Composite Structures 326 (2023) 117606

Contents lists available at ScienceDirect

Composite Structures
journal homepage: www.elsevier.com/locate/compstruct

Three-point bending response and energy absorption of novel sandwich

beams with combined re-entrant double-arrow auxetic honeycomb cores
Huiling Wang a, Junhua Shao a, Wei Zhang a, b, *, Zhi Yan a, Zhengyi Huang a, Xuan Liang a
a
Hubei Province Key Laboratory of Systems Science in Metallurgical Process, College of Science, Wuhan University of Science and Technology, Wuhan 430065, China
b
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Key Laboratory of Extreme Environment and Protective Technology, Xi’an Jiaotong
University, Xi’an 710049, China

A R T I C L E I N F O A B S T R A C T

Keywords: The response and energy absorption of novel sandwich beams with combined re-entrant double-arrow auxetic
Sandwich beam honeycomb (RDAH) cores subjected to three-point bending were studied experimentally and numerically. Two
Auxetic honeycomb typical sandwich beams loaded at different loading positions were considered. Quasi-static three-point bending
Three-point bending
experiments were conducted to obtain the failure modes and force–displacement curves. The reliable numerical
Energy absorption
Negative Poisson’s ratio
simulation models were further established based on experimental validations. The results indicate that when the
loading roller is located directly above the re-entrant cell, the RDAH core sandwich beam has better load-
carrying and energy absorption capacity. Subsequently, the influence of face sheet distribution, cell-wall
thickness, impact velocity and cell configuration on the structural response were explored. For the sandwich
beams with same total mass, the arrangement where the thickness of the front face sheet is larger than that of the
back face sheet is beneficial for improving the load-carrying and energy absorption capacity. In addition, the cell-
wall thickness has an influence on the local deformation mode of the sandwich beam, and increasing its value can
produce more stable deformation and improve the load-carrying capacity. Increasing impact velocity has a
significant influence on the initial deformation but little influence on the final deformation of the sandwich
beams. As the impact velocity increases, the total energy absorption of the sandwich beam gradually increases,
and the negative Poisson’s ratio characteristic of the core still exists. Compared to the traditional re-entrant
honeycomb (RH) core sandwich beams, RDAH core sandwich beams have better energy absorption capacity
and bending resistance.

1. Introduction The bending performance of sandwich beams is an important index

that must be considered in engineering applications. In recent years,
Compared with traditional monolithic structures, sandwich struc­ scholars have carried out relevant researches on the bending response
tures have the advantages of lightweight, high specific strength, high and failure modes of sandwich structures with different core construc­
specific stiffness, excellent energy absorption performance and impact tions such as corrugated core [13–15], honeycomb core [16–18], metal
resistance [1–7]. As load-carrying or functional components, sandwich foam core [19–22] and lattice core [23–25]. Yu et al. [26] explored the
structures are widely applied in the industrial fields such as aerospace, bending response and failure of sandwich beams with aluminum-foam
automotive, shipping, and packaging [8–12]. Typical sandwich struc­ core under quasi-static and low-velocity impact experiments. Lv et al.
tures consist of two thin face sheets and a lightweight core that separates [27] studied the bending properties of 3D honeycomb sandwich struc­
the face sheets to maintain their relative positions. The mechanical tures with different cross-sections. Compared to a triquetrous cross-
properties of sandwich structures depend on the material and geometric section and a quadrangular cross-section, the 3D honeycomb sandwich
parameters of the face sheet and core, as well as the core configuration. structure with a hexagonal cross-section has the maximum load. Xia
Relatively speaking, selecting a suitable core can have a significant in­ et al. [28] compared the three-point bending performances of sandwich
fluence on the performance of sandwich beams, and therefore has been panels with corrugated, honeycomb, aluminum foam, pyramidal truss,
widely studied. double sine corrugated, and 3D re-entrant auxetic cores experimentally

* Corresponding author.
E-mail address: zhangweiok@wust.edu.cn (W. Zhang).

https://doi.org/10.1016/j.compstruct.2023.117606
Received 15 May 2023; Received in revised form 25 August 2023; Accepted 5 October 2023
Available online 10 October 2023
0263-8223/© 2023 Elsevier Ltd. All rights reserved.
H. Wang et al. Composite Structures 326 (2023) 117606

Fig. 1. Schematic diagram of a novel sandwich beam with RDAH auxetic core.

