes nested
within a larger tube, achieved a significant mass reduction exceeding 27%, enhancing the

Appl. Sci. 2024, 14, 9635 21 of 23
specimen’s overall efficiency despite a slight decrease in absorbed energy compared to
aluminum nested specimens. Based on these findings, the NT3-TS+TM combination stands
out as the optimal sample for maximizing energy absorption efficiency in nested tubular
structures. Future studies should explore the integration of different material combinations
and investigate the effects of varying tube dimensions and wall thicknesses on energy
absorption characteristics. Additionally, dynamic impact tests and real-world crash simula-
tions would provide further validation of the observed trends and enhance the practical
applicability of the findings in automotive and aerospace safety design.
Author Contributions: Conceptualization, M.M.Y. and M.İ.Ö.; methodology, M.M.Y. and M.İ.Ö.;
formal analysis, M.M.Y. and M.İ.Ö.; investigation, M.M.Y. and M.İ.Ö.; writing—original draft prepa-
ration, M.M.Y. and M.İ.Ö.; writing—review and editing, M.M.Y. and M.İ.Ö.; visualization, M.M.Y.
and M.İ.Ö. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: The original contributions presented in the study are included in the
article, further inquiries can be directed to the corresponding author.
Conflicts of Interest: The authors declare no conflicts of interest.
References
1. Tran, T.; Hou, S.; Han, X.; Nguyen, N.; Chau, M. Theoretical prediction and crashworthiness optimization of multi-cell square
tubes under oblique impact loading. Int. J. Mech. Sci. 2014, 89, 177–193. [CrossRef]
2. Nia, A.A.; Chahardoli, S. Mechanical behavior of nested multi-tubular structures under quasi-static axial load. Thin-Walled Struct.
2016, 106, 376–389. [CrossRef]
3. Usta, F.; Türkmen, H.S. Experimental and numerical investigation of impact behavior of nested tubes with and without honeycomb
filler. Thin-Walled Struct. 2019, 143, 106256. [CrossRef]
4. Wang, Y.; He, Q.; Li, L.; Jiang, Y. Mechanical properties of a novel nested tube and its application as anti-explosion layer. Mater.
Today Commun. 2022, 31, 103242. [CrossRef]
5. Yang, K.; Chen, Y.; Liu, S.; Qiao, C.; Yang, J. Internally nested self-locked tube system for energy absorption. Thin-Walled Struct.
2017, 119, 371–384. [CrossRef]
6. Baroutaji, A.; Sajjia, M.; Olabi, A.-G. On the crashworthiness performance of thin-walled energy absorbers: Recent advances and
future developments. Thin-Walled Struct. 2017, 118, 137–163. [CrossRef]
7. Magliaro, J.; Altenhof, W.; Alpas, A.T. A review of advanced materials, structures and deformation modes for adaptive energy
dissipation and structural crashworthiness. Thin-Walled Struct. 2022, 180, 109808. [CrossRef]
8. Dehghanpour, S.; Safari, K.H.; Barati, F.; Attar, M.M. Comparative Analysis of Energy Absorption Capacity of Single and Nested
Metal Matrix Composite Tubes Under Quasi-Static Lateral and Axial Loading. J. Solid Mech. 2021, 13, 134–143. [CrossRef]
9. Yao, R.; Pang, T.; Zhang, B.; Fang, J.; Li, Q.; Sun, G. On the crashworthiness of thin-walled multi-cell structures and materials:
State of the art and prospects. Thin-Walled Struct. 2023, 189, 110734. [CrossRef]
10. Wang, H.; Yang, J.; Liu, H.; Sun, Y.; Xu, T.X. Internally nested circular tube system subjected to lateral impact loading. Thin-Walled
Struct. 2015, 91, 72–81. [CrossRef]
11. Xu, B.; Wang, C.; Xu, W. An efficient energy absorber based on fourfold-tube nested circular tube system. Thin-Walled Struct. 2019,
137, 143–150. [CrossRef]
12. Wang, Y.; Zhai, X.; Liu, S.; Lu, J.; Zhou, H. Energy absorption performance of a new circular–triangular nested tube and its
application as sacrificial cladding. Thin-Walled Struct. 2020, 157, 106992. [CrossRef]
13. Ying, L.; Wang, S.; Gao, T.; Dai, M.; Hu, P.; Wang, Y. Crashworthiness analysis and optimization of multi-functional gradient
foam-aluminum filled hierarchical thin-walled structures. Thin-Walled Struct. 2023, 189, 110906. [CrossRef]
14. Al Galib, D.; Limam, A. Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum
tubes. Thin-Walled Struct. 2004, 42, 1103–1137. [CrossRef]
15. Mahdi, E.-S.; El Kadi, H. Crushing behavior of laterally compressed composite elliptical tubes: Experiments and predictions
using artificial neural networks. Compos. Struct. 2008, 83, 399–412. [CrossRef]
16. Elahi, S.A.; Rouzegar, J.; Niknejad, A.; Assaee, H. Theoretical study of absorbed energy by empty and foam-filled composite
tubes under lateral compression. Thin-Walled Struct. 2017, 114, 1–10. [CrossRef]
17. Niknejad, A.; Elahi, S.A.; Liaghat, G.H. Experimental investigation on the lateral compression in the foam-filled circular tubes.
