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Article published in
International Journal of Mechanical Sciences, Vol. 251 (2023) 108334
https://doi.org/10.1016/j.ijmecsci.2023.108334
A stretchable sandwich panel metamaterial with auxetic rotating-square
surface
Xing Chi Teng a, Wei Jiang a, Xue Gang Zhang a, Dong Han a, Xi Hai Ni a, Hang Hang Xu a, Jian Hao a, Tong Guo b, Yu Fei
Wu c, Yi Min Xie d, Xin Ren a, *
a Centre for Innovative Structures, College of Civil Engineering, Nanjing Tech University, Nanjing, Jiangsu, 211816, PR China
b Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast University, Nanjing, 211189, China
c Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen University, Shenzhen, 518060, China
d Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, 3001, Australia
* Corresponding author: Xin Ren. Email: xin.ren@njtech.edu.cn
Abstract:
Sandwich panels find use as energy-absorbing devices and protective structures in various fields.
However, due to their mostly rigid surfaces, they might not meet the protection requirements in complex
conditions like non-Euclidean geometries of protected objects. To address this issue, a novel sandwich panel
structure inspired by the synclastic curvature behavior of auxetic metamaterial was proposed. The surface
of the proposed sandwich panel features rotating squares that allow for horizontal stretching, resulting in an
improvement in controllability, auxeticity, flexibility, and synclastic curvature compared to traditional
sandwich panels. Experimental and numerical methods were used to compare the similarities and
differences between the novel and traditional sandwich panels under uniaxial compression. Additionally,
different rotation angles and numbers of unit cells were simulated to examine their mechanical properties.
The study also explored the auxeticity, stretchability, synclastic curvature, and potential applications of the
novel sandwich panel. It was found that appropriate cuts on the sandwich panel can enhance energy
absorption. These findings could pave the way for new opportunities in the application and basic research
of sandwich panels while providing ideas for enhancing the survivability of panel structures in complex
conditions.
Keywords: Rotating square; Auxetic; Sandwich panel; Mechanical metamaterials; Synclastic curvature.
1. Introduction
Metamaterials are a class of new materials emerging from the 21st century [1-4]. Existing
metamaterials include optical metamaterials, electromagnetic metamaterials, acoustic metamaterials,
thermal metamaterials, and mechanical metamaterials [5-13]. Negative Poisson's ratio (NPR) metamaterials,
also known as auxetics, are a branch of mechanical metamaterials [14-16]. Auxetic materials and structures
have some advantages in shear resistance, indentation resistance, fracture resistance, synclastic curvature,
permeability variability, and energy absorption performance [17-23]. Auxetic metamaterials can be further
divided into re-entrant structures [24-34], rotating polygonal structures [35,36], chiral structures [37,38],
perforated plate structures [39-41], auxetic tube structures [42,43], etc. Fig. 1 shows the auxetic behavior of
rotating square structures (one of the rotated polygons). When the entire system is subjected to tension
(compression), the square blocks rotate around the apex, causing structural expansion (shrinkage).
Fig. 1. Auxetic behavior of the rotating square structure.
Due to the simple design and the apparent auxetic effect, the rotating polygon structures become a
potential candidate for further exploration [44,45]. Earlier, Grima et al. [46,47] discussed the potential of
rotating quadrilateral systems composed of rigid rectangles. When a uniaxial load is applied, these rigid
rectangles will rotate, resulting in an auxetic behavior. Alderson et al. [48] deduced an analytical expression
of Poisson's ratio for a tetrahedral model of rotation. It is proposed that the rotating tetrahedral model can
have positive and negative Poisson's ratios, the values of which are determined by the frame geometry and
the relative strength of the two mechanisms. The research also provides design avenues for materials and
structures with ultra-high Young's modulus. Chen et al. [49] studied three lightweight rotating square
structures and gave analytical formulas for Poisson's ratio, Young's modulus, and shear modulus. Inspired
by ancient geometric figures, Ahmad et al. [50] proposed a mechanical metamaterial with a negative
Poisson's ratio and elucidated the main design principles governing the bistable auxetic state. The bistable
structure maintains its shape after unloading. Later, with the development of additive manufacturing
technology [51,52], more properties of rotating polygons were studied and applied. Jang et al. [53] designed
a meta-display using the large stretchability and high deformation uniformity of the rotating square. Such
displays can be stretched without image distortion. Chen et al. [54] proposed a new method to enhance the
performance of auxetic nonlinear piezoelectric energy harvesting by increasing the unit cell number of the
auxetic structure. Sorrentino et al. [55] investigated the mechanical response of bio-inspired titanium
mechanical metamaterials with NPR evolved from rotating squares. The work confirms the great potential
of biologically inspired auxetic metamaterials, which can be designed to obtain tailored mechanical
properties while improving the elastic strain capabilities of the system. Inspired by snake skin, Jiang et al.
