Comparative Study of Core Material's Stiffness on Sandwich Panel with
Composite Face Sheets beyond the Yield Point
NASSER S. BAJABA
Yanbu Industrial College,
Yanbu,
SAUDI ARABIA
Abstract: - The study aims to explore the performance of sandwich panels exceeding the yield point
stiffness of the core material. Sandwich panels have gained growing attention among designers owing to
their excellent corrosion properties, and lightweight, and speedy installation process. They have been applied in
numerous industrial sectors, including aerospace, architectural, marine, and transportation. Typically, sandwich
panels are composed of a single central core sandwiched by a pair of outer face sheets, where the core is
normally developed using softer materials compared to the face sheets. Given that past studies have primarily
focused on sandwich panels in the elastic range, this present study explored the performance of sandwich
panels exceeding the yield point stiffness of the core material. The univariate search optimization method was
utilized to assess the elastic modulus ratio of the core (typically foam) to the face sheet (composite material).
The load was elevated in a quasi-static order until the face sheets reached their yield point. Subsequently, the
panel was simulated using the finite element analysis commercial package ANSYS APDL, with simply
supported boundary conditions used on all sides of the panel. The proposed model was verified by comparing
the numerical and experimental data from recent literature. Based on the results, the panel's increased load-
carrying capacity corresponded as the core material stiffness exceeded its yield limit. Moreover, the
transmission of load to the face sheets increased as the core stiffness decreased. In summary, stiffer core
materials caused the sandwich panel to behave more as isotopic face sheets. Thus, the face sheets yielded ahead
of the core material.
Key-Words: - Sandwich panels, Core material, Face sheets, Yield limit, Elastic modulus, Composites.
Received: April 11, 2024. Revised: August 19, 2024. Accepted: September 21, 2024. Published: November 25, 2024.
1 Introduction
Sandwich panels are mechanical structures
constructed using two pieces of face sheets made
from robust and stiff materials partitioned by a
lightweight core. These highly optimized sandwich
panels are extensively employed in numerous field
applications, such as aerospace, automotive, and
navy, given the high stiffness of the face sheets and
the low specific weight of the core material. Despite
their significant application, sandwich panels are
susceptible to various defects and failures due to the
considerably differing properties of the core and
face sheets. Previous investigation has revealed the
impact of the core material stiffness on the
mechanical strength of sandwich panels beyond the
core material's yield point. A recent study evaluated
the elastic modulus ratio of the core material (foam)
to the face sheet (metal) using the univariate search
optimization approach, [1]. Accordingly, multi-span
sandwich panels made with slightly profiled steel
facings and polyurethane foam core were identified
as the optimal design, which offers cost-effective,
minimal variance in the panel types, and potential
for a full-scale application that satisfied the
conflicting requirements in the market, [2]. In
another study, the mechanical strength of sandwich
composites made using a hollow glass microsphere
containing syntactic foam in an epoxy resin matrix
(core material) and hybrid kenaf/glass fibers (face
sheet) was assessed, [3]. The study used four
distinct face sheet combinations (glass-glass, kenaf-
kenaf, kenaf-glass, and glass-kenaf) to develop an
acceptable lightweight composite panel for
structural applications. Subsequently, a thorough
analysis of each design's mechanical performance
and failure mechanisms was conducted. Meanwhile,
a limited component analysis was carried out to
evaluate the stability of a sandwich panel design
made of steel with a center that was practically
determined, [4]. Polyethylene terephthalate (PET)
fiber-reinforced polymer (FRP) composite was used
to create the steel-based sandwich beams, with
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recycled PET (R-PET) from post-consumer plastic
bottles serving as the foam core. Using the three-
point bending approach, the sandwich beams were
studied and experimented with beyond their
proportionality limit. A control group with glass
FRP facings and a core density of 100 kg/m3 was
used to examine the effects of R-PET at three core
densities of 70, 80, and 100 kg/m3.
The present study aims to explore the performance
of sandwich panels exceeding the yield point
stiffness of the core material. This study is very
important because sandwich panels have gained
growing attention among designers owing to their
excellent corrosion properties, lightweight
applications, and speedy installation processes that
have been applied in numerous industrial sectors,
including aerospace, architectural, marine, and
transportation.
The characteristics of the steel were then
assessed numerically using ceramic as the interface
zone for up to ten individual layers. For the volume
portions of K = 2, the FGM was assumed. All 12 of
the examined beam specimens showed non-linear
load-deflection behavior, as evidenced by the fixed
beam geometry during the investigation.
