Archives of Civil and Mechanical Engineering (2020) 20:89

https://doi.org/10.1007/s43452-020-00095-1

ORIGINAL ARTICLE

Mechanical performances of metal‑polymer sandwich structures

with 3D‑printed lattice cores subjected to bending load
Zhaobing Liu1,2,3 · Hantang Chen1 · Shuaiqi Xing1

Received: 25 March 2020 / Revised: 6 July 2020 / Accepted: 13 July 2020

© Wroclaw University of Science and Technology 2020

Abstract
In this article, we propose a new class of metal-polymer architected sandwich structures that exhibit different mechanical
behaviors. These lightweight sandwich structures have been made of aluminum face sheets and 3D-printed lattice cores with
2D (Bi-grid, Tri-grid, Quadri-grid and Kagome-grid) and 3D (face-centered cubic-like and body-centered cubic-like) topolo-
gies. Finite element simulation and experimental tests were carried out to evaluate mechanical performances of the proposed
sandwich structures under quasi-static three-point bending load. Specifically, the damage-tolerant capability, energy absorp-
tion and failure mechanisms of these sandwich structures were investigated and evaluated through a combination of analytical,
numerical and experimental methods. It is found that sandwich structures with 3D face and body-centered cubic-like cores can
provide more excellent flexural stiffness, strength and energy absorption performance. These enhanced mechanical features
could be further explained by a so-called ‘Stress Propagation’ mechanism through finite element analysis (FEA) that can
facilitate sandwich structures with 3D cores, especially body-centered cubic-like one, to transfer bending loads from central
lattice units across neighboring ones more efficiently than 2D cores. Furthermore, core cracking is the main failure mode
for the proposed sandwich structures, which is primarily caused and dominated by bending-induced tensile stress followed
by shear stress. It is worth mentioning that our findings provide new insights into the design of novel lightweight sandwich
composites with tailored mechanical properties, which can benefit a wide variety of high-performance applications.

Keywords Sandwich structures · 3D printing · Lattice cores · Failure mechanism · Energy absorption

1 Introduction compression and shear loads, and with solid face sheets that
can carry in-plane and bending loads. In order to achieve
Lightweight sandwich structures assembled by face sheets the optimal performance, many studies have been conducted
and various cores are extensively used in aerospace, trans- concerning the effects of geometrical parameters (length,
port, civil and military sectors as they can offer excellent width and thickness) [6, 10, 11, 15], mass (relative density)
multifunctional properties such as high stiffness/strength- [13, 25], properties of materials used to construct face sheets
to-weight ratio, good thermal insulation and high energy- and the core [3, 25], and core topology [12, 22], of which
absorption capabilities [1, 2]. The mechanical performances the effect of core topology could be the most important
of lightweight sandwich structures can be enhanced and one. Among all possible core topologies, sandwich struc-
optimized with well-designed cores that can carry flexural, tures with closed-cell foam cores [3–8] and 2D honeycomb
cores [9–14] have been extensively studied in terms of their
mechanical properties as they are stiff and lightweight, and
* Zhaobing Liu
zhaobingliu@whut.edu.cn; zhaobingliu@hotmail.com have excellent energy absorption performance in applica-
tions. For example, the deformation and failure modes of
1
School of Mechanical and Electronic Engineering, Wuhan sandwich beams with foam materials like PVC [3, 4] and
University of Technology, Wuhan 430070, China aluminum [5–8] were systematically analyzed under bending
2
Hubei Digital Manufacturing Key Laboratory, Wuhan and/or impact loads. Pan et al. [9] investigated the trans-
University of Technology, Wuhan 430070, China verse shear mechanical behavior and corresponding failure
3
Institute of Advanced Materials and Manufacturing of aluminum honeycomb cores. Experimental and numeri-
Technology, Wuhan University of Technology, cal study were performed on honeycomb sandwich panels
Wuhan 430070, China

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 89 Page 2 of 17 Archives of Civil and Mechanical Engineering (2020) 20:89