[56] proposed a novel E-armor, which not only has mechanical flexibility and electronic functions similar
to electronic skin, but also can protect itself and the underlying soft body from external physical damage.
Czajkowski et al. [57] demonstrated that the low-energy deformation of engineered intumescent
metamaterials would be governed by scalar field theory. The non-uniform, nonlinear deformations observed
under general loading correspond to conformal maps that have been studied.
The traditional sandwich panels consist of two layers of profiled surface and an inner core in the middle
of the panels [58,59]. The common surface materials are plywood, fiberboard, plastic board, and metal sheet.
Core materials include balsa wood, rubber, acetate, plastic, and resin-impregnated (or non-impregnated)
paper or cloth and metal materials [60,61]. Through numerical and experimental studies, Yan et al. [62]
demonstrated the good ballistic impact performance of auxetic honeycomb sandwich panels (AHSPs)
fabricated from carbon fiber reinforced polymers (CFRP). Pelinski et al. [63] carried out three-point bending
tests on beams made of plywood, high-density fiberboards, cardboard, and wood epoxy. The results illustrate
the influence of the thickness on the stiffness, strength, energy absorption, and dissipation of sandwich
beams with an auxetic core. Hu et al. [64] developed a thermodynamic analysis model to describe the
thermal shock behavior of ceramic sandwich structures (CSSs). The transient temperature distribution and
associated thermal stress field under thermal shock are determined. Usta et al. [65] described the low-
velocity impact behavior of composite sandwich panels with different types of auxetic structures and non-
auxetic prismatic core structures. Juliette et al. [66] fabricated an acoustic sandwich panel with a wide range
of sound-absorbing properties. The designs developed in this work will help improve additive
manufacturing processes for multifunctional structures for aerospace applications. Li et al. [67] developed
an ultralight sandwich structure with thin ceramic matrix composite panels combined with thick insulation
as an integrated thermal protection system (ITPS) structure to protect the substructure of a hypersonic
vehicle.
Although the performance of sandwich panels with different cores has been extensively studied,
research on the surface of sandwich panels is still in its infancy [68-71]. Likewise, auxetic rotating squares
metamaterials have been studied by a large number of scholars, but most of them are two-dimensional
structures, and the performance of out-of-plane compression is usually forgotten. Inspired by auxetic
metamaterials with synclastic curvature, a novel sandwich panel structure is proposed. As energy-absorbing
protective structures, the proposed sandwich panels enable the protected objects with non-Euclidean
geometry surfaces that are inaccessible with ordinary sandwich panels. In this paper, the rotating square
metastructure is used as the surface to realize a sandwich panel structure that can be stretched horizontally.
Compared with traditional sandwich panels, the novel sandwich panel has a qualitative improvement in
terms of stretchability, auxeticity, flexibility, and synclastic curvature. The similarities and differences
between the novel sandwich panel (NSP) and the traditional sandwich panel (TSP) under uniaxial
compression are compared experimentally and numerically. After that, to study their mechanical properties,
the rotating square sandwich panels with different rotation angles and different numbers of elements are
discussed. Finally, the auxeticity, stretchability, and synclastic curvature of the novel sandwich panel are
studied and analyzed, and some potential applications for the new sandwich panel are stated briefly.
2. Design methodology and experiment
A series of stretchable sandwich panel metamaterials with different angles were fabricated using 3D
printing technology after the detailed geometrical design. For investigating their mechanical properties
under compression, quasi-static compression load was applied for the experiment.
