Thin–Walled Structures 151 (2020) 106713
Contents lists available at ScienceDirect
Thin-Walled Structures
journal homepage: http://www.elsevier.com/locate/tws
Full length article
Performance of a 3D printed cellular structure inspired by bone
Abdallah Ghazlan **, Tuan Nguyen , Tuan Ngo *, Steven Linforth , Van Tu Le
University of Melbourne, Australia
A R T I C L E I N F O
A B S T R A C T
Keywords:
Bioinspired
3D printing
Trabecular bone
Thin-walled cellular structure
Numerical analysis
Biological thin-walled cellular structures have intricate arrangements that facilitate lightweight and high energy
absorption. A prime example is trabecular bone, which possesses a unique thin-walled cellular structure of
connected rods or plates, to minimise weight whilst meeting the loading demands from the body. For example,
the femur has a closed cell structure of plates to transmit heavy loads to the ground, whereas a carpal bone has an
open cell structure of connected rods. Although existing lightweight thin-walled cellular structures with
controlled arrangements have been investigated extensively, such as those with re-entrant geometries, asym­
metric instability due to local buckling can hinder their energy absorption capacity. Mimicking the features of
trabecular bone can offer the designer a greater degree of control over the buckling and collapse mechanisms of
thin-walled cellular structures. This can lead to the development of high-performance protective systems with
superior energy absorption capabilities. This study employs 3D printing and finite element analysis techniques to
mimic and investigate several key features of the plate-like thin-walled cellular structure of trabecular bone. The
performance of the developed bioinspired structure is benchmarked against traditional hexagonal and re-entrant
designs. The controlled and progressive buckling and collapse mechanisms observed in the bioinspired structure
result in superior energy absorption over its re-entrant and hexagonal counterparts.
1. Introduction
The intricate arrangements of biological thin-walled cellular struc­
tures facilitate lightweight and high energy absorption. These include
thin-walled cellular structures that have been optimised over many
years of evolution, including those of porous or trabecular bone [1–4],
porcupine quills [5–8], turtle shells [9–12] and toucan beak [13–16]. In
particular, trabecular bone (Fig. 1) shows a unique cellular arrangement
that minimises weight whilst meeting the loading demands of the
human body. Engineered thin-walled cellular structures, such as those
with honeycomb, re-entrant, spiral and hexachiral geometries, to name
a few, have been extensively investigated for numerous applications,
including extreme loading (blast and impact) [17–20] and crashwor­
thiness [21–24]. Although auxetic (or negative Poisson’s ratio) cellular
structures, such as those with re-entrant geometries, have been found to
show the best performance in terms of lightweight and energy absorp­
tion, asymmetric instability due to local buckling has been found to
hinder their energy absorption capacity [17,18]. Mimicking the buck­
ling and collapse mechanisms in the intricate structure of trabecular
bone can guide the development of superior lightweight thin-walled
cellular structures for protective applications.
Bone is a sandwich structure that consists of a soft core (trabecular or
spongy bone) and a dense outer shell (compact bone). Bone grows in
response to the loads applied to it. As such, the density of bone in a
particular location of the body depends on the magnitude of the applied
loads. In this study, the closed thin-walled cellular structure of a
trabecular bone (see Fig. 1) is mimicked for energy absorption appli­
cations. Similar to man-made sandwich structures, the mechanical
behaviour of bone depends on the properties of its components and their
geometry [25–27]. Generally, trabecular bone has a closed-cell plate-­
like structure, an open-cell strut-like structure or a hybrid of the two.
Plate-like structures (Fig. 1b) can be found in denser bones that can
support high loads, such as the human femur. Some of the plate-like
elements have small openings in them to allow for the interconnection
of marrow spaces. Open cell strut-like structures can be found in other
types of bone, such as the carpal bone, which is not typically subjected to
high loads. Schilling et al. [28] predicted the relative volume of carpal
bone by CT scanning a spherical volume of interest (VOI). They defined
the relative volume as the ratio of the volume of bone (trabeculae) to the
total volume of the VOI. The thickness of the strut-like elements (e.g., in
* Corresponding author. Department of Infrastructure Engineering, The University of Melbourne, Victoria, 3010, Australia.
** Corresponding author. Department of Infrastructure Engineering, The University of Melbourne, Victoria, 3010, Australia.
E-mail addresses: ghazlana@unimelb.edu.au (A. Ghazlan), dtngo@unimelb.edu.au (T. Ngo).
https://doi.org/10.1016/j.tws.2020.106713
Received 26 August 2019; Received in revised form 17 February 2020; Accepted 4 March 2020
Available online 19 March 2020
0263-8231/© 2020 Elsevier Ltd. All rights reserved.