under bending and in-panel compression [10]. The effects of 3D lattice topologies have been created over the last few
several key structural parameters on crashworthiness char- years [20–26]. For example, Jin et al. [22] investigated the
acteristics and collapse mechanism were explored. He et al. failure and energy absorption characteristics of four lattice
[11] analyzed the low-velocity impact behavior of aluminum structures that were manufactured by selective laser melting
honeycomb sandwich structures with CFRP face sheets tak- (SLM) under dynamic loading. The effects of cell topol-
ing into the effect of structural parameters. Mechanical per- ogy and relative density on the dynamic behavior of these
formances of sandwich beams with four 3D-printed poly- structures were studied through a combination of experi-
mer honeycomb cores were analyzed using finite element mental tests and numerical simulation. Sandwich panel
method [12]. Wang et al. [13] studied the strength, stiff- with an auxetic (i.e. exhibiting negative Poisson’s ratio) lat-
ness, and panel peeling strength of carbon fiber-reinforced tice core using wood composites and 3D print technology
composite sandwich structures with aluminum honeycomb was proposed in [23]. The mechanical strengths and failure
cores by three-point bending tests. The effects of the core mechanisms under bending load were estimated experi-
material thickness and density on the material properties of mentally, analytically and numerically. A full mechanical
composite sandwich honeycomb structures were evaluated. characterization of three types of 3-D printed lattice cores
A kind of innovative honeycomb sandwich with ceramic was performed to evaluate the feasibility of using additive
tile (ceramic sandwich) was proposed in [14]. The bending manufacturing (AM) of lightweight polymer-based sand-
behavior was analyzed using FEA. It was concluded that the wich panels for structural applications [24]. Effects of the
bending performance heavily relies on the geometric con- geometry of the three lattice structures on the compression,
figuration of the sandwich panel. shear and bending strength has been experimentally inves-
Although foam and honeycomb cellular materials have tigated. Li and Wang [25] designed a new class of sandwich
achieved wide applications, their weakness cannot be structures that were made of 3D printed core materials with
ignored. For instance, honeycomb cores are highly aniso- truss, conventional honeycomb, and re-entrant honeycomb
tropic and exhibit very little strength and stiffness in the topologies. They concluded that the sandwich composites
lateral directions [2]. Besides, due to gas retention and mois- with re-entrant honeycomb core exhibit a sequential snap-
ture trapping, foam cores with closed-cell architecture usu- through instability, which significantly enhances the energy
ally suffers from the problems such as weight increase and absorption abilities. Sarvestani et al. [26] introduced a new
gravity center shift [26]. To eliminate the above-mentioned class of lightweight and 3D printable architected sandwich
drawbacks of closed-cell architecture, cores with open-cell structures. Their failure mechanism, energy absorption and
architecture are of growing interest since they have multifari- multi-hit capability were investigated through analytical,
ous cell structures and high porosity, and can significantly numerical and experimental methods. Moreover, inspired
increase the buckling resistance and energy absorption capa- by crystal microstructure in nature, optimized topology of
bility of sandwich structures when compared to regular foam architected materials would be realized with 3D printing
and 2D honeycomb cores. Liu and Schaedler [15] carried [27]. Hardening mechanisms found in crystalline materi-
out a comprehensive modeling and numerical study on the als were utilized to develop robust and damage-tolerant 3D
quasi-static crush behavior and energy absorption of hol- metamaterials.
low tube microlattice. Liu et al. [16] developed an analytical In the present work, we aim to introduce a new class of
model to predict the collapse strength and strain of multi- metal-polymer architected sandwich structures with six dif-
layer BCC lattice structures. Bending behavior of composite ferent 3D-printed lattice cores, e.g. 2D (Bi-grid, Tri-grid,
sandwich structures with graded corrugated truss cores were Quadri-grid and Kagome-grid) and 3D (Face-centered
investigated in [17, 18]. Failure modes and critical loads for cubic-like and Body-centered cubic-like) topologies. The
corrugated sandwich structure under three-point bending in characteristics of the proposed hybrid sandwich structures
both longitudinal and transverse direction were analyzed. include: (i) varied lattice core topologies from 2 to 3D.
Hwang et al. [19] developed a pyramidal Kagome (PK) Especially for 3D cores, the design ideas are inspired by the
structure to strengthen the sandwich structure. The bending basic crystal microstructure of metals and alloys, which are
deformation modes of the SCC-based PK sandwich structure expected to obtain enhanced mechanical properties; (ii) 3D
were investigated. printing to manufacture the lattice cores. It offers a robust
However, although the 3D cellular cores have attracting manufacturing process for controlling the architecture and
excellent performances, the complexity in spatial cellular geometrical features of complex core structures; (iii) the
core structure makes it difficult to be manufactured with con- choice of materials for face sheet and lattice cores. The alu-
ventional fabricating methods. The recent advances of 3D minum alloy was chosen as face sheet material, which is the
printing or additive manufacturing (AM) technologies have main structural material widely used in different industrial
enabled fabrication of cellular materials with more complex sectors [10]. For lattice cores, Somos GP Plus resin was
architectures, and many novel architected materials with used. It is noted that parts produced with Somos GP Plus