Consequently, decreased secant elastic and shear
moduli under incremental load capacity were used
to build a non-linear analytical model. A parametric
assessment of the mechanical strength was carried
out under various scenarios after the suggested
model was validated, [5]. A previous study
considered numerous core models, including hybrid,
corrugated, derivative, foam, folded, honeycomb,
hierarchical, gradient, truss, hollow, and smart core,
along with several composite materials to fabricate
novel face sheets, including metal matrix
composites, fiber-reinforced composites, and
polymer matrix composites, [6]. Additionally, a
study performed a delamination test using a double
cantilever beam specimen, [7]. The study employed
the hand lay-up technique, where two face sheet
layers composed of glass fiber composite laminates
sandwich a plate/core to modify and enhance the
fracture properties of the specimen. Face sheet/core
delamination describes the process of separating the
core material in a sandwich panel from the face
sheet layer. Another research assessed the flexural
strength of a sandwich roof panel made of Glass
Fiber-reinforced Polymer (GFRP) using ANSYS
WORKBENCH, a commercial FEM program. The
top and bottom thin GFRP face sheets of the
specimen were created using two distinct densities
of multilayer polyurethane foam core. As a result,
the optimal stacking order for GFRP sandwich
panels with diverse multilayer cores was
investigated, [8]. This allows for the placement of
distinct core material layers on top of one another. A
fundamental review that covered the topic of weight
reduction in automotive applications was recently
published, [9]. The review described a variety of
lightweight composite materials with advantageous
mechanical characteristics. Concurrently, a recent
study created a novel fiber composite sandwich
panel for use in constructing buildings and other
structural infrastructures, [10]. This panel is made
up of a high-strength core material and skins
reinforced with glass fiber. To assist technical staff
and construction teams grasp a better understanding
of this next-generation sandwich panel's behavior
for real-world applications, its features have been
intensely studied. This innovative sandwich panel
was the subject of preliminary research using point
loading in one- and two-way spanning floor
applications. The findings suggest that the fiber
arrangement of the sandwich skins had an impact on
the stiffness of the sandwich. One study applied the
bioinspired method of hybrid material layers to
develop a flimsy material composed of an aluminum
face sheet with an interlayer of glass fabric and
foam core as an alternative material in automotive,
aeronautical, and marine applications, [11]. A GFRP
sandwich composite filled with stiff polyurethane
foam was created and characterized, according to
another study, [12]. The study examined the impact
of the volume of epoxy resin, which serves as a
binder between the polyurethane core and the GFRP
layer, on the mechanical strength metrics of tensile,
flexural, and compressive strength. Additionally,
one research provided a synopsis of the
development of structural insulated panels (SIP) as
well as the standard methods and components
utilized in SIP fabrication, [13]. The paper also
reviewed recent research related to SIPs in terms of
their applications and limitations, permitting
developers to enhance these materials. Apart from
that, static indentation and subsequent unloading
were applied and assessed using foam core
sandwich beams, [14]. They were considered to be
consistently supported by a rigid platen to minimize
global bending. Moreover, the flexural analysis of a
composite SIP with magnesium oxide board facings
was performed using an analytical model that
assumed an elastically perfect plastic compressive
behavior of the foam core, [15]. To integrate
material bi-modularity, a novel bespoke coding
process was created, which significantly improved
the accuracy of computational results and failure
mode prediction. A thorough investigation
combining numerical models and laboratory
experiments on CSIP beams of varied lengths under
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three- and four-point bending revealed material
model parameters within the non-linear behavior
range. Furthermore, finite element analysis was
utilized to ascertain the impacts on the
characteristics of sandwich composites composed of
polymer lamina reinforced with carbon fiber, [16].
The A-shaped cores of the composite sandwich
structures exhibit exceptional mechanical
characteristics under quasi-static plane compression
loads compared to the W-, X-, and Y-shaped cores.
Furthermore, a study fabricated two different
sandwich panels composed of expanded
polypropylene and extruded polystyrene foams as
the core materials and aluminum as the face sheet
material, [17]. The flexible epoxy-based adhesive
was applied to combine the two aluminum face
sheets and foam cores under a 20 N static
compression load. Using post-mortem imaging, the
damage behavior of the fabricated sandwiches was
examined, which showed that the sandwiches
damaged perfectly plastic deformation. An
experimental study developed and evaluated the
characteristics of a new type of SIP comprising an
insulated foam manufactured from natural rubber
loaded with wood particles (core layer) and three
commercial wood-composite boards (cement
particle, plywood, and fiber-cement) as the surface
layer, [18]. Lastly, composite panels with carbon
fiber face sheets and Kevlar honeycomb cores in
different configurations were evaluated using finite
element analysis, [19]. The influence of varying
face-sheet thicknesses on the bending rigidity (U),
bending stiffness (D), and load-to-deflection ratio of
the composite panel was conducted during the
analysis.