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 1. a) Bone sandwich structure; b) Closed cell plate-like structure of trabecular bone, which is composed of concave, convex and hybrid (both concave and
convex) cells (adapted from Ref. [25]); and c) 3D printed hybrid thin-walled cellular structure that mimics the cell geometries of plate-like trabecular bone.
the carpal bones of a human) is approximately 200 μm with a relative
volume of 17.31 [29]. However, researchers have observed variabilities
in the thickness of the struts and relative volumes among different
species. For example, the carpal bone of a gorilla is 370 μm thick with a
relative volume of 34.09 [28]. Hybrid plate-like and strut-like structures
can be found at the transition zone in bone, namely the interface be­
tween the compact shell and the thin-walled cellular core.
Trabecular bone typically has a relative density that is less than 0.7
[25]. Compact bone has a higher relative density than 0.7. The relative
density of open cell rod-like structures is typically less than 0.13. In
contrast, the relative density of closed cell plate-like structures is greater
than 0.2. At intermediate relative densities, the structure of a trabecular
bone is composed of a combination of rod- and plate-like elements [25].
Concave and convex cell geometries can be observed in the plate-like
thin-walled cellular structure of trabecular bone (Fig. 1b). Mimicking
these structural characteristics can provide a method for controlling the
Fig. 2. a) Unit cell arrangements obtained from the cell walls of different Voronoi diagrams: a) Hexagons; b) Pentagons; c) Hybrid quads-hexagons; and d) Hybrid
oriented hexagons. e) Procedure for obtaining a re-entrant unit cell (concave) from a hexagonal cell (convex).
2
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 3. A graphical representation of the numerical and manufacturing framework for generating the finite element model and 3D printed sample of the bio­
inspired structure.
buckling collapse mechanisms of thin-walled cellular structures, which
can thereby enhance their energy absorption capacity. In trabecular
bone, only about 20% of the volume is filled with bone material and the
remainder with bone marrow [27,29]. At the nanoscale, it is composed
of Type 1 collagen/apatite building blocks [2,3]. Trabecular bone has
been reported to possess several hierarchical levels of porosity, from the
nano-scale to the macro scale: collagenapatite (10 nm), canalicular (100
nm), lacunar (up to 8 μm), vascular (50 μm), and intertrabecular (up to
1 mm) [2,30]. These facilitate several biological functions such as fluid
transport.
Voronoi diagrams have been extensively used to model biomimetic
structures [31–35], foams [36,37] and polycrystalline solids [38,39].
Given their controlled randomness, Voronoi diagrams have been used to
model the longitudinal and transverse trabeculae of a trabecular bone to
assess age-related losses [1]. Given that a trabecular bone is a
thin-walled cellular material, its stress-strain curve has three distinct
regions. In the linear elastic region, the cell walls bend or compress
axially. This is followed by a plateau region, which is roughly constant,
where the cells begin to collapse by elastic buckling, plastic yielding or
brittle fracture of the cell walls. In the densification regime, which is
represented by the steep portion of the stress-strain curve, there is
contact between the cell walls [19,40].
Advancements in 3D printing technologies have enabled the fabri­
cation of complex prototypes with high accuracy, including cellular
structures and bi-material composites [33,41]. Consequently, 3D print­
ing is the dominant manufacturing method employed by researchers for
fabricating
prototypes
of
cellular
structures
[22–24,42].
Extrusion-based methods are quite popular due to their effectiveness in
fabricating polymeric prototypes with intricate geometries from a wide
range of materials, including Nylon, acrylonitrile butadiene styrene
(ABS) and polyurethane. Extrusion-based 3D printing is thereby
employed in this research to develop a thin-walled bio-mimetic cellular
structure that is targeted at energy absorption applications. To this
effect, several key features of plate-like trabecular bone are mimicked.
An example is shown in Fig. 1c, where a bone-like structure is 3D printed
using hybrid concave and convex cell geometries. Experimental in­
vestigations are conducted to benchmark the performance of the
bone-like structure against well-known re-entrant and honeycomb ge­
ometries, using the peak load and energy absorption as the key perfor­
mance criteria. A finite element (FE) model is then developed and
validated to simulate the buckling and collapse mechanisms of the
bone-like structure to pave a path for the development of design pa­
rameters. The FE method is employed for simulating the behaviour of
cellular structures due to the availability of commercial software.
2. Numerical and manufacturing framework
2.1. Generating the bone-like unit cell designs
To generate a thin-walled cellular structure based on the architecture
of a trabecular bone, several unit cells were extracted from different
Voronoi diagrams (see Fig. 2a–d). The Voronoi approach is a powerful
tool to generate the bioinspired and benchmark (hexagonal and reentrant, Fig. 2a,e) structures. These designs were quickly obtained by
manipulating the sites (or points) of the Voronoi diagram. The locations
of the sites control the boundaries of the Voronoi polygons. The math­
ematical description of a Voronoi diagram is given in Ref. [41] and more
comprehensive proofs are provided in textbooks on computational ge­
ometry [43]. Although Voronoi diagrams can only produce convex re­
gions, a unit cell can be extracted and transformed to obtain concave
geometries, which is demonstrated in Fig. 2e. The unit cell in Fig. 2d was
chosen as the representative bioinspired structure because it has two
different sub-cells that can be manipulated simultaneously. Therefore,
the hybrid thin-walled cellular features of trabecular bone can be
mimicked more closely (see Fig. 1b). The hexagonal (Fig. 2a) and the
re-entrant configurations (Fig. 2e) were chosen as the benchmark cases
3
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 4. The hybrid oriented hexagonal design. The design parameters that were manipulated to obtain the 3D printed bioinspired structure (see Fig. 3) are
also presented.