and numerically. Three different deformation modes were observed and core is an effective method to enhance the mechanical properties of
it was found that honeycomb core sandwich beam has the highest spe­ sandwich beams due to the high load-carrying capacity. Li et al. [51]
cific energy absorption for the same relative density of core. Zaharia investigated the bending behavior and energy absorption capacity of
et al. [29] studied the bending performance of lightweight sandwich sandwich beams with three different cores (re-entrant honeycomb,
structures with honeycomb, diamond-celled and corrugated cores using conventional honeycomb and truss) under three-point bending tests.
three-point bending experiments, and observed three main failure The results indicated that the sandwich beams with re-entrant honey­
modes, i.e. face yielding, face wrinkling and core/face debonding. comb core exhibit a sequential snap-through instability which signifi­
Yazdani et al. [30] conducted three-point bending and low-velocity cantly enhanced the energy absorption capacity. Hou et al. [52]
impact experiments to investigate the failure mechanism and energy conducted dynamic three-point bending tests on auxetic core and non-
absorption capability of 3D printed polymeric meta-sandwich structures auxetic core sandwich panels, and found that the re-entrant core sand­
made of cubic, octet and Isomax cellular cores. It was found that Isomax wich panel performed best in both force mitigation and energy dissi­
meta-sandwich structures show higher quasi-static and dynamic energy pation when the impact energy was appropriate. Li et al. [53]
absorption capabilities. Farrokhabadi et al. [31] investigated the dam­ systematically explored the influences of face sheet thickness, core to­
age mechanism, contact force, and energy absorption of the sandwich pology, core depth and core direction on the deformation mode and
panels with different corrugated cores (rectangular, trapezoidal, and mechanism of the sandwich structures with auxetic and non-auxetic
triangular) under three-point bending loading. Overall, it is of great honeycomb core under out-of-plane three-point bending. Zhao et al.
significance to improve the bending performance of sandwich structures [54] used three-point bending experiments and numerical simulations
by changing the configuration of the core and designing geometric to investigate the bending response and energy absorption of star-
dimensions. triangular honeycomb core sandwich beam. Subsequently, the effects
Among these sandwich cores, honeycomb is an important choice due of loading position, geometric parameters and configuration on the
to the excellent load-carrying and designability. Compared to traditional deformation modes and bending performances of the sandwich beam
honeycomb, auxetic honeycomb undergoes lateral aggregation (expan­ were discussed. So far, some research has been conducted on the
sion) when subjected to axial compression (tension), exhibiting a bending performance of the sandwich structures with traditional auxetic
negative Poisson’s ratio effect [32]. This unique behavior makes the honeycomb core. However, the research on designing new types of
auxetic honeycomb have more excellent mechanical properties, auxetic honeycomb core and revealing the bending behaviors and en­
including enhanced shear resistance [33], indentation resistance [34], ergy absorption capacity of these novel sandwich structures is still
fracture toughness [35] and energy absorption ability [36,37]. With the relatively limited.
development of 3D printing technology, different auxetic honeycomb In this work, a novel auxetic honeycomb core sandwich beam is
structures have been manufactured and studied, including re-entrant designed and studied experimentally and numerically, which combines
structures [38–40], chiral structures [41–43], rotating structures re-entrant honeycomb and double-arrow honeycomb, to reveal its
[44–46] etc. The application of auxetic honeycomb as the core of bending response and energy absorption mechanism. Two typical
sandwich beams has great potential for improving mechanical proper­ sandwich beam samples loaded at different loading positions are man­
ties [47], and it has attracted extensive attentions in recent years. ufactured by 3D printing process. The deformation modes and force­
To evaluate the effect of auxetic core on the bending properties of –displacement response of the sandwich beams are obtained by three-
sandwich structures, Namvar et al. [48] experimentally and numerically point bending experiments, and the established numerical simulation
researched the out-of-plane bending performance of sandwich structures models are verified. Subsequently, the effects of mass distribution of the
with different cores, such as honeycomb, tetra chiral, re-entrant, face sheets, cell-wall thickness of core, and impact velocity on the
arrowhead, and star-shaped arrangements. Li et al. [49] investigated deformation modes and bending properties of the sandwich beams are
the nonlinear bending behavior of the sandwich beams with functionally systematically discussed. Finally, the mechanical properties of the novel
graded negative Possion’s ratio (NPR) honeycomb core in thermal en­ sandwich beams are compared with the traditional re-entrant honey­
vironments. The finite element (FE) simulation results showed that the comb (RH) core sandwich beam. This study is expected to provide some
NPR core sandwich beams have lower load-bending moment curves guidance for further optimize and design novel sandwich structures with
compared with those with positive Poisson’s ratio cores. Najafi et al. auxetic core.
[50] adopted experimental and finite element methods to evaluate the
flexural behavior and energy absorption of the sandwich beams with
chiral, arrowhead and re-entrant auxetic cores, and compared with
conventional honeycomb core. The results showed that using auxetic