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resin are durable, accurate and water and moisture resist- dimensions of 160 mm × 40 mm × 10 mm. Geometric param-
ant, which is ideal for functional prototypes, concept models eters of sandwich structures are presented in Table 1.
and low volume production parts. In this study, we combine The proposed lattice cores were fabricated using a ste-
these two materials together to provide a solution for fast reolithography (SLA) 3D printer (UnionTech RS6000) with
and low-cost manufacture of metal-polymer sandwich struc- a low-viscosity stereolithography resin (­ Somos® GP Plus
tures while ensuring proper functionality. The mechanical 14122). The mechanical properties of the used resin were
performances including damage-tolerant, energy absorp- obtained by following the ASTM standard D638 and D790.
tion capabilities and failure mechanism under three-point In order to eliminate the influence of anisotropic nature of
bending tests were investigated and compared to target the 3D printing technology on the mechanical properties of
metal-polymer hybrid sandwich structure with relatively the material, all the core specimens were printed under the
higher performance. Analytical, FEA and experimental same printing parameters, such as the same orientation, layer
methods are comprehensively implemented to identify the thickness (0.1 mm) and scanning speed (8 m/s). The face
failure modes. “Stress Propagation” mechanism has been sheet is aluminum alloy (AA) 1060-O with a thickness of
proposed to explain the underlying differences of mechani- 1.0 mm. The sandwich structures were made by gluing two
cal responses among the proposed sandwich structures. The AA1060-O face sheets and one core together with adhesive
investigation is expected to provide some fundamental data (3M Scotch-Grip 1357). Before bonding, the surfaces of face
and design guide for a more efficient metal-polymer hybrid sheets and cores were polished slightly. After bonding, they
sandwich structure with lighter weight and higher damage- were kept under moderate pressure and dried for one day to
tolerant capacity of protection applications such as in auto- make sure adhesion with high quality between the core and
mobile and building sectors. face sheets. The basic mechanical properties of face sheet
The rest of this article is organized as follows. Section 2 and core are provided in Table 2.
introduces the materials and experimental method. Ana-
lytical models and corresponding failure mode examination 2.3 Three‑point bending tests
methods are presented in Sect. 3. Finite element modeling
has been developed in Sect. 4. Section 5 presents and dis- Three-point bending tests were performed in a universal
cusses the results. Conclusions are summarized in the last testing machine (Model: DNS-100, Sinotest Equipment
section. Co., Ltd.) with a maximum load of 100 kN. The transverse
quasi-static load was applied by a central roller with 15 mm
diameter. The support span length between two outer cylin-
drical rollers was 80 mm. The data acquisition rate for tests
2 Materials and experiments
was set as 10 Hz for loads and displacements. According to
GB-T1456-2005, the sandwich samples were loaded up to
2.1 Lattice core design
material failure at a displacement rate of 2 mm/min with a
preload of 5 N.
In this study, six types of sandwich lattice cores were
designed as shown in Fig. 1, which can be categorized
3 Analytical models and failure modes
into two groups: (i) 2D lattice structures (Bi-grid (B-grid),
of sandwich structures
Tri-grid (T-grid), Quadri-grid (Q-grid) and Kagome-grid
(K-grid)); (ii) 3D lattice structures (face-centered cubic-like
3.1 Prediction of flexural stiffness
(FCC) and body-centered cubic-like (BCC)). It is noted that
the designed 3D lattice structures are inspired by the basic
In this section, an analytical model for flexural stiffness is
crystal microstructure of metals and alloys and mimicked on
presented [3, 5, 7, 25]. The total deflection 𝛿 of the sandwich
a macroscopic scale by constructing a lattice unit cell that
structure under a load P is the sum of bending deflection 𝛿b
consists of an ordered arrangement of nodes (analogous to
and shear deflection 𝛿s , which can be expressed as:
atoms) connected by struts (equivalent to atomic bonds) with
a specific recurring arrangement over a volumetric region. Pl3 Pl
This kind of design is expected to obtain enhanced mechani- 𝛿 = 𝛿b + 𝛿 s = + , (1)
48(EI)eq 4(AG)eq
cal properties, which is originally discussed in [27].
where the equivalent flexural rigidity (EI)eq and the equiva-
lent shear rigidity (AG)eq are defined as:
2.2 Fabrication of sandwich structures
Ef wt3f Ec wt3c Ef wtf (tf + tc )2
The sandwich structure consists of two aluminum face (EI)eq = + + , (2)
6 12 2
sheets and a lattice core as shown in Fig. 2, which has overall

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Fig. 1  Lattice core topologies and dimensions

Fig. 2  The proposed sandwich

structures w B-grid

l T-grid
Aluminum Face
Sheets Q-grid

K-grid
tf tc
FCC
BCC

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Table 1  Geometric parameters of sandwich structures (unit: mm)

Geometry Length (l) Width (w) Total thickness (tT) Core thickness (tc) Face sheet thickness (tf) Span length (ls)

Sandwich beams 160 40 10 8 1 80

Table 2  Basic mechanical Properties Face-sheet (AA1060-O) Core material

properties of face sheet and core ­(Somos® GP Plus
material 14122)