2.1 Structural design
The geometrical design and modeling of the proposed structure were conducted using modeling
software Rhino. The rotating square is designed as the surface, and the re-entrant hexagonal honeycomb is
designed as the core. Fig. 2 is the overall design of the novel sandwich panel (NSP). As shown in Fig. 2(c),
the shape of the rotated square panel is uniquely determined by the square side length , the connector side
length , and the rotation angle . Then, the length of the space occupied by the surface, equivalent
Poisson's ratio , and the area of rotating square can be expressed by the following four formulas
respectively:
(1)
(2)
(3)
Where , n is the cell number of each side.
As shown in Fig. 2(b), two orthogonal lateral re-entrant bars of the hexagonal honeycomb structure
serve as the core of the sandwich panel. The combination of core and surface produces deformations similar
to re-entrant honeycombs. The height , thickness , and re-entrant angle are used to determine its
shape.
The relative density of the unit cell structure (2 2) is defined as the ratio of the cellular volume to
the total volume of the space where it is located, which can be expressed as:
(4)
In our previous work, the re-entrant structure of the core structure has been studied, which is a high-
quality energy-absorbing structure [72]. And the focus of this paper is on the effect of rotating square surface
on the novel sandwich panel. Therefore, uniform geometrical parameters are adopted by the core. In this
work, the height of the core is , the thickness is , and the re-entrant angle is .
Fig. 2. (a) The novel sandwich panel (NSP) with a rotation angle of (local transparency is for
demonstrating the inner structures). The design parameters of (b) the unit cell, and (c) rotating square
surfaces.
2.2 Fabrication of the novel sandwich panel
To ensure the accuracy of the experimental data, novel sandwich panels (NSP) with different angles
were produced instead of stretching to change the rotation angle and then reuse the specimens. As shown in
Fig. 3, 3D printing technology was used to manufacture the traditional sandwich panel (TSP) and novel
sandwich panels with rotation angles of 0 and 45 , respectively. The geometric parameters of the
specimens are in Table 1.
The specimens were fabricated by the HS403P printer (Hunan Farsoon High-Technology Ltd. China),
which is a high-resolution 3D printer with a resolution of 0.06 mm. The laser system and power supply
requirements are respectively CO laser and 380V, 50/60 Hz, 15 KVA. Selective laser sintering (SLS) used
in printing, which makes the structure basically isotropic. The material of the print is thermoplastic
polyurethane powder, and the sintering temperature is 190 °C.
Fig. 3. The 3D printed models of (a) traditional sandwich panel, (b) novel sandwich panel with a rotation
angle of 0, and (c) novel sandwich panel with a rotation angle of 45. The scale bar is 10 mm.
Table 1.
Geometric parameters of the surface.
Models
Direct design parameters (mm)
Calculated parameters
l
d
TSP
2
2
40
0.23
NSP-1
2
2
0
42.00
0.21
NSP-2
2
2
58.57
0.11
2.3 Uniaxial compression experiments
Material and structural properties were determined through uniaxial tensile and compression
experiments conducted on the specimens. The experimental setup is shown in Fig. 4. The material properties
of the experimental panels were obtained by uniaxial tensile tests of standard dumbbell-shaped specimens.
Five TPU standard dumbbell-shaped tensile test specimens were made and tested at the speed of 100
mm/min according to ISO 37:2017 “International standard rubber, vulcanized or thermoplastic-
determination of tensile stress-strain properties” standard. The test of uniaxial tension and sandwich panel
compression was performed using a universal testing machine (WANCE ETM-104 B, China) with a
measuring range of 20 kN and a maximum error of the test force indication value less than 0.5. In
uniaxial compression experiments, the compression rate of sandwich panels was set to 1 mm/min which is
corresponding to the quasi-static compression process. Fig. 4(d) is the stress-strain curve of the TPU
specimen. According to the data obtained from the test of specimens, the verification and parameter analysis
of the finite element model can be carried out.