for assessing the performance of the bioinspired structure. Importantly,
re-entrant and hexagonal geometries have been extensively studied for
extreme loading applications, where energy absorption is of paramount
importance [17–19,40,44].
� Generate a pattern of the unit cell to obtain a vertical scaffold. This
will ensure that a uniform 2D finite element mesh is generated in
subsequent steps, which is extruded in the out-of-plane direction
� Export the geometry of the scaffold into the International Graphics
Exchange Specification (IGES) CAD format and import it into the
finite element software (ABAQUS) for meshing
� Mesh half the scaffold due to its symmetry about the vertical plane
� Copy the mesh and scaffold to obtain the final finite element model
and 3D printed structure.
2.2. Constructing the numerical model and 3D printed bioinspired
structure
Fig. 3 illustrates a flow chart of the numerical and manufacturing
framework that was used to generate the finite element model and 3D
printed sample of the bioinspired structure. The key steps of the
framework are summarised as follows:
2.3. The bioinspired structure with simplified design parameters
The meshed finite element model and 3D printed sample of the
bioinspired structure (Fig. 3) were obtained by manipulating the pa­
rameters of the hybrid oriented hexagonal design (Fig. 2d). These design
parameters are presented in Fig. 4 and described as follows:
� Generate a Voronoi diagram of the desired biomimetic design
(hybrid oriented hexagons in this case)
� Extract the edges of a unit cell from the Voronoi diagram and export
the geometry to a format that is compatible with a commercial
computer-aided design (CAD) program
� Thicken the unit cell walls and modify its design parameters as
necessary (e.g., cell angles, lengths of the struts and ties, and wall
thickness)
� W ¼ 20 mm,H ¼ 20 mm: Width and height of the unit cell,
respectively
� lut ¼ 8 mm, llt ¼ 4 mm: Length of the upper and lower tie,
respectively
� tw ¼ 2 mm: Thickness of the cell walls
Fig. 5. 3D printed thin-walled cellular structures with the same number of cells across the width and depth: a) Hexagonal; b) Re-entrant; c) Bioinspired. The specific
energy absorption (kJ/kg) is compared to assess their performance (see Table 1) as the structures do not have an identical mass.
4
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 6. Tensile engineering stress-strain curve for Markforged Tough Nylon.
Fig. 7. Force-displacement curves for the 3D printed
bioinspired and benchmark (hexagonal and reentrant) structures under displacement controlled
uniaxial compression. The dimensions of the tested
specimens (60 � 60 mm) can be visualised in Fig. 4.
The values of the ends of the linear-elastic and
plateau regions for each structure are labelled by L
and P on the displacement axis, respectively. C1 and
C2 signify a minimum and maximum in the plateau
region, which are referred to later in the text.
Fig. 8. Buckling and collapse mechanisms of the hexagonal structure.
5
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 9. Buckling and collapse mechanisms of the re-entrant structure.
� α ¼ 63� , β ¼ 45� : Angle of the upper and lower cell strut, respectively
� ws: The distance between the upper and lower struts, which is
identical at the top and bottom of the cell due to its periodicity. This
parameter is determined by the above design parameters.
Table 1
Comparing the mechanical performance of the bioinspired thin-walled cellular
structure with the benchmark cases (hexagonal and re-entrant). The average
values between the two tests are presented for each structure.
The out-of-plane thickness of the model was chosen as 30 mm to
ensure that only in-plane buckling occurs.
3. Sample fabrication and experimental parameters
The CAD files of the bioinspired and benchmark structures (hexag­
onal and re-entrant), which were generated using the manufacturing
framework (see Section 2), were converted to the Standard Triangle
Language or stereolithography (STL) format. The STL files were subse­
quently converted to 3D printing instructions. The 3D printed samples
(Fig. 5) were fabricated using the Markforged Mark Two desktop 3D
printer, which has a build volume of 320 � 132 � 154 mm. Two samples
were fabricated for each type of structure to assess the repeatability of
the test results. To print the geometry illustrated in Fig. 4, a heated
filament of Markforged Tough Nylon, a standard plastic material, was
extruded layer-by-layer through a 200 μm nozzle onto a heated print bed
at 250� C. Each printed layer has a thickness of 200 μm and the total
height of the printed model is 30 mm, which corresponds to its overall
thickness. This popular 3D printing technique is well-known as layer-bylayer deposition [45]. Each layer of the cellular structure was printed
using a random pattern to reduce the directional dependence of the
mechanical response. The tensile engineering stress-strain curve of the
material is presented in Fig. 6, which was obtained from quasi-static
tension tests conducted at the University of Melbourne, Australia. The
3D printed samples were subjected to quasi-static compression at a
displacement-controlled loading rate of 3 mm/min.