Young’s modulus (GPa) 50 2.51

Tensile yield strength (or flexural) (MPa) 110 (86) 37.0 (67.3)
Ultimate yield strength (MPa) 138.3 –
Elongation at break 21% 7.5%
Poisson’s ratio 0.33 0.41
Material density (g/cm3) 2.70 1.16

w(tf + tc )2 Gc 3.2.1 Face‑sheet failure

(AG)eq = , (3)
tc
(i) Face-sheet compressive/tensile fracture
where Ef , Ec , and Gc are longitudinal modulus of the face   The plastic deformation occurs when the normal
sheet, Young’s modulus of the core and shear modulus of stress in face sheets reaches the yield stress of face
the core, respectively. It is worth mentioning that Ec can be material. Once the critical failure stress is reached,
obtained using the computational homogenization technique the ultimate fracture takes place. Here, face sheet
[28], e.g. standard mechanics or asymptotic homogenization, failure includes compressive fracture and tensile
and Gc can be derived by considering a periodic lattice core fracture in the top face sheet and bottom face sheet,
under a shear strain in FEA [29]. It is noted that the three respectively. However, the bottom face sheet may fail
terms on the right side of Eq. (2) describe the bending stiff- only if the core strength is high enough to resist local
ness of the face sheets and the core about their own centroid, deformation of the top face sheet. This failure mode
and the bending stiffness of the face sheets about the cen- has not reported in usual experimental results. Thus,
troid of the sandwich structure, respectively. Since the first in this work, the compressive failure mode will be
two terms are small compared to the third term, Eq. (2) can considered to possibly occur in the top face sheet
be further simplified as: due to localized deformation. The critical load Pyf,max
for the top face-sheet compressive failure is given by
Ef wtf (tf + tc )2 [3, 26]:
(EI)eq ≈ , (4)
2 𝜎fc w
Pyf ,max = (( ) ( )) ,
Therefore, the theoretical flexural stiffness Dt of the sand- ls (6)
wich structures can be derived as: 4tf (tf +tc )
+ 4t62 𝜂
f

2
P 4w(tf + tc ) where
√𝜎/ fc is the face-sheet compressive yield stress;
Dt = = . (5)
/
𝜂 = 4 k 4Df , where k = Ec tc and Df = Ef tf3 12 ;
/
𝛿 l3 tc l
6t E
+ G
f f c
Df is the bending stiffness of the face-sheet about its
neutral axis; Ec and Ef are young’s modulus of the
core and longitudinal modulus of the face-sheets,
3.2 Failure modes respectively.
(ii) Face-sheet wrinkling
Sandwich structures under quasi-static three-point bending   Wrinkling may occur in the top face sheet due to
can fail in several modes [5]: (i) face-sheet failure (fracture, the local buckling related to the waviness of the face
wrinkling or local buckling and indentation), (ii) core failure sheet as well as the difference between the moduli of
(core cracking and buckling), (iii) interfacial failure (face- the face sheet and core materials [3]. It is noted that
sheet and core debonding). if the sandwich structures have relative high-strength

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cores, high elastic moduli of the face sheet and lattice 3.2.3 Interfacial failure
core materials and small amplitude in waviness of
the face sheet, the face sheet wrinkling failure mode The adhesive debonding between interfaces of face sheets
does not occur. In this study, FEA and experimental and core may occur when the interfacial strength is lower
observation are used to examine this failure mode. than the core shear strength [3]. It is noted that a perfect
(iii) Face-sheet indentation bonding is assumed in this work, which will be further
  The indentation failure is a localized failure mode, examined according to the experimental results.
which does not involve the overall deformation of It is worth mentioning that the analytical models above
the sandwich structures. This failure mode usually could only provide a simplified prediction about the corre-
occurs when the sandwich structure is designed with sponding failure modes as the influence of core topology and
thick and soft core as well as thin top face sheet. its property is not fully considered in these formulae, which
In addition, loading tool in bending test with a rela- is one of the dominant factors in determining the mechanical
tive small radius may also easily cause indentation behaviors of sandwich structures with various lattice cores.
deformation. In this work, this failure mode will be Thus, analytical, FEA and experimental methods are com-
examined through FEA and experimental observa- prehensively utilized to identify the failure modes, as listed
tion. in Table 3.

3.2.2 Core failure 4 Finite element simulation

Core failure is one of the most common modes in sand- Finite element (FE) models were established to character-
wich structures under bending load. Expected failure modes ize the stress changes and predict the core fracture dur-
include shear cracking by the overall deflection, compres- ing the bending process of different sandwich structures
sive/tensile cracking and buckling by the local deflection. with ABAQUS 6.14/Explicit. The details of FE model
are shown in Fig. 3. The dimensions of the model are the
(i) Core shear failure same as the bending tests. The lattice cores were discretized
  Core shear-induced cracking may occur, especially using 8-node linear brick element with reduced integra-
for sandwich beam with thick face sheet and weak tion (C3D8R) or 4-node linear tetrahedron element (C3D4)
core. An analytical formula is used to approximately depending on the complexity of core geometry. Face sheets
estimate the critical shear failure strength 𝜏cs,max that were modeled using a second-order 10-node modified tet-
leads to core shear failure [3, 26]: rahedron element (C3D10M) with single-layer structure to
avoid the stiff behavior induced by using a linear brick ele-
Pcs,max
𝜏cs,max = ( ), (7) ment and thus improve computation accuracy. The size of
2w tf + tc the elements for face sheets was 1 mm. For lattice cores,
they were meshed with the element size ranging from 0.2 to
where Pcs,max represents the maximum load.
0.5 mm to avoid the convergence problem and guarantee the
(ii) Core compressive/tensile failure
simulation efficiency and accuracy.
  The critical core compressive failure strength
𝜎cc,max for core compressive cracking can be
expressed as [3, 26]:
Table 3  Summary of failure modes of sandwich structures and cor-
Pcc,max 𝜂 responding examination methods
𝜎cc,max = , (8)
2w Failure type Failure mode Method