Fig. 4. (a) Experimental setup for testing the 3D-printed specimens. (b) Standard dumbbell tensile specimens
and (c) Tensile tests for TPU specimens. (d) Stress-strain curves of the TPU standard dumbbell specimens.
3. Finite element analyses and results
Finite element simulations were used to model the structures in the experiment and the results were
found to match the experimental outcomes. In order to explore the influence of design parameters on the
structure, novel sandwich panel (NSP) structures with different surface types are studied.
3.1 Finite element (FE) modeling and FE model validation
The modeling software Rhino was used for the creation of the model, and the commercial finite element
software Abaqus/Explicit was used for the numerical simulation. Fig. 5 is the FE model of the NSP with a
rotation angle of 0°. For the mesh properties, hexahedron linear solid elements composed of 8 nodes with
reduced integration (C3D8R) were adopted. After convergence analysis of meshes, the size of 0.5 mm was
selected, which can take into account the accuracy and efficiency of simulation calculations. The interaction
between the structures was defined by general contact. The mechanical material model used to build the
FEM analysis was set to hyperelastic. Then, the mass density and Poisson’s ratio were set to 1.11 g/cm3 and
0.45, respectively. In addition, the uniform and isotropic material distribution was set in Abaqus. The strain
energy potential is “Mooney-Rivlin” with the input source of the test data of uniaxial compression. Finally,
in order to simulate a more accurate stress-strain curve, the strain energy potential order was set to 2. The
sandwich panels are compressed between two discrete rigid bodies. The bottom discrete rigid body is fixed,
while the top rigid body moves down with a smooth analysis step of 20 mm in 1 second. The target time
increment in quality scaling was set to to improve the efficiency of computer calculation.
Fig. 5. The finite element model of the novel sandwich panel with a rotation angle of .
The experiment was simulated and verified, and the comparison between the result of the finite element
method and the experiments is shown in Fig. 6. By comparing the experimental results, it can be seen that
the numerical results are in good agreement with the experimental results. However, 3D-printed specimens
have subtle differences from FEM in terms of contact characteristics, material parameters, boundary
conditions, etc. Errors in the experimental process and flaws in printing technology led to lower
experimental data. In addition, some uncertain cracks in the 3D printed specimens lead to lower load and
faster compaction. In general, the error is within an acceptable range, and the FE simulation can be used to
study the designed structure.
Fig. 6(d) is the space occupied by the surface of these three kinds of sandwich panels. The area
increases as the rotation angle increases (0 45). The surface area of NSP can be 1.86 times that
of TSP. This shows that the NSP can adjust and control the space area arbitrarily within a certain range while
maintaining the load. Under uniaxial compression, the bearing capacity of the sandwich panel depends on
the number of core elements, and has little relationship with the form of the surface. Compared with the
fixed and single TSP, the adjustable NSP increases the application scope of the sandwich panel.
Fig. 6. The load-displacement curves of (a) traditional sandwich panel, (b) novel sandwich panel with a
rotation angle of , and (c) novel sandwich panel with a rotation angle of . (d) The surface area of the
three sandwich panels.
3.2 Energy absorption capacity and densification point
The sandwich panel is a lightweight structure with load-bearing and energy-absorbing properties.
Energy absorption (EA) is an important energy absorption indicator for sandwich panels, which is defined
by the following:
(5)
Where is the displacement during compression, and is the load under compression.
The displacement of the refers to the effective EA phase, that is, the phase preceding the
densification phase. The displacement of the densification point is determined by the displacement of
the energy efficiency peak point, as the following formula:
, (6)
Where is the stress value corresponding to instantaneous strain . The densification strain is
available through maximum energy absorption efficiency.
For different structures that are not of the same weight, it is unfair to compare only their total energy
absorption. Their energy absorption capacity is also affected by relative density. Therefore, specific energy
absorption (SEA) is calculated and defined as the ratio of energy absorption per unit mass (m):
(7)
Fig. 7 shows the EA and SEA of the sandwich panels under different strains in the experiment. As the
quality of sandwich panels is similar, their EA and SEA have the same trend according to the formula. EA
and SEA are two important indicators to reflect the performance of the sandwich panel structure. The
following part of the parametric analysis will study the influence of different design parameters of the
surface on the load-displacement curve, energy absorption, and specific energy absorption.