Structure
Relative
Density
Peak
Load
(kN)
Stiffness
(N/mm)
Energy
absorption
(J)
Specific
energy
absorption
(kJ/kg)
Hexagonal
Re-entrant
Bioinspired
0.33
0.47
0.38
2.1
2.6
1.5
478.9
849.3
418.2
57.5
19.6
97.3
8.91
2.11
12.97
elastic, plateau and densification), which demonstrates that the 3D
printing quality is consistent. As per the typical force-displacement
behaviour of cellular structures reported in the literature, several re­
gions of interest can be observed, namely linear-elastic, followed by a
plateau region and a final densification region. It can be observed that
once the peak load is reached in the benchmark structures (hexagonal
and re-entrant), the load carrying capacity diminishes before the initi­
ation of the plateau region. In contrast, the bioinspired structure
maintains a relatively increasing load carrying capacity throughout the
experiment. This results in a larger area under the force-displacement
curve before the onset of densification, which demonstrates its supe­
rior energy absorption capacity over the benchmark structures. Impor­
tantly, densification initiates in the bioinspired and hexagonal structures
at a similar displacement of around 33 mm. In contrast, the re-entrant
structure is highly unstable (see Fig. 9) and thereby reaches densifica­
tion much earlier (at a displacement of around 18 mm). The unstable
behaviour of the re-entrant structure results in a relatively smooth
plateau region. In contrast, several peaks can be observed in the plateau
regions of the bioinspired and hexagonal structures due to progressive
buckling and collapse. This behaviour is further investigated by ana­
lysing the collapse mechanisms in each structure individually.
The energy absorption capacity of thin-walled cellular structures is
typically quantified before the onset of densification. The peak load,
4. Experimental results and discussion
The stress-strain curves for the hexagonal, re-entrant and bioinspired
designs under uniaxial compression are presented in Fig. 7. Similar
mechanical behaviour can be observed for each sample (i.e., linear
6
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 10. Buckling and collapse mechanisms of the bioinspired structure at prominent displacements. These prominent deformations of the structure were observed in
the experiment at different displacements to those in Figs. 8 and 9.
stiffness and energy absorption of the three structures are summarised in
Table 1. It can be deduced that the bioinspired structure shows the
softest response in the linear elastic region (418.2 N/mm), reaches the
lowest peak load (1.5 kN) before the initiation of the plateau region (i.e.,
the end of the linear-elastic region labelled in Fig. 7) and has the highest
energy absorption capacity (97.3 J). This equates to a 29% reduction in
the peak load and 69% increase in energy absorption (area under the
curve before the end of the plateau region labelled in Fig. 7) compared to
the hexagonal structure. Furthermore, from the force-displacement
curve, it can be observed that the load in the bioinspired structure
does not diminish in the plateau region but shows a relatively monotonic
increase, which results in superior energy absorption over the bench­
mark structures. The mechanisms that may be attributed to these su­
perior performance enhancements are further analysed below using
experimental observations.
The buckling and collapse mechanisms of the hexagonal structure
can be observed in Fig. 8. At a displacement of u ¼ 4:5 mm, the structure
is relatively stiff and the cells can be observed to deform uniformly. This
corresponds to a peak force of 2 kN on the force-displacement curve. At
u ¼ 7:5 mm, the lower cells rotate counter-clockwise and begin to
collapse, whilst the upper cells rotate clockwise. At u ¼ 10:5 mm, the
lower cells completely collapse, which corresponds to the first minimum
observed in the plateau region of the force-displacement curve (labelled
as C1 in Fig. 7). This process repeats, whereby the upper cells begin to
buckle at a displacement of u ¼ 13:5 mm, which corresponds to a peak
in the plateau region of the force-displacement curve (labelled as C2 in
Fig. 7). This mechanism of progressive buckling and collapse repeats
until densification initiates at a displacement of u ¼ 33 mm. Impor­
tantly, the complementary rotations of the upper and lower cells induce
a torsional effect that tends to stabilise the structure. Contrary to the reentrant structure analysed further below, the hexagonal structure does
not buckle in one direction due to these complementary stabilising
effects.