Mater. Des. 2012, 36, 24–34. [CrossRef]

Appl. Sci. 2024, 14, 9635 22 of 23
18. Ding, H.; Zhu, G.; Xiang, C.; Pei, F.; Chen, J.; Wang, Y.; Chen, Q. Excellent combination of plasticity and ultra-high strength in a
low-alloy automotive steel treated by conventional continuous annealing. Mater. Sci. Eng. A 2020, 791, 139694. [CrossRef]
19. Adanur, Ö.; Varol, F. Investigation of the effect of friction force on the energy absorption characteristics of thin-walled structures
loaded with axial impact force. Mater. Today Commun. 2023, 36, 106420. [CrossRef]
20. Dubey, P.P.; Rex, A.V.; Raj, A.; Paul, S.K. Influence of pre-strain on tensile response of extra deep drawing (EDD) steel under
varying strain rates and crash performance. J. Alloy. Met. Syst. 2023, 4, 100036. [CrossRef]
21. Shabani, B.; Rad, S.G.; Alijani, A.; Darvizeh, A.; Rajabiehfard, R. Dynamic plastic behavior of single and nested rings under lateral
impact. Thin-Walled Struct. 2021, 160, 107373. [CrossRef]
22. Olabi, A.G.; Morris, E.; Hashmi, M.S.J.; Gilchrist, M.D. Optimised design of nested circular tube energy absorbers under lateral
impact loading. Int. J. Mech. Sci. 2008, 50, 104–116. [CrossRef]
23. Baroutaji, A.; Gilchrist, M.D.; Olabi, A.G. Quasi-static, impact and energy absorption of internally nested tubes subjected to lateral
loading. Thin-Walled Struct. 2016, 98, 337–350. [CrossRef]
24. Kahraman, Y.; Akdikmen, O. Experimental investigation on deformation behavior and energy absorption capability of nested
steel tubes under lateral loading. Eng. Sci. Technol. Int. J. 2021, 24, 579–588. [CrossRef]
25. Atxaga, G.; Arroyo, A.; Canflanca, B. Hot stamping of aerospace aluminium alloys: Automotive technologies for the aeronautics
industry. J. Manuf. Process. 2022, 81, 817–827. [CrossRef]
26. Hatzigeorgiou, G.D.; Beskos, D.E. Minimum cost design of fibre-reinforced concrete-filled steel tubular columns. J. Constr. Steel
Res. 2005, 61, 167–182. [CrossRef]
27. Wu, J.; Zhang, Y.; Li, J.; Lai, X.; Duan, N. Energy absorption characteristics of nested corrugated-elliptical tubes subjected to a
lateral crushing load. Compos. Struct. 2022, 297, 115926. [CrossRef]
28. Yang, X.; Ma, J.; Sun, Y.; Yang, J. An internally nested circular-elliptical tube system for energy absorption. Thin-Walled Struct.