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2.2. Sample preparation

Fig. 2 shows the RDAH core sandwich beam samples prepared by a

Multi-Jet Fusion (MJF) process using high toughness nylon material.
The face sheet and core of the sample are modeled and printed as a
whole to avoid debonding between the face sheet and core during the
loading process. The geometric parameters of cell of the sample are
√̅̅̅
selected as l1 = 6mm, l2 = l3 = 6 3mm, θ = 30◦ , α = 30◦ ,
h = 1mm. The thickness of the face sheet is 1.5 mm. Since the com­
bined re-entrant double-arrow honeycomb is composed of re-entrant
honeycomb and double-arrow honeycomb, the loading roller at
Fig. 2. RDAH core sandwich beam samples at different loading positions.
different positions may result in different deformation modes. Two
typical sandwich beam samples loaded at different positions are pre­
Table 1 pared to investigate the effect of loading positions on the three-point
Overall dimension parameters of the sandwich beam samples. bending response of the sandwich beams. The loading roller located
directly above the middle of the two double-arrow cells is defined as
Sample L(mm) H(mm) B(mm) Mass(g)
position-1, and the loading roller located directly above the re-entrant
Sample-position-1 211.24 23.74 20.00 41.43 cell is defined as position-2. The number and dimension of cells for
Sample-position-2 211.46 23.80 20.10 41.65
the two types of samples are the same. The specific dimension param­
eters of the samples are shown in Table 1.

2.3. Material properties

The dog-bone shaped tensile samples were designed to obtain the

mechanical properties of the matrix material according to ASTM D638
standard, which were prepared using the same manufacturing process as
the sandwich beam samples. The tensile experiments were carried out
with a constant loading velocity of 2 mm/min on an electronic universal
testing machine (INSTRON, 50KN). The obtained stress–strain curves of
the matrix material are shown in Fig. 3. It can be found that the me­
chanical properties of the matrix material have good consistency. The
detailed mechanical property parameters of the matrix material are
summarized in Table 2. Although the mechanical properties of the
matrix materials are slightly lower compared to similar materials
[55–60], they are used to prepare samples to explore the three-point
bending response and energy absorption mechanism of the sandwich
beams and to validate the numerical model is feasible.
Fig. 3. Tensile stress–strain curves of matrix material of the sandwich beam.
2.4. Experimental setup and process

Table 2 According to ASTM C-393 standard, the quasi-static three-point

Property parameters of matrix material of the sandwich beam. bending experiments were conducted on an electronic universal testing
Materials Density Elastic Poisson’s 0.2 % offset yield machine (INSTRON, 50KN) to explore the three-point bending perfor­
(kg/m3) modulus (MPa) ratio strength (MPa) mance of RDAH core sandwich beams, as shown in Fig. 4. The sample is
Nylon 943 641.44 0.33 18.16 placed on two supporting cylindrical rollers, and a loading cylindrical
roller moves along the symmetrical center of the sample with a constant
loading velocity of 3 mm/min. The span of the supporting rollers is 120
2. Experimental mm, and the diameters of the supporting roller and the loading roller are
both 10 mm. The final loading displacement of the loading roller is set to
2.1. Structural design 25 mm to better observe the deformation mode of the RDAH core
sandwich beam. During the experiment, the load–displacement curves
A novel sandwich beam with auxetic core is designed by periodically can be automatically obtained from the testing machine and recorded in
arranged re-entrant double-arrow honeycomb (RDAH) cell, which the computer system. The entire deformation processes of the samples
combines the re-entrant honeycomb and the double-arrow honeycomb, were captured using a digital camera.
as shown in Fig. 1. The geometric parameters of the sandwich beam
include the length L, width B, and height H of the beam, where L and H
3. Numerical simulation
are determined by the dimension and number of cells, and B is fixed at
20 mm. In the present model, the cell number of vertical and horizontal
The finite element (FE) simulations of the RDAH core sandwich
arrangement is Ny × Nx = 2 × 8. The thickness of the front and back face
beams were also carried out to explore the three-point bending behav­
sheets is hf and hb , respectively. The geometric parameters of cells
iors more extensively using ABAQUS/Explicit software. The established
mainly include the length l1 of the short inclined wall, the length l2 of the FE model is shown in Fig. 5. Similar to the three-point bending experi­
horizontal wall, the length l3 of the long inclined wall, the angle θ be­ ment, the sandwich beams were placed on two fixed rigid cylindrical
tween the short inclined wall and the vertical direction, the angle α supporting rollers, and the rigid cylindrical loading roller compressed
between the long inclined wall and the horizontal direction, and the the sandwich beam with a constant loading velocity of 0.1 m/s. In order
thickness h of the cell wall. to improve the computational accuracy and efficiency, the face sheets