Fig. 7. (a) EA-strain histogram and (b) SEA-strain histogram of the experimental specimens.
3.3 Parametric analysis
In this section, novel sandwich panel (NSP) structures with different surface types are studied. The
study concludes that changing the rotation angle of sandwich panels does not affect their bearing capacity
and energy absorption, allowing for flexible adjustments in surface area.
Fig. 8(a) is the sandwich panel (6 × 6) with different angles, and their load-displacement curves, total
EA, and SEA are shown in Fig. 8(b). The values of EA and SEA are the data when the displacement reaches
10 mm. At this point, the structure reaches the dense stage and the stress begins to rise rapidly. Overall, their
load-displacement curves, EA and SEA are not much different. When the displacement is 6 mm, the core
layers of the sandwich panel are in contact with each other, and the stress rises faster. When the displacement
is about 8 mm, the curve drops sharply as the ligaments of the core layer buckle. Fig. 8(c) is the deformation
buckling mode of the core layer (section view in Y direction). The buckling is due to the random dislocation
of the core members. According to the numerical data, the load-displacement curves of NSP with different
angles are very close. This again confirms that changing the rotation angle will not change the core layer
that affects the bearing capacity. Compared with NSP, TSP has higher stress under the same displacement.
The surface of the TSP is a whole, and the NSPs are connected by hinges. When the core buckles and
deforms, the whole structure will not buckle. The parametric study of the rotation angle shows that changing
the rotation angle will not bring down the bearing capacity and energy absorption. This means that the
structure can adjust the surface area as much as needed without losing the energy absorption.
Fig. 8. (a) The sandwich panels (6 × 6) with different angles and (b) their load-displacement curves, EA and
SEA at the displacement of 10 mm. (c) The buckling of the core layer occurs due to random dislocation at
the displacement of 8 mm. The circled place is the steep drop position of the curve corresponding to the
buckling of the structure.
Then, the number of rotatable unit cells is studied parametrically. The different number of core lattices
under each rotating square platen is designed by changing the size of the surface.
As shown in Fig. 9, all NSPs have 36 core lattices, while the numbers of rotating squares on the surface
are 4, 9, and 36 respectively. Fig. 9 (b) is the results of mechanical properties. The NSP with 36 rotating
squares has the lowest bearing capacity, followed by the single TSP structure, and the bearing capacity of 4
and 9 rotating squares is the highest. The EA and SEA also have the same trend. As shown in Fig. 9(c), all
cells under the same rotating square have the same tendency to rotate. The 36 cells of the TSP have the same
rotation trend (clockwise), and the structure will have a twisting effect. The NSP with 4 and 9 rotating
squares weakens the torsional effect. The reason is that the adjacent rotating squares have opposite rotating
tendencies, keeping the entire structure in balance. The stability of each unit of the NSP with 36 rotating
squares is relatively poor, and the unit itself twists randomly. Thus, the whole structure produces an uncertain
torsion effect.
As shown in the load-displacement curve in Fig. 9(b), the bearing capacity of the NSP structure is
higher than that of the TSP structure. Just like tiling tiles, expansion joints are reserved between each tile to
reduce damage. For traditional sandwich panels, this may provide a new idea to reduce the buckling effect
and increase the service life.
Fig. 9. (a) The sandwich panels with different numbers of rotating squares and (b) their load-displacement
curves, EA and SEA at the displacement of 10 mm. (c) The torsional effects of stress contours due to random
dislocation of the core (Top view). The red curve illustrates the concentration of force on the structure, and
the curved arrows indicate the rotation trend of the structure.
4. Result and discussion
Compared with the traditional panels, the novel ones have the characteristics of auxeticity, synclastic
curvature, and conformability. In this section, these desirable characteristics of the NSP structure are also
carefully considered and discussed.