Geometry and Physical Model of the Sandwich
Panel
Generally, the sandwich panel is composed of two
composite materials that form the face sheets, with a
thickness of t each. A softcore material made of
foam with a thickness of c and smoother than the
face sheets is sandwiched between the two face
sheets. The square-shaped panel has a side length of
a and an overall thickness of h. Figure 1 depicts the
geometry of the sandwich panel with values a, t, and
c of 610 mm, 1.0 mm, and 40 mm, respectively.
Fig. 1: Schematic diagram of the sandwich panel
geometry
Assumptions
This research mainly considers the non-linearity
of the sandwich panel materials. Several
assumptions were established to elucidate the model
without disregarding the physical aspects of the
problem, as follows:
1. Both the core and face sheets are perfectly
bonded without any delamination occurring
between the layers.
2. The face sheets maintain their elastic behavior
throughout the loading time due to their
substantially greater yield strength and elastic
modulus than the core. The analysis halts the
moment the face sheets begin to yield.
3. All sides of the panel are supported.
4. The core material is considered to adopt a non-
linearity behavior.
Boundary Conditions and Material Properties
Materials that are used as face sheets in sandwich
panels should possess desirable properties, including
sturdy, durable, and able to withstand the impact of
resistance. Additionally, nearly all structural
materials that are available as thin sheets can be
utilized as the face sheet in sandwich panels. These
valuable properties are essential to prevent itself
from bending and fracturing through in-plane
shearing and out-of-plane compressive load. In this
particular case, the composite face sheet can be
compared to isotopic materials that fulfill the above
conditions. Recent studies have demonstrated the
potential applications of composite skins in
numerous industrial sectors. For example, these
composites are very often employed as panels to
minimize weight in aircraft designs. The face sheet
material is widely grouped into metal-matrix
composites, fiber-reinforced composites, and
polymer matrix composites, as listed in Table 1,
while the varying softcore materials A, B, C, and D
are presented in Table 2.
Table 1. The characteristics of the composite fiber
sheets applied in this study
Elastic
modulus
(GPa)
Fiber volume
fraction (GPa)
Fiber
230
0.785
Tensile
yield
(MPa)
Compression
yield (MPa)
Carbon
fiber
945
686
Epoxy
79.6
108
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Table 2. Properties of the four isotropic core materials applied in this study
Material
Reference
Young's
modulus
(MPa)
Poisson's
ratio
Shear
modulus
(MPa)
Shear
strength
(MPa)
0.2% offset
yield
strength
(MPa)
Strain at yield
point
(mm/mm)
AirexR63.50
core A
Rao, 2002
37.5
0.335
14.05
0.45
0.637
0.019
H100
core B
Kuang,
2001
138.6
0.35
47.574
1.2
1.5
0.0108225
HerexC70.200
core C
Rao, 2002
180
0.37
65.69
1.6
2.554
0.0162
H250
core D
Kuang,
2001
402.6
0.35
117.2
4.5
5
0.014
The upper and lower face sheet composite
material are stacked into several layers of the
orthotropic, as illustrated in Figure 2. The load was
gradually exerted onto the square-shaped loading
area on the top center of the face sheet until the
stress strain reached its yield strength (Figure 3).
Besides, Figure 4 elucidates the stress-strain curve
of the core materials A, B, C, and D. These
materials were selected due to their broad
applications in many industries.
Fig. 2: Upper and lower face sheet composite
material and stacking
Fig. 3: Load distribution on the center of the upper
face sheet
Fig. 4: Stress-strain curve for core materials A, B,
C, and D
2 Problem Formulation
2.1 Finite Element Model (FEM)
The ANSYS APDL was used to develop the FEM
for the varying proposed sandwich panels and assess
their flexural behavior. The isotropic solid element
(solid 186) with 3 translational degrees of freedom
at each node was utilized to model the light and stiff
foam cores. Meanwhile, the orthotropic shell
element (shell 281) has 8 degrees of freedom at each
node and was applied to model the face sheets. Shell
elements were used to achieve effective outputs,
making it easier to design thinner components with
fewer mesh elements, leading to significant cost-
effective computation. To prevent any delamination
in the panels, full contact behavior was applied
between the sandwich panel components. Following
the mesh convergence analysis, sufficient mesh size
was equipped to achieve the most reliable findings.