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H. Wang et al. Composite Structures 326 (2023) 117606

Fig. 4. Experimental setup of quasi-static three-point bending of the sandwich beam.

and core were meshed by four-node shell elements (S4R) with a size of 1
mm based on mesh convergence testing. The supporting rollers and the
loading roller with a diameter 10 mm and a length 30 mm were meshed
by the discrete rigid elements (R3D4). General contact was adopted
between the front face sheet and the rigid loading roller, as well as be­
tween the back face sheet and the rigid supporting rollers. The friction
coefficient of tangential behavior was set to 0.2, and the normal
behavior was set to hard contact. Due to the fact that the face sheets and
the core of the samples were modeled and printed as a whole, while they
were modeled separately in the FE model, “Tie” constraint was used to
simulate the bonding between the face sheets and the core to ensure that
debonding does not occur during the loading process. Apply a vertical
downward displacement to the loading roller and restrict its other de­
Fig. 5. FE model of RDAH core sandwich beam under three-point bending. grees of freedom. All degrees of freedom of the supporting rollers were
restricted. For verification, the FE model was established, which is
consistent with the geometric parameters and material properties of the
RDAH core sandwich beam samples. Further, based on the verified FE

Fig. 6. Experimental and numerical deformation and failure processes of the sandwich beam loaded at position-1 under different loading displacements.

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H. Wang et al. Composite Structures 326 (2023) 117606

Fig. 7. Experimental and numerical force–displacement curves of the sandwich beam loaded at position-1.

Fig. 8. Experimental and numerical deformation and failure processes of the sandwich beam loaded at position-2 under different loading displacements.

model, the influences of different thicknesses of the face sheets (1.0 mm, processes of the sandwich beam loaded at position-1 under different
1.5 mm, 2.0 mm), different cell-wall thicknesses of core (0.5 mm, 0.6 compressive displacements. In the initial stage, the sandwich beam
mm, 0.8 mm, 1.0 mm, 1.2 mm) and different impact velocities (1 m/s, 5 undergoes overall elastic bending deformation. When the compression
m/s, 10 m/s, 15 m/s, 20 m/s, 25 m/s) on the deformation modes and displacement is d = 8 mm, the RDAH cells between two supporting
bending performances of the RDAH core sandwich beams are explored. rollers undergo rotation and bending of the re-entrant inclined walls,
forming two symmetrical inclined shear bands, while the change of the
4. Results and discussion cell below the loading roller is not obvious. When d = 15 mm, the right
front face sheet undergoes local bucking, compressing the upper hon­
4.1. Bending response of sandwich beams loaded at position-1 eycomb cells bonded to the front face sheet, causing distortion of the cell
walls. As the compression displacement continues to increase, the
Fig. 6 shows the experimental and numerical deformation and failure honeycomb cells below the loading roller are further compressed,

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Fig. 9. Experimental and numerical force–displacement curves of the sandwich beam loaded at position-2.