4.1 In-plane auxetic behavior
The in-plane deformation ability of sandwich panel structures is overlooked by most scholars. The in-
plane negative Poisson's ratio characteristics of the novel sandwich panels are explored here. The NSP (6 ×
6) was built to explore the in-plane auxetic behavior and stability. As shown in Fig. 10, the sandwich panels
are compressed between two discrete rigid bodies. The bottom discrete rigid body is fixed, while the top
rigid body moves down with a smooth analysis step of 45 mm in 1 second. The target time increment in
quality scaling was set to to improve the efficiency of computer calculation.
The in-plane compressive stress distribution and load-displacement curve of the NSP structure with a
rotation angle of 30 are shown in Fig. 10 and Fig. 11. Due to the unique deformation mechanism of the
rotated quadrilateral, the lateral direction shrinks inward under compression. A pronounced auxetic effect is
manifested by the compression of the NSP. When the structure is compressed in the plane, the auxetic
deformation mode occurs step by step from bottom to top. This is the reason for the multiple peaks in the
curve and the steep drop after the peaks (Fig. 11). After compaction, the rotating square will be staggered
out of the plane, causing the curve to fluctuate violently. The NSP can stably undergo gradual deformation
without buckling in-plane or out-plane. The connecting hinge is the main stress location during deformation.
The load remains at a relatively constant value throughout the in-plane compression of the structure.
The strength of the connecting rod determines the amount of force required for deformation. That is to say,
in-plane tension and compression of the sandwich panel can be easily accomplished if soft hinges or other
freely rotatable connecting rods are used.
Fig. 10. The stress distribution of the NSP under in-plane compression reveals the stress concentration in
connecting hinges.
Fig. 11. Load-displacement curve of the NSP under in-plane compression.
4.2 Synclastic curvature
Synclastic curvature refers to the type of curvature where the surface or object curves in the same
direction on both sides of a plane or axis. An example of synclastic curvature is the surface of a sphere. The
2D rotating polygon has synclastic curvature behavior, which shows excellent fit ability, so the synclastic
curvature of NSP is studied. As shown in Fig. 12(a), the non-auxetic plate exhibits a saddle-shaped response
under bending, while the response of the auxetic plate is dome-shaped. Fig. 12(b) shows a bending test of
the NSP made by additive manufacturing technology. The actual shooting explained the synclastic curvature
is also exhibited by the NSP (domed deformation).
Uniquely, the synclastic curvature of NSP is completed by the cooperation of the upper and lower
surfaces. When the rotating squares on the bottom surface shrink inward and the rotating squares on the top
surface stretch outward, the whole structure will naturally exhibit obvious synclastic curvature. In Fig. 12(c)
and (d), the simulation of NSP compressed by a sphere is conducted. The simulation is to determine the
performance of the NSP when the structure is partially in contact with irregular objects. In the simulation,
the displacement of the four sides of the NSP (6 6) is fixed, and a rigid sphere is set to move along the
negative direction of the Z axis at a speed of 50 mm/s. The size of the sandwich panel unit is 20 mm and the
diameter of the rigid ball is 50 mm.
When subjected to local loads, NSP exhibits synclastic curvature. The height of the core layer of the
sandwich panel decreases, while the rotation angle increases. During the whole process, the lower
hemispherical surface is attached to the top surface of the NSP. The load-displacement curves for this case
show that the local reaction force of the TSP is much higher. Even under local loads, TSP is the deformation
of the structure as a whole. While the NSP structure has better flexibility, and only part of the structure is
deformed. Fig.13 is the load-displacement curves of the finite element for uniaxial compression. Compared
with the high load of TSP, the bearing capacity of NSP under the same displacement is lower. The synclastic
curvature and local low reaction force of the NSP structure may be a potential application (such as wearable
devices and soft robots). Using this property, the structure can better fit the joint and move with less binding
force.
Fig. 12. (a) Deformation pattern of non-auxetic and auxetic materials under out-of-plane bending. (b) The
top view and side view of a novel sandwich panel under out-of-plane bending. (c) The simulation of novel
sandwich panels compressed by a sphere. (The four sides of the novel sandwich panel are fixed.) (d) The
stress legend from a side view of the deformation response.
Fig. 13. The finite element analysis results of sandwich panels compressed by a sphere under uniaxial
compression.