The sandwich panel was designed as a simply
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supported panel, with roller support at one side and
pinned support at the other side. Then, the load was
equally distributed onto the sandwich panels.
This model was convenient to evaluate thin to
moderately thick shell structures. The Shell Element
(SHELL 281) model consists of 8 nodes with 6
degrees of freedom at each node comprising
translations in the X-, Y-, and Z-axes and rotations
about the X-, Y-, and Z-axes. Although the plane
elements required a longer computational duration,
the primary advantage of the eight-node shell
element (rather than SHELL elements) is its notable
yielding behavior, the stress/strain profile
throughout the plate thickness, and the development
of plastic hinges. The stress-strain results are also
relatively straightforward to describe. Moreover, the
shell elements required lesser computation efforts
and faced fewer convergence issues than plane
elements.
Fig. 5: The FEM mesh of the sandwich panel (upper
and lower face sheets)
Fig. 6: The FEM mesh of the sandwich panel (core
material)
Nevertheless, shell models need more post-
processing to describe the findings. Solid 186 was
applied to develop the three-dimensional (3D)
modeling of the solid structures. The element
consists of 21 nodes with 3 degrees of freedom at
each node: translation in the X-, Y-, and Z-nodal
directions (Figure 5). The element appears to exhibit
several behaviors, including creep, huge deflection,
immense strain, plasticity, swelling, and stress
stiffening. The ANSYS finite element program was
utilized to design the sandwich panel. Both the two-
dimensional (2D) and 3D simulations were
modeled, and the convergence analysis was
conducted to measure the consistency.
2.2 Model Validation
In previous literature, FEM was validated by
comparing specific cases from the literature. The
relative difference in the results was lower than 1%.
To verify the FM and its results, experimental
validation was performed. The experimental
procedure utilized a sandwich panel made of Herex
C70-200 as the core material and an E-glass mat
(denoted as G300) as the face sheet [20]. The
mechanical properties of both the core material and
face sheet were obtained during the experiment
following ASTM guidelines. Figure 6 shows the
relationship between the deflection at the specimen's
center point and the applied load for both
experimental and FEM procedures, which
demonstrates a strong agreement between the
results. The maximum relative error was also lower
than 6%. The experimental procedures were
repeated multiple times, and the average values are
shown in Figure 7.
Fig. 7: Comparison of the center panel deflection vs.
load step (kPa) between the predicted FEM and the
actual experimental result, [20]
3 Problem Solution
The impact of the core stiffness of the sandwich
panel was evaluated by varying the mechanical
properties of the core material. Materials with non-
linear behaviors were considered in this parametric
study by applying the ANSYS software, stress and
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all its components, as well as strain and all its
components, such as plastic strain and deformation.
It was found that plastic deformation occurred near
the panel support (the point at which the boundary
conditions were applied), which holds in the
physical sense. The load exerted was concentrated
on the loading area where the simply supported
boundary conditions were applied and became a
reaction force. As a result, the area reached the yield
stress before other panel parts. The load step on the
FEM was halted when any of the face sheets started
to yield, which met the designer's requirement to
prevent permanent panel distortion. The yielding of
the face sheet indicates that non-reversible
deformation has taken place. As a result, the applied
loading does not exceed the limit and does not lead
to the face sheet yielding. The sample displayed the
sandwich panel's behavior in terms of each
parameter. Thus, the results would help design
engineers to achieve (or select) optimal parameters
that suit their design.
Figure 8 shows the center of deflection of the
entire sandwich panel vs. the load step. It was
noticed that the core stiffness increased as the
sandwich deflection decreased. Figure 9 and Figure
10 depict that the core stiffness caused the load-
carrying capacity (shear and total load) of the panel
to rise before the core material reached the shear
yield limit (shear strength and yield strength).
Meanwhile, the impact of the core stiffness on the
upper and lower face sheets is portrayed in Figure
11.
Fig. 8: The center of deflection of the entire
sandwich panel (mm) vs. load step (kPa) using
varying strength of core material stiffness
Fig. 9: The maximum core shear stress to the yield
shear strength of each core material vs. the load step
(kPa)
In general, the upper face sheet was found to
start yielding first, followed by the lower face.
Besides, the face sheets were able to withstand the
tension stresses, noting that the results simulate the
actual behavior. According to the Van Misses
stresses the two face sheet layers were exposed to
tension stresses, whereas the upper layer exhibited a
higher value since it was directly exposed to the
pressure. Figure 11 presents the impact of the core
stiffness on the maximum Von Misses stress for the
upper and lower face sheets vs. the load step that
causes the sheets to yield just before 130 kPa, 305
kPa, 570 kPa, and 760 kPa when using core
materials A, B, C, and D, respectively. The stability
of the core material influenced the transfer of stress
to the face sheets, increasing their values as they
carried the load on the upper and lower face sheets.