Fig. 10. Comparisons of force–displacement curves of the sandwich beams loaded at different positions.

resulting in cell wall fracture at d = 22.5 mm. Due to the asymmetric are in good agreement.
buckling of the front face sheet, the sandwich beam experiences slight Experimental and numerical force–displacement curves of the
sliding. During this process, the deformation is mainly concentrated in sandwich beam loaded at position-1 are shown in Fig. 7. In the linear
the region near the loading roller, while the cells near the two sup­ elastic stage, the compressive force increases proportionally with the
porting rollers do not undergo significant deformation except for rota­ compressive displacement. Subsequently, during the overall bending of
tion. In addition, lateral shrinkage deformation of RDAH cell is observed the sandwich beam and the shear deformation of the core, the force
in the loading region. Overall, the experimental and numerical defor­ increases to reach the initial peak value. Further, due to the asymmetric
mation and failure processes of the sandwich beam loaded at position-1 local buckling of the front face sheet, the load-carrying capacity of the

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H. Wang et al. Composite Structures 326 (2023) 117606

Fig. 11. Comparisons of energy absorption capacity of the sandwich beams at

different loading positions (d = 25 mm).
Fig. 13. Comparisons of force–displacement curves of the sandwich beams
with the same total mass of the face sheets.

Fig. 14. Comparisons of specific energy absorption curves of the sandwich

Fig. 12. Comparisons of deformation modes of the sandwich beams with the beams with different mass distributions of the face sheets.
same total mass of the face sheets (d = 25 mm).
deformation, manifested as inward bending of the horizontal wall of the
sandwich beam is reduced, resulting in a certain decrease of force. re-entrant cell and the front face sheet bonded to it. In addition, the
However, due to the compression deformation of the honeycomb cells bending and rotation of the inclined walls between the two supporting
and the bending of the sandwich beam, the force will then further in­ rollers lead to shear deformation of the core. As the compressive
crease. As the compression deformation of the RDAH cell continues, the displacement of the loading roller continues to increase, the bending
cell wall breaks, resulting in a rapid decrease of force. Finally, due to the degree of the horizontal wall of the upper re-entrant cell and the face
mutual contact of cell walls in the loading region, the compressive force sheet bonded to it in the loading region increases, and the cell walls
continues to increase and tends to stabilize. The slightly higher nu­ compress longitudinally, contract laterally, and come into contact with
merical result compared to the experimental result is mainly due to the each other. In this stage, the sandwich beam exhibits obvious indenta­
fact that the fracture of the cell wall is not considered in the FE simu­ tion deformation. When d = 22.5 mm, the lower RDAH cell below the
lation, and the cell-wall thickness of printed sandwich beam is not loading roller undergoes lateral shrinkage deformation, showing a local
completely uniform. However, in general, the trend of the experimental negative Poisson’s ratio effect. Overall, the experimental and numerical
and numerical force–displacement curves is consistent, and the error deformation processes of the sandwich beam loaded at position-2 are in
magnitude is acceptable reasonably. good agreement.
The experimental and numerical force–displacement curves of the
sandwich beam loaded at position-2 are shown in Fig. 9. Three stages
4.2. Bending response of sandwich beams loaded at position-2
can be observed from the curves. In the first stage, the sandwich beam
undergoes elastic deformation, and the force increases linearly with
Fig. 8 shows the experimental and numerical deformation and failure
displacement. After d = 8 mm, the re-entrant cell below the loading
processes of the sandwich beam loaded at position-2 under different
roller undergoes compression and local bending, and the force­
loading displacements. Similarly, the sandwich beam also undergoes
–displacement curve enters a relative platform stage. Subsequently, as
overall bending deformation in the initial stage. When d = 8 mm, the
the cell walls further compress, contract laterally, and come into contact
upper RDAH cell below the loading roller experiences significant local

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Fig. 15. Comparisons of maximum mid-span deflections of the back face sheet of the sandwich beams with different mass distributions of the face sheets (d =
25 mm).

