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Characterization of a Mechanically Tunable Gyroid Photonic Crystal Inspired by the Butterfly Parides Sesostris

Authors:
  • AMOLF & Eindhoven University of Technology

Abstract and Figures

A mechanically tunable macroscale replica of the gyroid photonic crystal found in the Parides sesostris butterfly's wing scales is systematically characterized. By monitoring both photonic frequency changes and the distribution of stress fields within the compressed structure, electromagnetic transmission features are found and can be frequency-tuned and the structure only contains localized high stress fields when highly compressed.
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geometries. Using the naturally occurring photonic gyroid
found in the wing scales of Parides sesostris butterfl ies
[ 28 ] as an
experimental model system ( Figure 1 ), we employed high-reso-
lution additive manufacturing to replicate its 3D architectural
details in a reversibly deformable macro-scale analogue. We
specifi cally used a fi lling fraction of 40% that closely matches
the fi lling fraction of the butterfl y gyroid.
[ 28 ] The tunability of
the deformable PC’s electromagnetic properties can be inves-
tigated by imposing controlled anisotropic deformations of the
crystal structure through compressive loading. By fabricating
exible dielectric PCs with centimeter-scale unit cells, it is pos-
sible to produce materials with tunable photonic responses
in the microwave regime (0.3–300 GHz). By exploiting the
scale-invariance of Maxwell’s equations and of the elastic
material response, the structure–function relationships of
photonic materials can be directly investigated. By working
at the macroscale, we are taking full advantage of the design
freedom of additive manufacturing, comprehensive optical
characterization using microwave technology, and the in situ
3D structural characterization capabilities of microscale X-ray
computed tomography. This method could readily be applied
to assess any other structural motif in a similar manner. Once
the fundamental structure–function relationships underlying
the dynamics of reversibly deformable photonic materials are
understood at the macroscale, this insight can be applied for
the realization of structural motifs at smaller length scales to
create tunable photonic devices for the Terahertz, Telecom,
Near-IR, visible, UV, and X-ray frequency ranges.
Inspection of P. sesostris (Figure 1 ) reveals that the brightly
colored metallic appearance of the green wing patches origi-
nates from scales that are not individually resolvable by the
human eye (Figure 1 C–E). These scales have a complex mor-
phology, including surface ridges (Figure 1 D–G),
[ 33–35 ] spec-
trally selective pigment-based absorbers, as proposed by Wilts
et al.,
[ 35 ] and an underlying gyroid PC (Figure 1 G),
[ 28,33–38 ] rst
proposed by Michielsen and Stavenga
[ 28 ] arranged in intrascale
domains (Figure 1 F), [ 28,33–38 ] which are all expected to contribute
to the scales’ optical appearance.
[ 28,30,35–38 ] A graphical repre-
sentation of the gyroid is presented in Figure 1 H, with its unit
cell highlighted in green. Using the key dimensional parame-
ters obtained from previous transmission electron microscopy
(TEM) studies,
[ 28 ] a fl exible macroscale model of the gyroid was
fabricated using high-resolution 3D printing ( Figure 2 A,B).
The resulting structure was investigated to see if its photonic
response could be deliberately tuned and controlled by system-
atically varying the applied compressive load.
In order to characterize the gyroid’s deformation modes,
X-ray computed microtomographic (micro-CT) reconstructions
were obtained from the fl exible 3D-printed models at various
Characterization of a Mechanically Tunable Gyroid Photonic
Crystal Inspired by the Butterfl y Parides Sesostris
Caroline Pouya , * Johannes T. B. Overvelde , Mathias Kolle , Joanna Aizenberg ,
Katia Bertoldi , James C. Weaver , and Pete Vukusic *
Dr. C. Pouya, Prof. P. Vukusic
School of Physics and Astronomy
University of Exeter
Exeter EX4 4QL , UK
E-mail: C.Pouya@exeter.ac.uk; P.Vukusic@exeter.ac.uk
J. T. B. Overvelde, Prof. K. Bertoldi
School of Engineering and Applied Sciences
Harvard University
Cambridge , MA 02138 , USA
Dr. M. Kolle, Prof. J. Aizenberg, Dr. J. C. Weaver
Wyss Institute for Biologically Inspired Engineering
Harvard University
Cambridge , MA 02138 , USA
Dr. M. Kolle
Department of Mechanical Engineering
MIT, Cambridge , MA 02139 , USA
DOI: 10.1002/adom.201500436
Photonic crystals [ 1–5 ] (PCs) can be used to selectively refl ect spe-
cifi c frequencies of electromagnetic radiation. Since most PCs
are static in material composition and geometry, their refl ec-
tion or transmission behavior can only be changed through
angular reorientation. In contrast, fl exible PCs can exhibit tun-
able photonic responses,
[ 3,5–7 ] where refl ected or transmitted
frequencies can be controlled through structural deformation.