where Pcc,max represents the maximum load. Face sheet failure Face sheet compressive fracture 1, 2, 3
  In this study, we will examine the failure caused by Face sheet wrinkling 2, 3
core tensile stress with FEA and experimental meth- Face sheet indentation 2, 3
ods. Core failure Core shear failure 1, 2, 3
(iii) Core buckling Core compressive failure 1, 2, 3
  No analytical model is applied here. FEA and Core tensile failure 2, 3
experimental observation are used to capture this Core buckling 2, 3
type of failure mode. Interfacial failure Adhesive debonding between face 3
sheets and core

Note: 1, 2 and 3 represent analytical, FEA and experimental methods

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Fig. 3  Finite element model for Experimental configuration

three-point bending Loading tool
z(3) y(2)

x(1)

Face sheets

Supports
3D-printed core

In addition, the bonding interface between the lattice core the experimental values, which are similar to the findings
and face sheets is assumed to be perfect. Tie constraints were in [26] and could be explained by several reasons: (a) As
applied between the surfaces of face sheets and lattice core. the sandwich structure under three-point bending test is
The contacts between the face sheets, loading tool and sup- subjected to a complex stress state, including tension, com-
ports were considered to be frictionless. Displacement con- pression and bending, the simplified constitutive models
trol and smooth analysis steps were imposed to ensure that adopted in current FE models that describe the mechanical
the simulation is a quasi-static simulation. Furthermore, the behaviors of face sheet and core materials may not fully
load was applied by assigning a finite displacement to the capture the stress evolution, thereby causing the difference
loading tool. between FEA and experimental results. (b) 3D printed lattice
Two supports and loading head were defined as a per- cores are assumed to be bonded perfectly between printing
fectly rigid body with radii of 30 mm and 15 mm, respec- layers in FE models, which may slightly over predict the
tively. The aluminum face sheets were modeled as homo- strength and stiffness. (c) The 3D printed stereolithography
geneous and elasto-plastic, following the Von Mises yield polymer specimens could slightly lose their properties due
criterion. As the polymer elongation at break (7.5%) as to the influence of environmental factors when implementing
shown in Table 2, is very close to the brittle materials, for experimental tests.
the sake of simplicity of analysis, we assumed the material
of cores to be brittle material in this study. Brittle cracking 5.2 Damage‑tolerant capacity
was used in FE simulation as core failure criterion. In this
criterion, when the stress of the integral point in the element Experimental three-point bending load–deflection curves
reaches the predefined fracture strength (37 MPa), there will for different architected sandwich structures, corresponding
be a crack in this position. Consequently, the material begins cores and face sheet are presented in Fig. 5. The experimen-
to fail and the failed elements will be removed from analysis. tal results show that lattice core topologies have a signifi-
cant effect on the load–deflection characteristics. For core
bending only, K-gird core has the largest bending stiffness
5 Results and discussion and the maximum load, followed by T-grid core. B-grid,
Q-grid and FCC cores have the similar trends of bending
5.1 FE model verification stiffness, while the maximum force of Q-grid core is slightly
larger than the other two cores. Noticeably, BCC core has
To verify the FE models, the comparison of force–deflec- the smallest bending stiffness and maximum force among
tion curves of sandwich structures under three-point bending all the lattice cores. For aluminum sheet bending, the bend-
obtained from FE simulations and experimental tests has ing stiffness and maximum bending force obtained from
been made, as presented in Fig. 4. It is shown that a rea- load–deflection curve are 21.27 N/mm and 102.79 N, which
sonable agreement can be observed in the force–deflection are much smaller than those of lattice cores. Interestingly,
curves between the numerical and experimental results for when the aluminum sheets and lattice cores were fabricated
displacement range up to the position of failure occurrence. to sandwich structures, the evolution trends of load–deflec-
Furthermore, Table 4 presents the maximum load and tion curves are changed. Sandwich structure (FCC core) with
flexural stiffness of sandwich structures obtained by experi- the second largest flexural stiffness, only slightly smaller
ments and FEA. For each structure, three experiments were than sandwich structure (K-grid core), has the largest maxi-
performed and the corresponding experimental values were mum bending force followed by sandwich structure (K-grid
given by means and deviations. The differences between core). Sandwich structures (B-grid, Q-grid and FCC cores)
the FE predictions and experimental maximum loads and have similar maximum bending force, only smaller than that
flexural stiffness for all cases are less than 6% and 7%, of sandwich structure (T-grid). In addition, sandwich struc-
respectively. The simulated results are slightly higher than tures (B-grid, T-grid and BCC cores) have similar flexural

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Fig. 4  FEA and experimental force–deflection curves of the proposed sandwich structures