with each other, the force continues to increase. The increased force­ energy absorption (SEA) is defined as the energy absorption (EA) per
–displacement curve is influenced by the negative Poisson’s ratio effect unit mass of a sandwich beam. It can be seen that the sandwich beam
of the auxetic core. In general, the FE results are basically consistent sample loaded at position-2 exhibits more excellent energy absorption
with the experimental results, verifying the reliability of the FE model. capacity. When the loading displacement is d = 25 mm, the specific
energy absorption of the sandwich beam sample loaded at position-2 is
26.49 % higher than that at position-1. Therefore, the following series of
4.3. Influence of loading position studies will only focus on the RDAH core sandwich beams loaded at
position-2.
From the comparison of deformation modes in Figs. 6 and 8, it can be
observed that when the loading roller is located at different positions,
the overall deformation modes of the sandwich beams are similar, but 4.4. Influence of mass distribution of face sheets
there are significant differences in the local deformation modes. When
loaded at position-1, the buckling of the front face sheet leads to In order to investigate the influence of face sheet distribution on the
asymmetric local deformation, causing the loading position to move mechanical properties of the sandwich beams under three-point
towards to the right side of the sandwich beam. When loaded at position- bending, different mass distributions of front and back face sheets of
2, the front face sheet and the re-entrant honeycomb cell below the the sandwich beams are designed and compared. Fig. 12 shows the
loading roller bend inward, resulting in a relatively stable deformation comparisons of deformation modes of the sandwich beams with the
and a smaller indentation area compared to loaded at position-1. same total mass of the front and back face sheets. It can be observed that
Fig. 10 shows the comparison of the force–displacement curves of when hf < hb , the front face sheet in contact with the loading roller
RDAH core sandwich beam samples loaded at different positions. It can exhibits a significant indentation deformation, while when hf > hb , the
be found that the initial stage of the force–displacement curves is back face sheet in contact with the supporting rollers exhibits a signif­
consistent, but the subsequent trends are inconsistent. When icant local bending deformation. With the increase of hf /hb , the inden­
8mm < d < 15mm, the force of the sandwich beam loaded at position-1 tation deformation of the front face sheet decreases, and the local
is higher than that loaded at position-2. This is because the sandwich bending deformation of the back face sheet increases.
beam loaded at position-1 mainly exhibits core shear deformation dur­ Comparisons of force–displacement curves of the sandwich beams
ing this loading process, while the sandwich beam loaded at position-2 with the same total mass of the face sheets are shown in Fig. 13. It can be
exhibits indentation deformation of the front face sheet and the hori­ found that the elastic bending stiffness is less affected by the mass dis­
zontal wall below the loading roller, resulting in a relatively low force. tribution of the face sheets, and the force–displacement curves show the
When d⩾15mm, for the sandwich beam loaded at position-1, the un­ same characteristics and trends. The difference is that as the proportion
stable deformation of the front face sheet in contact with the loading of the front face sheet thickness increases, the load-carrying capacity of
roller results in cell-wall buckling and contact of the cells in the loading the sandwich beam gradually increases during the large deflection stage.
region. As deformation proceeds, the cell wall of the core in the defor­ This may be that the front face sheet has a smaller thickness and lower
mation region breaks, leading to a significant decrease of the load- stiffness, resulting in more obvious indentation mode, thereby reducing
carrying capacity of the sandwich beam. However, the deformation of the load-carrying capacity.
the sandwich beam is relatively stable when loaded at position-2. The comparisons of specific energy absorption of the sandwich
Therefore, the load-carrying capacity of the sandwich beam at beams with different mass distributions of the face sheets are shown in
position-2 is higher than that at position-1. Fig. 14. It is found that increasing the thickness of the face sheet can
The comparison of the energy absorption capacity of the sandwich significantly improve the energy absorption capacity of the sandwich
beam samples at different positions is shown in Fig. 11. The specific beam, while maintaining a constant thickness of the back face sheet and

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Fig. 16. Comparisons of deformation modes of the sandwich beams with different cell-wall thicknesses of core (d = 25 mm).

increasing the thickness of the front face sheet has greater influence. beams, five types of sandwich beams with different cell-wall thicknesses
Besides, for the same mass of sandwich beam, the arrangement where of core are designed, and the final deformation mode (d = 25 mm) are
the front face sheet thickness is greater than the back face sheet thick­ compared and shown in Fig. 16. When h < 0.8 mm, the RDAH cells in the
ness has better energy absorption capacity than other arrangements. loading region exhibit significant unstable buckling deformation. The
In addition, the maximum mid-span deflections of the back face sheet other RDAH cells between the supporting rollers undergo significant
of the sandwich beams with different mass distributions of the face shear deformation. When h = 0.8 mm, the front face sheet and the
sheets also vary greatly. When the thickness of one face sheet is constant, horizontal wall of the upper RDAH cell below the loading roller undergo
increasing the thickness of the other face sheet significantly reduces the symmetrical inward bending deformation, while the lower RDAH cell
maximum mid-span deflection of the back face sheet, as shown in exhibits significant lateral shrinkage deformation. When h > 0.8 mm,
Fig. 15. In general, increasing the thickness of the face sheets can the indentation mode of the front face sheet and the cell in contact with
significantly improve the load-carrying capacity and energy absorption the loading roller increases, while the local yield deformation on both
capacity of the sandwich beam. sides of the loading roller weakens and transforms into shear deforma­
tion of the cells. In addition, due to the increase of cell-wall thickness of
4.5. Influence of cell-wall thickness of core the core, the upper RDAH cell bears more load, and the lateral shrinkage
deformation of the lower RDAH cell directly below the loading roller
The relative density of the core is another important factor affecting gradually weakens, but there is still a local negative Poisson’s ratio
the mechanical properties of the sandwich beams. To reveal the effect of effect.
the relative density of the core on the bending response of the sandwich Fig. 17 shows comparisons of the force–displacement curves of