Tunable responses can also be achieved via the application
of voltage,
[ 8,9 ] by adsorption of vapors,
[ 10,11 ] via temperature
modulation,
[ 12,13 ] or by the application of strain.
[ 14–16 ] Recently,
increased efforts have been aimed at fabricating 1D,
[ 16 ] 2D, [ 17,18 ]
and 3D
[ 19 ] tunable PCs. Since the requirements imposed on PC
geometry and material compositions vary between applications,
the development of robust fabrication strategies for the custom-
izable and large-scale production of 3D PCs is a research area
of great interest. Accordingly, material scientists have embraced
the study of structurally colored biological photonic systems
to gain inspiration for synthesis routes that can facilitate the
fabrication of novel optical materials with exploitable proper-
ties.
[ 16–20 ] Such biological photonic structures found in terres-
trial and aquatic environments typically comprise polymeric
materials including keratin, cellulose, and chitin. They exhibit a
wide range of geometries including colloidal particles,
[ 21,22 ] con-
tinuous
[ 23 ] or discrete units of multilayers,
[ 24,25 ] concentric cylin-
ders,
[ 16,26 ] and bicontinuous gyroids.
[ 27–30 ] Despite the promise
of new biologically inspired design routes for photonic material
production, there is currently a dearth of cost-effective high-
throughput methods by which synthetic analogues of these bio-
photonic materials can be fabricated.
In an effort to address these limitations, we have utilized
an effi cient experimental approach to investigate electromag-
netic responses
[ 31,32 ] and structural properties of tunable gyroid
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stages of compression ( Figure 3 ). The reconstructions of the
deformed gyroid models were then compared to the results
obtained from the fi nite element analysis (FEA) compression
simulations ( Figure 4 A). The nonlinear fi nite element simula-
tions were performed on virtual gyroid models constructed from
approximately 10 000 tetrahedral elements per unit cell, which
were compressed uniaxially by applying a vertical displacement
to the top face, while leaving all lateral faces free to expand. The
results obtained from these studies revealed that the mechan-
ical response of the gyroid was only moderately affected by the
number of unit cells. Models comprising 3×3×3, 5×5×5, and
7×7×7 unit cells exhibited a similar extent of lateral expan-
sion. In particular, for a gyroid containing 7×7×7 unit cells, the
maximum lateral expansion was measured to be 2.15%, 4.38%,
6.78%, and 9.25% for applied strain values of 5.6%, 11.1%,
16.7%, and 22.2%, respectively. These values correlated well
with the 10×10×10 structure tested experimentally, in which
the maximum lateral expansion was observed to be 9.7% at a
compression of 22.2%. The results of these simulations are pre-
sented in Figure 4 , clearly showing the large geometric changes
induced by the applied compression. The contour colors cor-
respond to the Von Mises stress ij ij kk
σσσσ
=−
3
2
1
2
VM
2,
σ
ij
denoting a component of the Cauchy stress), where the most
highly stressed regions are denoted in red. Signifi cantly, these
stress fi eld intensity data (Figure 4 A) revealed that, at moderate
compressions, the stress is very uniformly distributed over the
unit cell, only beginning to show the tendency to localize at
much higher compressions. This form of resistance to shear
stress in the gyroid, highlighted previously by different studies
on primitive and diamond structures,
[ 39 ] is a property that
would improve the system’s toughness.
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Figure 1. Mechanistic origins of structural color in the neotropical butterfl y, Parides sesostris. Located on A) the wings of P. sesostris are B) striking
metallic green patches and C–F) high-resolution structural characterizations of their constituent scales reveals a complex composite architecture con-
sisting of E) surface ridges and F) an underlying photonically active multi-domain gyroid.
[ 33,34 ] D) shows an electron beam Moiré pattern, generated by
matching the e-beam scanning periodicity with the structural periodicity of the wing scales. G)
[ 33,34 ] shows a the 3D structure present within P. sesostris
wing scales, which can be graphically represented by H) the photonic gyroid structure with an individual unit cell highlighted in green. For reference,
each scale measures 150 µm in length. Scale bars: A) 1 cm, B) 5 mm, C) 200 µm, D) 50 µm, E) 10 µm, F) 4 µm, G) 2.5 µm.