Table 4  FEA and experimental data of the maximum load and flexural stiffness (SD: standard deviation)
Core type Maximum load (N) Flexural stiffness (N/mm)
Experiment (mean, SD) FE prediction Error (%) Experiment (mean, SD) FE prediction Error (%)

B-grid (651.80, ± 36.05) 677.70 3.97 (170.30, ± 30.54) 178.46 4.79

T-grid (809.45, ± 77.20) 829.66 2.50 (186.40, ± 48.82) 198.42 6.45
Q-grid (649.71, ± 33.63) 667.21 2.69 (134.20, ± 22.43) 141.19 5.21
K-grid (871.60, ± 78.53) 880.93 1.07 (221.34, ± 41.02) 235.07 6.20
FCC (929.90, ± 24.59) 950.25 2.19 (213.59, ± 25.44) 225.66 5.65
BCC (692.28, ± 54.06) 701.81 5.70 (179.35, ± 34.62) 191.46 6.75

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Fig. 5  Load–deflection curves: a aluminum face sheet bending only, b core bending only, c bending of whole sandwich structures with different
core topologies

stiffness, larger than that of sandwich structure (Q-grid) shown in Fig. 6 to facilitate the analysis. It should be empha-
which has the smallest bending stiffness. sized that the above density is defined as the mass of lattice
To quantitatively analyze the influence of sandwich struc- core or whole sandwich structure divided by its enclosure
tures with different lattice cores on damage-tolerant capac- volume. BCC core has the smallest density of 408.20 (kg/
ity and other mechanical performances, densities of lattice m3) compared to T-grid and K-grid cores with the largest
cores (ρc) and their sandwich structures (ρw) are provided as ones of 686.81 (kg/m3) and 686.89 (kg/m3). The other three

Fig. 6  Comparison of densities for cores and sandwich structures: a density of different cores; b density of sandwich structures with different
cores

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cores, like B-grid, Q-grid and FCC have the similar level of level of flexural stiffness per density, of which the one with
density values. In addition, the density for sandwich struc- FCC core has the best damage-tolerant performance fol-
tures with different lattice core topologies follows the same lowed by sandwich structure with BCC core. In contrast,
trend as that of the core bending cases. sandwich structure with Q-grid core has the poorest damage-
With reference to the load–deflection curves in Fig. 5, tolerant performance.
damage evolution of the proposed sandwich structures can Stage II: this stage corresponds to the damage progres-
be divided to three stages as shown in Fig. 7. A similar sion. After the elastic region, the damage of sandwich struc-
deformation behavior is also discussed to investigate the ture initiates at the beginning of Stage II and the bending
relations between the strength and applied force in [16]. force continues to increase to reach the maximum value
Stage I: this is the elastic region that reflects the damage- when the final failure occurs. Figure 8 shows the maximum
tolerant capability. As shown in Table 5, flexural stiffness bending load per density. BCC core has the smallest maxi-
per density was calculated to quantitatively evaluate the mum bending load, followed by FCC core. However, the
damage-tolerant performance of sandwich structures with situation in sandwich structures has changed. The sandwich
different cores [26]. From the experimental data, sandwich structure with FCC core has the largest maximum bending
structures with FCC, BCC and K-grid cores have the similar load followed by the one with BCC core. On the other side,
as presented in Fig. 9, BCC core and its sandwich structure
have the largest deflection corresponding to the maximum
Stage II Stage III load position among all the cases, which illustrates that BCC
P
Stage I Failure occurs core and its sandwich structure have the most excellent load-
bearing capacity compared to the other five structures.
Damage Stage III: in this stage, the load-bearing capacity of sand-
initiation wich structures falls down dramatically. However, a certain
level of residual load-bearing capacity could be witnessed
for BCC core and its sandwich structure, as shown in Fig. 5b
Absorbed energy and c.

5.3 Quasi‑static energy absorption performance

δ
Energy absorption under bending load can be used to eval-
Fig. 7  Damage evolution of the proposed sandwich structures uate the performance of the proposed sandwich structures

Table 5  Comparison of flexural Lattice cores and sandwich structures Flexural stiffness (N/mm) (specific stiffness: data per density)
stiffness (specific stiffness:
data per density) between Theoretical prediction FE prediction Experimental data
lattice cores only and sandwich
structures obtained from B-grid
analytical formulation, FEA and Core only ρc = 519.67 (Kg/m3) – 88.08 (0.169) 83.76 (0.161)
experiments Sandwich ρw = 962.97 (Kg/m3) 153.61 (0.160) 178.46 (0.185) 170.30 (0.177)
T-grid
Core only ρc = 686.81 (Kg/m3) – 107.64 (0.157) 99.46 (0.145)
Sandwich ρw = 1103.13 (Kg/m3) 171.59 (0.156) 198.42 (0.180) 186.40 (0.169)
Q-grid
Core only ρc = 591.14 (Kg/m3) – 81.68 (0.138) 76.29 (0.129)
Sandwich ρw = 1021.25 (Kg/m3) 127.15 (0.125) 141.19 (0.138) 134.20 (0.131)
K-grid
Core only ρc = 686.89 (Kg/m3) – 123.42 (0.180) 118.60 (0.173)
Sandwich ρw = 1100.63 (Kg/m3) 183.17 (0.166) 235.07 (0.214) 221.34 (0.201)
FCC
Core only ρc = 551.57 (Kg/m3) – 94.12 (0.171) 84.23 (0.153)
Sandwich ρw = 997.34 (Kg/m3) 185.03 (0.186) 225.66 (0.226) 213.59 (0.214)
BCC
Core only ρc = 408.20 (Kg/m3) – 51.93 (0.127) 50.79 (0.124)
Sandwich ρw = 871.25 (Kg/m3) 164.97 (0.189) 191.46 (0.220) 179.35 (0.206)