The buckling and collapse mechanisms of the re-entrant structure
can be observed in Fig. 9. At a displacement of u ¼ 3 mm, the structure
begins to buckle inwards due to the negative Poisson’s ratio (auxetic)
effect, which is activated by the re-entrant geometry of the unit cells. At
this stage, the structure is behaving linear elastically. At u ¼ 4:5 mm (see
Figs. 7 and 9), instability is evident in the structure, which begins to
buckle towards the left. This asymmetric buckling is attributed to the
higher stiffness (Table 1) of the re-entrant structure compared to that of
the bioinspired and hexagonal structures. In effect, the horizontal ties
between the re-entrant unit cells provide relatively rigid lateral re­
straints that nullify the auxetic effect (see Fig. 9). This deformation
mechanism repeats through a displacement of u ¼ 7:5 mm and up to u ¼
13:5 mm, which corresponds to the minimum load reached in the
plateau region. Consequently, the plateau region in the forcedisplacement curve appears smooth, as the auxetic mechanism is not
activated due to the asymmetric buckling of the structure. This behav­
iour also causes the re-entrant structure to densify much earlier than the
hexagonal and bioinspired structures (see Fig. 7). Introducing more unit
cells across the width of the re-entrant sample may result in a wider and
more stable structure. However, this has been found to diminish the
auxetic (negative Poisson’s ratio) effect, which is not desired [17,18,20,
46]. Re-entrant structures are intended for activating the auxetic energy
absorption mechanism.
The buckling and collapse mechanisms of the bioinspired structure
can be observed in Fig. 10. At a displacement of u ¼ 4:5 mm and through
to u ¼ 9 mm, the structure is seen to buckle in the re-entrant regions of
the hybrid cells. These cells have a narrow re-entrant region and a
convex region. Given that the re-entrant region is narrow, the neigh­
bouring unit cells support the convex region of the hybrid cell when it
collapses. In effect, once the initial peak load (1.5 kN) is reached, the
load carrying capacity of the structure does not diminish at the initiation
of the plateau region. This is a key advantage over the re-entrant and
hexagonal structures, which are stiffer and reach a higher peak load that
diminishes near the onset of the plateau region. At u ¼ 16:5 mm, the
convex regions of the hybrid cells collapse onto the concave regions,
which induces a hardening effect in the plateau region i.e. the peak load
is seen to increase in a relatively monotonic manner up to the onset of
densification. After these hybrid cells densify, the lower cells at the base
of the structure collapse and densify at u ¼ 19:5 mm, which causes a
minor jump in the force-displacement curve. At u ¼ 25:5 mm, the
convex unit cells buckle and collapse until the onset of densification at
7
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 11. The densified structures: a) Hexagonal; b) Re-entrant; c) Bioinspired.
u ¼ 33 mm. Importantly, the progressive buckling and collapse mech­
anisms of the bioinspired structure are sequential, and the stable cells
effectively support the unstable cells. Essentially, the convex cells pro­
vide stability whilst the hybrid cells collapse and densify. These mech­
anisms result in a significant increase in energy absorption over the
hexagonal and re-entrant structures.
The final densified structures are shown in Fig. 11 for completeness,
and to provide further insight into the stability of the bioinspired
structure compared to the benchmark cases (hexagonal and re-entrant).
It can be observed that the hexagonal structure (Fig. 11a) is reasonably
stable, with relatively uniform densification throughout its structure.
The re-entrant structure does not densify effectively, as it buckles to­
wards the left, which compromises the load carrying capacity of the
perimeter cells. The bioinspired structure is observed to be the most
stable due to the progressive buckling and collapse mechanisms
described earlier. Hence, a hybrid cell that utilises the benefits of a soft
and stiff thin-walled cellular structure is required to maximise energy
absorption. By strategically arranging the hybrid and convex cells, the
energy absorption of thin-walled cellular structures can be amplified
significantly whilst enhancing their maximum load carrying capacity.
5. Validated numerical model
A finite element (FE) model of the bioinspired structure was devel­
oped using the commercial software package ABAQUS, and validated
using the experimental results reported and discussed in Section 4. The
purpose of this preliminary model is to capture the load-displacement
behaviour and deformation mechanisms of the bio-inspired cellular
Fig. 12. Finite element models of the bio-inspired cellular structure with different mesh densities.
8
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 13. Results from the mesh convergence study.
Fig. 14. Force-displacement curves for the finite element model and 3D printed samples of the bioinspired structure.
structure in the elastic and plateau regions. The model will be exten­
sively calibrated and validated under different loading conditions in a
future work to be used as a design tool for bioinspired protective cellular
structures under extreme loads, such as blast and impact.
The stress-strain curve for Markforged Tough Nylon (Fig. 6), which
has a Poisson’s ratio of 0.4, was input into ABAQUS to simulate the
mechanical response of the bioinspired cellular structure. The model
was assembled from hexagonal brick elements with reduced integration
(C3D8R). A displacement-controlled compressive load was applied to
the structure using ABAQUS explicit, which was chosen over the implicit
approach due to its stability in modelling large deformations and contact
problems. The simulation was terminated at a displacement of 42 mm i.
e., when the densification region in the experiment was adequately
captured. The ABAQUS explicit contact model was used to capture the
interactions between the cell walls: hard contact to predict the normal
behaviour; and the penalty formulation with a friction coefficient of 0.3
to predict the tangential behaviour. No interpenetration was observed
(see Fig. 15).