3
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Excluding the boundary effects where the physical gyroid
model contacted the compression plates, the X-ray computed
micro-tomography and FEA data sets agreed surprisingly well
within the bulk core of the gyroid, thereby providing a robust
model for performing realistic microwave electromagnetic
transmission simulations. Figure 4 B,C show the theoretical and
experimental transmitted fi eld magnitude data, respectively,
obtained using transverse magnetic incident polarization, with
respect to the plane of incident radiation, from the compliant
gyroid. The structure was compressed in the [100] direction by
0%, 5.6%, 11.1%, 16.7%, and 22.2% of the original size of the
gyroid model. The observed frequency shifts that occurred upon
compression of the sample were similar for both transverse
magnetic and the equivalent transverse electric polarizations.
Based on these observations and since the linear polarization
dependence of the gyroid has been discussed previously,
[ 29,32 ]
the transverse electric results are not presented here. The
sample was positioned at an azimuthal angle of
φ
= 0° and was
rotated over a polar angle range of 45°
θ
45° for each com-
pressed state (Figure 2 C). The dark bands in Figure 4 B,C are
representative of low electromagnetic transmission through the
gyroid PC structure for each of the indicated states of compres-
sion. The frequency axes are presented in normalized reduced
frequency units of c/a where c is the speed of light in free space
and a is the uncompressed lattice constant of 9 mm. In the
native, uncompressed state, two of the transmission minima
(labeled “P” and “Q” on the central graph of Figure 4 B) are in
very close proximity and appear to overlap or merge, particu-
larly at normal incidence. As compression of the sample begins
to extend beyond 11.1%, these previously overlapping features
separate into two discrete and distinctly resolvable bands (“P”
and “Q”). From theoretical electric fi eld plots (Figure S1, Sup-
porting Information) and geometric analyses, these two fea-
tures originate from standing wave-type resonances along the
[101] and [001 ] directions (labeled “P” and “Q,” respectively,
on the central graph of Figure 4 B). The resonant feature labeled
“P” on the central graph of Figure 4 B also results from signifi -
cant absorption. When the structure is uncompressed, the fre-
quency position of these features also lies close to the crossing
point of a third feature (labeled “R” on Figure 4 B), which origi-
nates from a standing wave-type resonance along the
[001 ]
direction. When compressed by 22.2%, in the [100] direction as
described, the gyroid model's central region expands by 9.7%
along the
[001 ] direction. From trigonometric analysis, and by
using these expansion values, we can identify similar expan-
sions across the [010],
[001 ], and [011] directions with corre-
sponding decreases in frequency of the resonant features (“Q”
and “R” on Figure 4 B) associated with these directions. Simi-
larly, the structural confi gurations in the [100] and
[101] direc-
tions are reduced to 77.8% and 95.1% of their original sizes:
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Figure 2. Fabrication and characterization of the gyroid photonic crystal. High-resolution additive manufacturing was used to generate a A,B) com-
pressible gyroid from a rubber-like polymer (permittivity of
ε
= 2.85 + 0.15i). C) illustrates a schematic diagram of the microwave transmission experi-
mental set-up, showing the relative positions of the broadband horns, the gyroid photonic crystal sample, and the compression device.
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Figure 4 B,C show a corresponding increase in frequency of the
associated resonant features along these directions (labeled “P”
on Figure 4 B). At 22.2% compression, the experimentally deter-
mined frequency shifts of each transmission minimum, in
reduced units, were measured to be 0.072 (c/a), 0.039 (c/a), and
0.177 (c/a) (Figure 4 C) for the features labeled “R,” “Q,” and
“P,” respectively, in Figure 4 B. These values were measured
at the polar angle of 45° (Figure 4 C). As a result of the gyro-
id's bicontinuous nature (consisting of a solid/polymer phase
and a void/air phase), the application of a compressive load
results in a net volume reduction of the structure (Figure 3 ).
This increase in material fi lling fraction directly corresponds
to a slight narrowing of the transmission minima, which is
observed both theoretically (Figure 4 B) and experimentally
(Figure 4 C). A very slight red-shift in frequency is also expected
from a change in fi lling fraction away from the optimum condi-
tion for large stop-band width as occurs in the uncompressed
gyroid structure.