The bold values refer to ‘Specific stiffness: data per density’

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Fig. 8  Maximum bending load (per density): a lattice cores only b whole sandwich structures

Fig. 9  Deflection (per density) at maximum load: a lattice cores only b whole sandwich structures

with different lattice cores. It is noted that the absorbed structure with the lightest and weakest BCC core has the
energy is equal to the area under load–deflection curve up most excellent energy absorption performance.
to the final failure position, as represented in Fig. 7, which
can be computed based on trapezoidal integral method. 5.4 Failure mechanisms
From the results in Fig. 10, it can be seen that FCC
and BCC core bending have the relatively low level of As mentioned in Sect. 3.2, sandwich structures may fail at
energy absorption (J/(kg/m3)) performance compared to a limit load caused by several failure modes. Here, failure
that of the other four cores. However, the situation for mechanisms are examined through analytical, FEA and
the whole sandwich structures bending is quite different experimental methods. A comparison of failure mecha-
from the core bending only cases. Sandwich structure with nisms for all sandwich structures has been made in Fig. 11.
BCC core has the best energy absorption (J/(kg/m3)) per- It is worth mentioning that our FE model can accurately
formance followed by the one with FCC core. Based on predict the crack position and morphology and the simi-
the discussions above, we can conclude that the sandwich lar results were also obtained in [14]. Additionally, FEA

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Fig. 10  Energy absorption performance: a lattice cores only b whole sandwich structures

results in Fig. 11 show that the top surface of core endures of our proposed sandwich structures compared to other
a much larger compressive stress that is still smaller than stress modes.
the maximum material compressive stress and the com- In addition, Table 6 reports the failure modes exam-
pressive stress can also play a role on suppressing the ined based on the analytical formulations developed in
crack occurrence. While the bottom side of core, espe- Sect. 3.2. It is evident that the maximum face fracture
cially its central area, is mainly influenced by tensile stress forces calculated analytically for all six sandwich struc-
that exceeds the maximum material tensile stress, thereby tures are greater than FEA and experimental data, which
leading to crack initiation from the bottom central area. means that there is face sheet yielding but no fracture
In [17], five failure modes have been identified for an occurrence. The theoretically predicted core shear stresses
adhesively bonded corrugated sandwich structure, includ- for the six sandwich structures are smaller or very close to
ing face yielding, face buckling, core yielding, core buck- the ones obtained from FEA, illustrating that core shear
ling and adhesive damage initiation. However, different deformation occurs during three-point bending process.
results were observed in this study. From further analysis Furthermore, as core compressive stress may occur along
of the FEA and experimental results in Fig. 11, failure width (s22) or thickness (s33) direction of sandwich struc-
mechanisms can be identified as follows: tures, the maximum value of s22 and s33 is used to verify
the core compressive mode. It is worth noting that the
• Face sheet yielding but no fracture found; FE predicted results are much smaller than the analytical
• No obvious core compression or buckling witnessed; values, which proves that there is no core compression
• No obvious debonding between face sheets and core deformation. This conclusion further confirms the findings
observed; obtained from experimental observation.
• Possible core tension and/or shear identified based on Figure 13 compares stress distributions of pure cores
crack morphology [12]. and their corresponding sandwich structures under three-
point bending. For pure core bending, stress distribu-
In order to further identify the dominant failure mode, tion is more localized in comparison with its sandwich
stress components of a selected point in crack region structure in terms of all types of cores. This phenomenon
through FEA have been presented in Fig. 12 to facilitate illustrates that crack is more likely to occur and develop
the analysis for proposed sandwich structures. From the from the bottom side of core due to tensile stress exceed-
FE results, we can clearly see that cores in sandwich struc- ing the maximum material tensile stress during pure core
tures are subjected to a very complex stress state includ- bending process. Moreover, the comparison of FE and
ing tension, compression and shear deformation. How- experimental results shows that the FE model can provide
ever, in all these deformation modes, bending-induced more accurate predictions of the crack morphology and
tensile stress plays a dominant role on the deformation

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Fig. 11  Comparison of failure mechanisms for all sandwich structures through FEA and experiments

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Fig. 12  Stress components of a selected point in crack region