A convergence study was conducted using an element side length (l)
of 0.5 mm, 0.25 mm and 0.125 mm as shown in Fig. 12, with 6, 12 and
24 elements through the thickness, respectively. It can be observed from
Fig. 13 that the three models exhibit an identical elastic response, with
slight discrepancies in the plateau and densification regions of the forcedisplacement curve. The model with ρ ¼ 0:125 mm terminates prema­
turely due to excessive distortions. Given the similarities of the plateau
and densified response of the dense models, the model with ρ ¼ 0:25 mm
was selected for validation with the experiment due to its stability and
computational efficiency.
It can be observed from Fig. 14 that the FE model captures the
prominent regions of the force-displacement curve of the bioinspired
thin-walled cellular structure, namely linear-elastic, plateau and densi­
fication. Although the onset of densification is predicted prematurely in
the simulation, the elastic stiffness, hardening behaviour in the plateau
region and deformation mechanisms were captured with high accuracy.
The premature prediction of the onset of densification may be attributed
to the 3D printing direction of the extruder, which introduces anisotropy
into the structure. It can be observed from Fig. 15 that the buckling and
collapse mechanisms observed in the experiment were captured, which
are analysed further below. This behaviour will be investigated further
in future research by: analysing the effects of several 3D printing pat­
terns and conducting extensive optimisation studies to extract the
optimal biomimetic design parameters for the intended loading condi­
tions, namely blast and impact. The deformation mechanisms captured
by the FE model are compared with those observed in the experiment
hereafter to further validate the model.
It can be observed in Fig. 15 that the FE model captures the key
buckling and collapse mechanisms in the bioinspired structure that were
observed in the experiment. These observations, which were reported
and analysed in detail in Section 4, are summarised as follows:
� At u ¼ 9 mm, the rotation and buckling mechanisms in the convex
regions of the hybrid cells are captured. However, the convex regions
collapse prematurely in the FE model, which may be attributed to the
artefacts introduced by the 3D printing extrusion process as dis­
cussed previously.
� At u ¼ 16:5 mm, the convex regions of the hybrid cells continue to
collapse and there is contact between their walls. The cells at the
9
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
Fig. 15. Deformation mechanisms of the bio-inspired thin-walled cellular structure. The fringe of the vertical displacement is presented.
base of the structure also collapse. The shapes of the collapsed cells
are relatively consistent with experimental observations.
� At u ¼ 19:5 mm, the hybrid cells have collapsed further. The convex
cells rotate and buckle, and thereby provide stability to the structure.
Their hourglass-like shapes are consistent with experimental
observations.
� At u ¼ 25:5 mm, the buckling and collapse mechanism discussed
above progresses through the structure until the onset of
densification.
6. Conclusions
This research mimicked the concave and convex hybrid cell geom­
etries in the plate-like thin-walled cellular structure of trabecular bone.
10
Thin-Walled Structures 151 (2020) 106713
A. Ghazlan et al.
To this effect, a numerical modelling and manufacturing framework was
developed to automatically generate a finite element model and 3D
printed sample of the bioinspired structure. Due to its automated
manufacturing functionality, the framework was also employed for
fabricating the 3D printed samples of two benchmark structures. The
performance of the bioinspired structure was benchmarked against
these two structures (hexagonal and re-entrant), which have been
extensively investigated in the literature. Compared to the hexagonal
structure, the bioinspired structure showed a 29% reduction in the peak
load and a 69% increase in energy absorption. These significant per­
formance enhancements were attributed to the sequential buckling and
collapse mechanisms of the bioinspired structure, where the hybrid cells
buckled and collapsed whilst the convex cells provided stability. In
contrast, the performance of the re-entrant structure was significantly
compromised due to asymmetric buckling. These results have positive
implications in the design of protective structures, where lightweight
and high energy absorption are of paramount importance. In future
work, several 3D printing patterns will be analysed extensively to study
the effects of anisotropy on the performance of bioinspired thin-walled
cellular structures. The design parameters of the bioinspired thinwalled cellular structure will also be optimised for blast and impact
loading.
[13] R.S. Fecchio, Y. Seki, S.G. Bodde, M.S. Gomes, J. Kolososki, J.L. Rossi, M.A. Gioso,
M.A. Meyers, Mechanical behavior of prosthesis in Toucan beak (Ramphastos
toco), Mater. Sci. Eng. C 30 (2010) 460–464.
[14] Y. Seki, M. Mackey, M.A. Meyers, Structure and micro-computed tomographybased finite element modeling of Toucan beak, J. Mech. Behav. Biomed. Mater. 9
(2012) 1–8.
[15] Y. Seki, M.S. Schneider, M.A. Meyers, Structure and mechanical behavior of a
toucan beak, Acta Mater. 53 (2005) 5281–5296.
[16] Y. Seki, S.G. Bodde, M.A. Meyers, Toucan and hornbill beaks: a comparative study,
Acta Biomater. 6 (2010) 331–343.