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Fig. 17. Comparisons of force–displacement curves of the sandwich beams with different cell-wall thicknesses of core.

structure. The specific energy absorption curves of RDAH core sandwich

beams with different cell-wall thicknesses are shown in Fig. 18. It can be
found that increasing the cell-wall thickness can significantly improve
the energy absorption capacity of the sandwich beam.

4.6. Influence of impact velocity

Fig. 19 shows the comparisons of deformation modes of RDAH core

sandwich beams subjected to different impact velocities. As shown in
Fig. 19 (a), when d = 5 mm, the deformation mode for the case of v ≤ 5
m/s is similar to that of quasi-static loading, while for the case of v ≥ 10
m/s, the horizontal wall of the RDAH cell below the loading roller bends
inward along with the front face sheet, resulting in an obvious inden­
tation mode. With the increase of impact velocity, the indentation
deformation mode becomes more significant, mainly due to the influ­
ence of inertial effects. When d = 25 mm, the sandwich beams all show
the deformation mode of indentation in the loading region, overall
bending of the sandwich, and shear deformation of the core, as shown in
Fig. 19 (b). In addition, the re-entrant cell in the loading region exhibits
Fig. 18. Comparisons of specific energy absorption curves of the sandwich significant shrinkage deformation, indicating a negative Poisson’s ratio
beams with different cell-wall thicknesses of core. effect. Overall, the sandwich beams exhibit similar final deformation
mode under different impact velocities.
RDAH core sandwich beams with different cell-wall thicknesses. It can The comparisons of force–displacement curves of RDAH core sand­
be found that the cell-wall thickness of the core has a significant influ­ wich beams subjected to different impact velocities are shown in Fig. 20.
ence on the bending stiffness and load-carrying capacity of the sandwich It can be found that when v ≥ 15 m/s, the force–displacement curves
beams. With the increase of h, the bending stiffness and load-carrying fluctuate sharply in the initial stage due to inertial effects. As the impact
capacity gradually increase. Due to the different deformation modes of velocity gradually increases, the initial peak force gradually increases.
sandwich beams with different cell-wall thicknesses, the trend of the The comparisons of energy absorption of RDAH core sandwich beams
force–displacement curves is also different. When h < 1.0 mm, due to under different impact velocities when d = 25 mm are shown in Fig. 21.
asymmetric local deformation of RDAH cells near the loading region, the As the impact velocity increases, the total energy absorption of the
force decreases when d = 13 mm and then remains relatively constant. sandwich beam gradually increases.
When h ≥ 1.0 mm, the force–displacement curves exhibit a significant
strengthening stage, where the force gradually increases with the in­ 4.7. Influence of cell configuration of core
crease of displacement. This is because as the loading displacement
continues, the horizontal wall in the loading region bends inward and In order to further reveal the excellent flexural performance of the
contacts with other cell walls, while the lower RDAH cell in the loading sandwich beams with RDAH core, it was compared with the traditional
region contracts laterally, enhancing the load-carrying capacity of the sandwich beams with re-entrant honeycomb (RH) core. The cell-wall
length and re-entrant angle of RH structure are consistent with RDAH

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Fig. 19. Comparisons of deformation modes of the sandwich beams subjected to different impact velocities. (a) d = 5 mm, (b) d = 25 mm.

Fig. 20. Comparisons of force–displacement curves of the sandwich beams subjected to different impact velocities.