Table 6  Failure modes Core type Failure modes

examined through analytical,
FEA and experimental methods Face sheet fracture Pyf,max Core shear stress 𝜏cs,max Core compressive stress
𝜎cc,max
Analytical FEA and experiment Analytical FE (|s23|) Analytical FEA
(Eq. (6)) (Eq. (7)) (Eq. (8)) max(|s22|,
|s33|)

B-grid 944.56 677.70 (651.80) 0.91 1.66 8.66 5.02

T-grid 949.69 829.66 (809.45) 1.12 1.51 11.00 6.62
Q-grid 930.8 667.21 (649.71) 0.90 2.56 8.13 6.66
K-grid 959.24 880.93 (871.60) 1.21 1.56 12.37 3.79
BCC 957.28 950.25 (929.90) 1.29 1.00 13.08 0.75
FCC 947.53 701.81 (692.28) 0.96 0.89 9.32 2.21

its location, which is marked by oval-shaped dashed line reasons is the different face sheet materials are used, car-
in the figures. bon fiber reinforced plastics (CFRP) in [12] vs. aluminum
alloy in this study. The big difference in material properties
5.5 Discussions leads to different deformation behaviors, thereby influenc-
ing the failure mechanisms of sandwich structures. Moreo-
It is worth mentioning that the bending capacity for sand- ver, we mainly focus on the effect of core topologies on the
wich structures with similar 2D core topologies were mechanical performance (structural responses) of sandwich
also investigated in [12]. It is found that the failure mode structures. Therefore, other process parameters, such as core
in B-grid sandwich structure is the interfacial debonding materials and dimensions [17], are omitted.
between the core and face sheet, while the failure of the
other three are caused by core shear. In our cases, there is
no interfacial debonding occurrence. One of the possible

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From the results in previous sections, it can be seen that investigated and compared to identify the one with optimal
the bending performances (elastic stiffness, bending load, mechanical performance and further clarify the underlying
deflection, energy absorption) of sandwich structures with failure mechanisms. It is found that a so-called ‘Stress Prop-
FCC and BCC cores are enhanced to some extent compared agation’ mechanism could be utilized to explain the likely
to the other four sandwich structures (2D cores). The reasons reasons of enhanced mechanical performances, which is
can be explained based on FEA (Figs. 11, 13) as follows: regarded as an interactive effect of top face sheet and core
topologies of sandwich structures compared to core bend-
• Stress is more likely concentrated for pure core bending. ing only. Moreover, the efficiency of ‘Stress Propagation’
It leads to crack initiation and development on the bot- determines the mechanical performances between different
tom side of cores, thereby degrading the bending perfor- sandwich structures. In this sense, the main research findings
mance. are highlighted in detail as follows:
• For sandwich structure bending, top aluminum face
sheet can enlarge the contact area with loading tool (1) In the elastic deformation region, sandwich structure
during plastic deformation, thereby facilitating lattice with FCC lattice core has the best damage-tolerant
cores to transfer bending loads efficiently from central capability followed by that with BCC lattice core,
lattice units across neighboring ones. This synergistic while sandwich structure with Q-grid lattice core has
deformation would also help reduce the risk of debond- the worst damage-tolerant performance.
ing between the core and face sheet, owing to the alu- (2) BCC lattice core and its sandwich structure have the
minum material used for face sheet rather than CFRP largest deflection corresponding to the maximum load,
[12]. Here, we call it as ‘Stress Propagation’ mechanism, which illustrates that BCC lattice core and its sandwich
which helps the proposed sandwich structures enhance structure have excellent load-bearing capacity.
the bending performance. This is quite noticeable in (3) Sandwich structure with BCC lattice core has the best
sandwich structures with 3D FCC and BCC cores. level of energy absorption (J/(kg/m3)) performance fol-
lowed by the one with FCC lattice core.
It is believed that the findings are not limited to the cases (4) Core cracking is the main failure mode for the proposed
in this study, which are also expected to provide theoretical sandwich structures. This is induced and dominated by
guidelines for a more efficient design of other metal-polymer tensile stress followed by shear stress, which has been
hybrid sandwich structures with lighter weight and higher verified by FEA.
mechanical performance. (5) In the ‘Stress Propagation’ mechanism, top aluminum
face sheet can facilitate lattice cores to transfer bending
loads from central lattice units across neighboring ones,
6 Conclusions which is found more efficient in the sandwich structures
with 3D FCC and BCC lattice cores.
A novel class of lightweight sandwich structures with six
different 3D-printed lattice core topologies has been pro-
posed in this work. Their mechanical performances under
quasi-static three-point bending were comprehensively eval-
uated by using a combined methodology including analytical
modeling, numerical simulation and experimental testing.
The damage-tolerant capability, energy absorption perfor-
mance and failure modes of these sandwich structures were

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◂Fig. 13  Stress distributions of cores only and their correspond- composite sandwich structures with aluminum honeycomb cores
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Funds for Overseas High-Level Talents Plan from Wuhan University 2014;67:39–49.
of Technology and the Fundamental Research Funds for the Central 16. Liu YB, Dong ZC, Liang J, Ge JR. Determination of the strength
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