4.3 Biomimetic shape adaptability
Some experiments with spheroids passing through the auxetic rotating square tube were conducted to
imitate the wriggling of snakeskin [56]. The novel sandwich panel structure is also transformed into a tubular
structure by way of coordinate transformation, as shown in Fig. 14(a). In addition to being able to travel
through all kinds of bad environments, snakes can swallow food thicker than themselves when eating. Then,
the performance and deformation response of the novel tubular structure under this working condition is
also worth studying.
Fig. 14(b) is the experiment performed using a universal testing machine. The sphere is made of
stainless steel and has a diameter of 60 mm. This sphere is customized made and fixed to the test machine
indenter to obtain the resistance of the sphere as it passes through the tube. The outer diameter of the tube
is 80 mm, and the inner diameter is 40 mm. Fig. 15 is the load-displacement curve. The load ramps up to
the first stress peak as the sphere begins to enter the tube. As the sphere continues downward, the curve
behaves like a wave. The lowest point of each wave segment means the movement of the sphere to the seam
of the rotating square. Throughout the process, the sphere moves with a relatively uniform force. When the
tube swallows a sphere with 1.5 times its internal diameter, it shows local expansion. The middle core
structure is compressed to absorb external energy, and the outer tube is less deformed. If it is used as a
transportation pipe, wearable device, electronic component housing, or esophageal stent, the tube could pass
through objects larger than the inner diameter and can play a protective role.
Compared with TSP which can only be compressed vertically, NSP has flexibility, synclastic curvature,
and conformability. Flexibility and auxeticity can prevent sandwich panels from unnecessary rigid damage.
And during transportation and application, the space occupied by the sandwich panel can be adjusted as
needed. In addition, synclastic is an excellent property in practical engineering applications. The domed
deformation can fit the ground or protected objects and adapt to different conditions better than TSP. If it is
integrated with medical and electronic optics, it may be used in wearables, light therapy, and load-resistant
displays [56].
Fig. 14. (a) Schematic legend and size parameters of the simulated sphere passing through the tube. The
outer diameter of the tube , and the inner diameter . The diameter of the sphere
60 mm. (b) The setup of the experiment to imitate the wriggling of snakeskin.
Fig. 15. The load-displacement curve of the tubular structure in the shape adaptability experiment.
5. Conclusion
This study introduces a novel concept of stretchable sandwich panels that significantly improves the
mechanical properties of conventional sandwich panels, rendering them suitable for applications being
required large deformability and flexibility. The proposed sandwich panels exhibit synclastic curvature,
auxetic behavior, and great conformability, while maintaining the bearing capacity of traditional sandwich
panels.
According to experimental and finite element simulation results, appropriately cutting the face panels
of sandwich panels can enhance their energy absorption capacity and specific energy absorption capacity.
In addition, the novel sandwich panel (NSP) combines the functions of sandwich panels and rotating square
structures, thus retaining the auxeticity and synclastic curvature similar to rotating square structures.
However, the synclastic of NSP is completed by the cooperation of double-layer surfaces. This work is a
preliminary exploration, and there is potential for further investigation into more properties of the proposed
sandwich panels. The structure can be further optimized in materials, hinges, and other places. Soft materials,
plastic materials, or rotational axis designs can be used as hinges to make the structure deform more
smoothly, without spring back or instability. Stiffer materials can be used for panels and core structures to
increase protection. The reasonable selection of surface and core materials can effectively meet the
performance requirements of pre-designed panels.
However, the sandwich panel with rotating squares has some limitations. A unique design is required
for the connecting hinge, which is the main location of force and deformation during in-plane tension. The
core needs to be an auxetic lattice structure to match the overall auxeticity and flexibility. Overcoming these
limitations may open up broad application prospects for the NSP in the field of soft robots that require
flexible activities and protection engineering that requires anti-collision and energy absorption.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (grant numbers
51978330, 51808286); Qing Lan Project of Jiangsu Province; Natural Science Foundation of Jiangsu
Province (grant number BK20220103); Postgraduate Research & Practice Innovation Program of Jiangsu
Province (grant number KYCX22_1325). The authors would like to thank Mr. Yi Zhang for his support in
this work.
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