With the core entering to yielding phase (shifting to
plasticity), the rate of increase of the maximum
stress diminishes, as shown in Figure 10. In other
words, the load was passed to the face sheets, which
highlights the key advantage of expanding the load
above the core material's yield limit. Note that the
different curvatures in Figure 11 for all loads in
each core material stiffness were a result of the
transformation of the core materials, with both the
upper and lower face sheets exhibiting similar
behavior.
Figure 12 depicts the contour deflection of the
entire sandwich panel under the maximum load step
for each core material with the face sheets loaded
with carbon fiber composite materials. Additionally,
Figure 13 portrays the shear stress contour of the
different core materials under the maximum load
step.
0
100
200
300
400
500
600
700
800
0 5 10 15 20
Load step (kPa)
Center panel deflection (mm)
A
B
C
D
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
0200 400 600 800
Shear core/core shear strength
Load step (kPa)
A
B
C
D
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Fig. 10: The maximum core Von Misses stress
(MPa) to the yield strength (MPa) for each core
material vs. the load step (kPa)
(a)
(b)
Fig. 11: The maximum Von Misses stress (MPa) to
the yield strength of each core material vs. the load
step (kPa) for the (a) upper face sheet and (b) lower
face sheet
Fig. 12: The contour deflection of the entire
sandwich panel under maximum load step using
various core materials
Fig. 13: Shear stress contour of the entire sandwich
panel under maximum load step using various core
materials
The shear stress contour took place at the edge
of all the core materials and showed a similar profile
at varying stiffness values. Meanwhile, Figure 14
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
0200 400 600 800
Von Misses stress (MPa)
Load step (kPa)
A
B
C
D
0
0,2
0,4
0,6
0,8
1
1,2
0200 400 600 800
Von Misses stress (MPa)
Load step (kPa)
A
B
C
D
0
0,2
0,4
0,6
0,8
1
1,2
0200 400 600 800
Von Misses stress (MPa)
Load step (kPa)
A
B
C
D
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presents the Von Misses stress contours of the
different core materials under the maximum load
step. Figure 15 and Figure 16 presents Von Misses
stress contour for the upper and the lower face
sheets material under maximum load step using
different core materials.
Fig. 14: Von Misses stress contour of the entire
sandwich panel under maximum load step using
various core materials
Fig. 15: Von Misses stress contour for the upper
face sheet material under maximum load step using
different core materials
Fig. 16: Von Misses stress contour for the lower
sheet material under maximum load step using
different core materials
4 Results Discussion
From previous results, the thickness of the core
material increases as the load-carrying capacity of
the panel increases. This is justifiable because the
increase in thickness increases the second moment
of the cross-section area of the panel. In addition,
the shear stress in the core decreases for the same
amount of loading because the shear load is
distributed over a larger area as the thickness
increases. When the core material reaches the yield
point, the shear stress stays constant while the load
is being increased. In the yield range, the core
material keeps deforming while stress is constant.
Increasing the area of loading increases the load-
carrying capacity of the panel. The results of this
work are generated according to the univariate
search optimization technique, [21].
5 Conclusion
This study investigated the performance of
sandwich panels beyond the core material yield
point. The non-linearity core material of the whole
sandwich panel model was generated using the
ANSYS software and validated using specific
analytical cases from past literature. The accuracy of
the model was also examined for certain cases and
compared with FEM. Overall, the model showed
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excellent agreement with past findings, as well as
the experimental data in this study when compared
to literature as shown in [22]. The increased load-
carrying capacity of the sandwich panel corresponds
to the impact of the core material as it exceeds the
yield limit. Furthermore, the load transferred to the
face sheets increased the stiffness of the core
materials increased. As such, the sandwich panel
tends to behave as an orthotropic composite sheet
with greater core material stiffness. As a result, the
face sheets yield before the core material.
Declaration of Generative AI and AI-assisted
Technologies in the Writing Process
During the preparation of this work the authors used
Grammarly for language editing. After using this
tool/service, the author reviewed and edited the
content as needed and takes full responsibility for
the content of the publication.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
Nasser S. Bajaba, carried out the simulation, review,
and writing of the article and the optimization.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
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(Attribution 4.0 International, CC BY 4.0)
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WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2024.19.14
Nasser S. Bajaba
E-ISSN: 2224-3429
134
Volume 19, 2024