[17] G. Imbalzano, T. Ngo, P. Tran, A numerical study of auxetic composite panels
under blast loadings, Compos. Struct. 135 (2015) 339–352.
[18] G. Imbalzano, P. Tran, T. Ngo, P.V. Lee, Three-dimensional modelling of auxetic
sandwich panels for localised impact resistance, J. Sandw. Struct. Mater. (2015)
1–26.
[19] C. Qi, A. Remennikov, L.Z. Pei, S. Yang, Z.H. Yu, T.D. Ngo, Impact and close-in
blast response of auxetic honeycomb-cored sandwich panels: experimental tests
and numerical simulations, Compos. Struct. 180 (2017) 161–178.
[20] A. Remennikov, D. Kalubadanage, T. Ngo, P. Mendis, G. Alici, A. Whittaker,
Development and performance evaluation of large-scale auxetic protective systems
for localised impulsive loads, Int. J. Prot. Struct. 10 (3) (2019) 390–417.
[21] P. Baranowski, P. Platek, A. Antolak-Dudka, M. Sarzynski, M. Kucewicz,
T. Durejko, J. Malachowski, J. Janiszewski, T. Czujko, Deformation of honeycomb
cellular structures manufactured with LaserEngineered Net Shaping (LENS)
technology under quasi-static loading: experimental testing and simulation, Addit.
Manuf. 25 (2019) 307–316.
[22] M. Kucewicz, P. Baranowski, J. Malachowski, A. Poplawski, P. Platek, Modelling,
and characterization of 3D printed cellular structures, Mater. Des. 142 (2018)
177–189.
[23] M. Kucewicz, P. Baranowski, M. Stankiewicz, M. Konarzewski, Modelling and
testing of 3D printed cellular structures under quasi-staticand dynamic conditions,
Thin-Walled Struct. (2019) 145.
[24] M. Kucewicz, P. Baranowski, J. Malachowski, A method of failure modeling for 3D
printed cellular structures, Mater. Des. (2019) 174.
[25] L.J. Gibson, The mechanical behaviour of cancellous bone, J. Biomech. 18 (5)
(1985) 317–328.
[26] M.A. Meyers, P.Y. Chen, A.Y.M. Lin, Y. Seki, Biological materials: structure and
mechanical properties, Prog. Mater. Sci. 53 (2008) 1–206.
[27] P. Fratzl, H.S. Gupta, E.P. Paschalis, P. Roschger, Structure and mechanical quality
of the collagen–mineral nano-composite in bone, J. Mater. Chem. 14 (2004)
2115–2123.
[28] A. Schilling, S. Tofanelli, J. Hublin, T.L. Kivell, Trabecular bone structure in the
primate wrist, J. Morphol. 275 (2014) 572–585.
[29] P. Fratzl, R. Weinkamer, Nature’s hierarchical materials, Prog. Mater. Sci. 52
(2007) 1263–1334.
[30] S.C. Cowin, Bone poroelasticity, J. Biomech. 32 (1999) 217–238.
[31] A. Ghazlan, T. Ngo, P. Tran, Three-dimensional voronoi model of a nacre-mimetic
composite structure under impulsive loading, Compos. Struct. 153 (2016)
278–296.
[32] A. Ghazlan, T. Ngo, P. Tran, Influence of geometric and material parameters on the
behavior of nacreous composites under quasi-static loading, Compos. Struct.
(2017) 457–482.
[33] T. Le, A. Ghazlan, T. Ngo, T. Nguyen, A. Remennikov, A comprehensive review of
selected biological armor systems - from structure-function to biomimetic
techniques, Compos. Struct. 225 (2019) 2–21.
[34] A. Ghazlan, T.D. Ngo, P. Tran, Influence of interfacial geometry on the energy
absorption capacity and load sharing mechanisms of nacreous composite shells,
Compos. Struct. 132 (2015) 299–309.
[35] A. Ghazlan, T. Ngo, N. Lam, P. Tran, A numerical investigation of the performance
of a nacre-like composite under blast loading, Appl. Mech. Mater. 846 (2016)
464–469.
[36] T. Wejrzanowski, J. Skibinski, J. Szumbarski, K.J. Kurzydlowski, Structure of foams
modeled by Laguerre-Voronoi tessellations, Comput. Mater. Sci. 67 (2013)
216–221.
[37] L. Tang, X. Shi, L. Zhang, Z. Liu, Effects of statistics of cell’s size and shape
irregularity on mechanical properties of 2D and 3D voronoi foams, Acta Mech. 225
(2014) 1361–1372.
[38] I. Benedetti, M.H. Aliabadi, A three-dimensional grain boundary formulation for
microstructural modeling of polycrystalline materials, Comput. Mater. Sci. 67
(2013) 249–260.