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H. Wang et al. Composite Structures 326 (2023) 117606

Fig. 23. Comparisons of deflection distribution of the back face sheet of the
Fig. 21. Comparisons of energy absorption of the sandwich beams subjected to sandwich beams with different cell configurations of core.
different impact velocities (d = 25 mm).

structure. The two types of sandwich beams have the same overall size,
face sheet thickness and relative density of the core.
Fig. 22 shows the comparisons of deformation modes of the sandwich
beams with different cell configurations of core. It is found that RDAH
core sandwich beam and RH core sandwich beam all exhibits overall
bending deformation in the initial stage. During this process, the cell
wall of the core rotates and bends, resulting in shear bands between the
two supporting rollers. As the loading displacement increases, the hor­
izontal wall below the loading roller of the two types of sandwich beams
begins to bend inward, forming a deformation mode of indentation, and
the degree gradually increases with the increase of loading displace­
ment. However, the RDAH core sandwich beam begins to produce
indentation earlier than the RH core sandwich beam. Both types of
sandwich beams exhibit lateral shrinkage deformation of the cells below
the loading roller, exhibiting a significant negative Poisson’s ratio effect.
When d = 22.5 mm, the indentation area of the front face sheet of the
RDAH core sandwich beam is larger than that of the RH core sandwich
beam. The comparisons of deflection distribution of the back face sheet
of the sandwich beams with different cell configurations of core are
Fig. 24. Comparisons of force–displacement curves of the sandwich beams
shown in Fig. 23. At the same loading displacement (d = 25 mm), the
with different cell configurations of core.
mid-span bending deflection of the back face sheet of RDAH core
sandwich beam is smaller than that of RH core sandwich beam.

Fig. 22. Comparisons of deformation modes of the sandwich beams with different cell configurations of core. (a) RDAH core sandwich beam, (b) RH core sand­
wich beam.

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H. Wang et al. Composite Structures 326 (2023) 117606

energy absorption. Increasing impact velocity has a significant influence

on the initial deformation but little influence on the final deformation of
the sandwich beams. As the impact velocity increases, the total energy
absorption of the sandwich beam gradually increases, and the negative
Poisson’s ratio characteristic of the core still exists. Compared with the
traditional re-entrant honeycomb core sandwich beams, RDAH core
sandwich beams have better energy absorption capacity and bending
resistance. This study provides a new strategy for the design and engi­
neering application of the sandwich structures with auxetic honeycomb
core.

CRediT authorship contribution statement

Huiling Wang: Writing – original draft, Investigation, Validation,

Visualization, Data curation. Junhua Shao: Resources. Wei Zhang:
Conceptualization, Methodology, Investigation, Visualization, Writing –
review & editing, Funding acquisition, Project administration. Zhi Yan:
Fig. 25. Comparisons of specific energy absorption curves of the sandwich Investigation, Data curation. Zhengyi Huang: Investigation, Visualiza­
beams with different cell configurations of core. tion, Data curation. Xuan Liang: Resources.

Fig. 24 shows the comparisons of force–displacement curves of the Declaration of Competing Interest
sandwich beams with different cell configurations of core. It can be
found that when d < 8 mm, the force of RDAH core sandwich beam is The authors declare that they have no known competing financial
significantly greater than that of RH core sandwich beam, indicating a interests or personal relationships that could have appeared to influence
greater stiffness of the RDAH core sandwich beam. The load-carrying the work reported in this paper.
capacity of RDAH core sandwich beams experience a decrease after
reaching its peak, while RH core sandwich beams do not. This is mainly Data availability
caused by the obvious indentation of the RDAH core sandwich beam.
Due to the lateral shrinkage deformation of the core and the mutual No data was used for the research described in the article.
contact between the cell walls, the load-carrying capacity of RDAH core
sandwich beam continues to increase after a certain decrease and Acknowledgements
continue to be higher than that of RH core sandwich beam. Fig. 25 shows
the comparisons of the specific energy absorption curves of the two The authors are grateful for financial supports of Project funded by
types of sandwich beams. To ensure that the relative density of the two China Postdoctoral Science Foundation (2021M702537), Natural Sci­
types of cores is the same, the cell wall thickness of RDAH is less than ence Foundation of Hubei Province of China (2021CFB029), Opening
that of RH. Nevertheless, it can be found that the energy absorption of projects of State Key Laboratory of Strength and Vibration of Mechanical
RDAH core sandwich beam is significantly better than that of RH core Structures (Xi’an Jiaotong University, SV2021-KF-23), Hubei Province
sandwich beam. Key Laboratory of Systems Science in Metallurgical Process (Wuhan
University of Science and Technology, Y202204).
5. Conclusion
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