2019, 139, 281–293. [CrossRef]
29. Altin, M.; Acar, E.; Güler, M.A. Foam filling options for crashworthiness optimization of thin-walled multi-tubular circular
columns. Thin-Walled Struct. 2018, 131, 309–323. [CrossRef]
30. Altin, M.; Güler, M.A.; Mert, S.K. The effect of percent foam fill ratio on the energy absorption capacity of axially compressed
thin-walled multi-cell square and circular tubes. Int. J. Mech. Sci. 2017, 131–132, 368–379. [CrossRef]
31. Wang, S.; Zhang, M.; Pei, W.; Yu, F.; Jiang, Y. Energy-absorbing mechanism and crashworthiness performance of thin-walled
tubes diagonally filled with rib-reinforced foam blocks under axial crushing. Compos. Struct. 2022, 299, 116149. [CrossRef]
32. Xu, B.; Wang, C.; Yuen, S.C.K. Deformation Pattern and Energy Absorption Characteristics of A Four-Tube Nested System Under
Lateral and Oblique Loadings. Lat. Am. J. Solids Struct. 2021, 18, e388. [CrossRef]
33. Wang, Y.; Zhang, R.; Liu, S.; Zhai, X.; Zhi, X. Energy absorption behaviour of an aluminium foam-filled circular-triangular nested
tube energy absorber under impact loading. Structures 2021, 34, 95–104. [CrossRef]
34. Zhang, W.; Xu, J. Advanced lightweight materials for Automobiles: A review. Mater. Des. 2022, 221, 110994. [CrossRef]
35. Fontana, M.; Araujo, A.L.; Madeira, J.F.A. Optimization of a thin-walled composite crash absorber. Thin-Walled Struct. 2020, 155,
106826. [CrossRef]
36. Sun, G.; Chen, D.; Zhu, G.; Li, Q. Lightweight hybrid materials and structures for energy absorption: A state-of-the-art review
and outlook. Thin-Walled Struct. 2022, 172, 108760. [CrossRef]
37. Patel, V.; Tiwari, G.; Dumpala, R. Review of the crushing response of collapsible tubular structures. Front. Mech. Eng. 2020, 15,
438–474. [CrossRef]
38. Magliaro, J.; Rahimidehgolan, F.; Altenhof, W.; Alpas, A.T. Superior energy dissipation mechanisms compounded within
composite AA6061/H130 foam structures. Int. J. Mech. Sci. 2023, 238, 107843. [CrossRef]
39. Gupta, N.K.; Sekhon, G.S.; Gupta, P.K. Study of lateral compression of round metallic tubes. Thin-Walled Struct. 2005, 43, 895–922.
[CrossRef]
40. Zhang, Z. Theoretical prediction of cross-sectional deformation of circular thin-walled tube in large elastic–plastic deformation
stage under lateral compression. Thin-Walled Struct. 2022, 180, 109957. [CrossRef]
41. Kumar, A.P.; Nagarjun, J.; Ma, Q. Potentiality of MWCNT fillers on the lateral crashworthiness behaviour of polymer composite
cylindrical tubes under quasi-static loading. J. Ind. Text. 2022, 51, 7014S–7033S. [CrossRef]
42. Sun, G.; Guo, X.; Li, S.; Ruan, D.; Li, Q. Comparative study on aluminum/GFRP/CFRP tubes for oblique lateral crushing.
Thin-Walled Struct. 2020, 152, 106420. [CrossRef]
43. Wazeer, A.; Das, A.; Abeykoon, C.; Sinha, A.; Karmakar, A. Composites for electric vehicles and automotive sector: A review.
Green Energy Intell. Transp. 2022, 2, 100043. [CrossRef]
44. Tran, T.N.; Le, D.H.; Baroutaji, A. Theoretical and numerical crush analysis of multi-stage nested aluminium alloy tubular
structures under axial impact loading. Eng. Struct. 2019, 182, 39–50. [CrossRef]
45. Bhutada, S.; Goel, M.D. Crashworthiness parameters and their improvement using tubes as an energy absorbing structure: An
overview. Int. J. Crashworthiness 2021, 1–32. [CrossRef]
46. Alagesan, P.K.; Dirgantara, T.; Jusuf, A.; Gladys, A.K.; Ma, Q. Comparison of the lateral crushing response of thin-walled
aluminum-thermoplastic polymer composite cylindrical shells. Mech. Adv. Mater. Struct. 2024. [CrossRef]

Appl. Sci. 2024, 14, 9635 23 of 23
47. Yang, H.; Guo, X.; Wang, H.; Qu, J.; Ma, Y.; Lei, H.; Chen, H. Low-velocity impact performance of composite-aluminum tubes
prepared by mesoscopic hybridization. Compos. Struct. 2021, 274. [CrossRef]
48. Yang, H.; Ren, Y. On energy absorption capability and controllable failure modes of CFRP circular tube using numerical simulation.
Thin-Walled Struct. 2024, 205. [CrossRef]
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