[39] Z. Fan, Y. Wu, X. Zhao, Y. Lu, Simulation of polycrystalline structure with Voronoi
diagram in Laguerre geometry based on random closed packing of spheres,
Comput. Mater. Sci. 29 (2004) 301–308.
[40] G. Imbalzano, S. Linforth, T.D. Ngo, P.V.S. Lee, P. Tran, Blast resistance of auxetic
and honeycomb sandwich panels: comparisons and parametric designs, Compos.
Struct. 183 (2018) 242–261.
[41] P. Tran, T.D. Ngo, A. Ghazlan, D. Hui, Bimaterial 3D printing and numerical
analysis of bio-inspired composite structures under in-plane and transverse
loadings, Composites Part B 108 (2017) 210–223.
[42] S.R.G. Bates, I.R. Farrow, R.S. Trask, 3D printed polyurethane honeycombs for
repeated tailored energy absorption, Mater. Des. 112 (2016) 172–183.
[43] M. de Berg, O. Cheong, M. van Kreveld, M. Overmars, Voronoi diagrams, in:
Computational Geometry: Algorithms and Applications, Springer-Verlag, Berlin
Heidelberg, 2008, pp. 147–170.
Declaration of competing interest
None.
CRediT authorship contribution statement
Abdallah Ghazlan: Conceptualization, Methodology, Writing original draft, Formal analysis. Tuan Nguyen: Investigation, Validation.
Tuan Ngo: Supervision, Funding acquisition. Steven Linforth: Writing review & editing. Van Tu Le: Validation.
Acknowledgements
This research was funded through the ARC Discovery Project
DP170100851.
References
[1] M.J. Silva, L.J. Gibson, Modeling the mechanical behavior of vertebral trabecular
bone: effects of age-related changes in microstructure, Bone 21 (2) (1997)
191–199.
[2] F. Bini, A. Pica, A. Marinozzi, F. Marinozzi, 3D diffusion model within the collagen
apatite porosity: an insight to the nanostructure of human trabecular bone, PloS
One (2017) 1–17.
[3] M.R. Rogel, H. Qiu, G.A. Ameer, The role of nanocomposites in bone regeneration,
J. Mater. Chem. 18 (2008) 4233–4241.
[4] H. Isaksson, S. Nagao, M. Malkiewicz, P. Julkunen, R. Nowak, J.S. Jurvelin,
Precision of nanoindentation protocols for measurement of viscoelasticity in
cortical and trabecularbone, J. Biomech. 43 (2010) 2410–2417.
[5] G.N. Karam, L.J. Gibson, Biomimicking of animal quills and plant stems: natural
cylindrical shells with foam cores, Mater. Sci. Eng. C 2 (1994) 113–132.
[6] F.G. Torres, O.P. Troncoso, J. Diaz, D. Arce, Failure analysis of porcupine quills
under axial compression reveals their mechanical response during buckling,
J. Mech. Behav. Biomed. Mater. 39 (2014) 111–118.
[7] J.F.V. Vincent, P. Owers, Mechanical design of hedgehog spines and porcupine
quills, J. Zool. A 210 (1986) 55–75.
[8] W. Yang, J. McKittrick, Separating the influence of the cortex and foam on the
mechanical properties of porcupine quills, Acta Biomater. 9 (2013) 9065–9074.
[9] B. Achrai, H.D. Wagner, The turtle carapace as an optimized multi-scale biological
composite armor–A review, J. Mech. Behav. Biomed. Mater. 73 (2017) 50–67.
[10] T.R. Lyson, B.S. Rubidge, T.M. Scheyer, K. de Queiroz, E.R. Schachner, R.M. Smith,
J. Botha-Brink, G. Bever, Fossorial origin of the turtle shell, Curr. Biol. 26 (14)
(2016) 1887–1894.
[11] Y. Shelef, B. Bar-On, Surface protection in bio-shields via a functional soft skin
layer: lessons from the turtle shell, J. Mech. Behav. Biomed. Mater. 73 (2017)
68–75.
[12] W. Zhang, C. Wu, C. Zhang, Z. Chen, Microstructure and mechanical property of
turtle shell, Theor. Appl. Mech. Lett. 2 (1) (2012) 44–48.
11
A. Ghazlan et al.
Thin-Walled Structures 151 (2020) 106713
[44] S. Linforth, P. Tran, M. Rupasinghe, N. Nguyen, T. Ngo, M. Saleh, R. Odish,
D. Shanmugam, Unsaturated soil blast: flying plate experiment and numerical
investigations, Int. J. Impact Eng. 125 (2019) 212–228.
[45] T.D. Ngo, A. Kashani, G. Imbalzano, K.T.Q. Nguyen, D. Hui, Additive
manufacturing (3D printing): a review of materials, methods, applications and
challenges, Composites Part B 143 (2018) 172–196.
[46] X. Ren, R. Das, P. Tran, T.D. Ngo, Y.M. Xie, Auxetic metamaterials and structures: a
review, Smart Mater. Struct. 27 (2) (2018).
12