[ 28,32 ] For the simulated gyroid modeling, when
the maximum compression of 22.2% was applied to the struc-
ture, the frequency shifts of each of the corresponding features
labeled “R,” “Q,” and “P,” respectively, in the theoretical data
plots (Figure 4 B) were measured to be approximately 0.057,
0.033, and 0.165, in reduced frequency units ( c/a ). These values
were also measured at the polar angle of 45° (Figure 4 C). These
frequency changes were marginally smaller than those obtained
from the experimental measurements, with a slight variability
in fi lling fraction and the lack of graded expansions, being the
most likely contributing factors.
[ 40 ]
In conclusion, through both theoretical and experimental
approaches, in this study, we have performed a quantitative
assessment of a fl exible gyroid PC structure and compression-
dependent optical response. We found that, when compressed,
previously overlapping transmission minima spectrally sepa-
rate. While this observed overlap in dispersion features and
consequent shifting behavior will only occur for specifi c geom-
etries, similar results are predicted for other PC structures that
exhibit a similar bcc Bravais lattice symmetry. Through the
structural investigation, we also found that the gyroid does not
tend to localize stresses but uniformly distributes them at mod-
erate compressions. This structural property is of particular
importance from a mechanical engineering perspective as it
would greatly enhance the toughness of the system. A robust
sample that can withstand variable degrees of structural defor-
mation is a necessity when designing and mechanically tuning
a robust photonic system.
As shown in these studies, the capacity of 3D printing to
rapidly create prototypes of almost any morphology in a broad
range of material compositions makes it an ideal tool to build
and systematically experimentally investigate macroscale
photonic materials that can be assessed electromagnetically in
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Figure 3. Micro-CT reconstructions of the compressible gyroid. X-ray computed microtomographic reconstructions of the 3D-printed gyroid in its
uncompressed state and when compressed by 22.2% of its original size, clearly showing the reduction of volume fraction upon loading and the cor-
responding lateral expansion of the structure.
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the microwave regime and structurally characterized through
micro-CT. Consequently, the photonic response of periodic
geometric solids, such as the single gyroid, can be dynami-
cally tuned for a specifi c application of interest, while providing
critical design cues for the fabrication of their micro- and
nanoscale structural analogues.
Experimental Section
Research Species : Dry specimens of P. sesostris were acquired from
commercial sources (Worldwide Butterfl ies (http://www.wwb.co.uk)).
For optical characterization, the wings were imaged with a Keyence
digital microscope (VHX-2000). The same samples were then mounted
to conductive carbon tape, sputter-coated with gold, and examined with a
Tescan VegaIII scanning electron microscope (SEM). For the generation
of electron beam Moiré patterns, the SEM scan line periodicity was
matched to the ridge periodicity in the wing scales, thus permitting the
illustration of nanoscale structural periodicity in a macroscale sample.
Using information from previously published TEM studies,
[ 28,34 ] the
critical parameters of the gyroid structure, principally its fi lling fraction
of 40%, were identifi ed.
Gyroid Modeling and Fabrication : Gyroid model rendering for
3D-printing compatible STereoLithography (.stl) fi les was achieved with
a custom-made MATLAB code.
[ 41 ] Briefl y, level set functions were used
as versatile approximations to calculate inter-material dividing surfaces
of the gyroid.
[ 28,42–46 ] In particular, to describe the surface of the gyroid
structure investigated in this study, we used Equation ( 1) with t = 0.3
and L = 9 mm.
[ 41 ]
LxLyLyLzLzLxtsin 2cos 2sin 2cos 2sin 2cos 2
ππ ππ ππ
()() ()() ()()
++= (1)
Vertices and facets of these surfaces were then rendered using
MATLAB’s isosurface function. Facet normals and vertex coordinates
were written to an STL fi le directly from MATLAB using a custom
script. The resulting 3D model had a material fi lling fraction of 40%
and a lattice constant a = 9 mm (Figures 2 , 3 ), designed so that the
model’s structure was directly analogous to the P. sesostris wing-scale
Adv. Optical Mater. 2015,
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Figure 4. A) Finite element compression simulations of the gyroid and B) its corresponding theoretical and C) experimental photonic responses. FEA
simulations of A) the fl exible gyroid reveal a relatively uniform strain fi eld through the entire experimental loading regime. The results shown here are
extracted from a 6×6×6 unit cells simulation, and show the internal deformation, which is not affected by boundaries. B) Theoretical and C) experimental
transmitted fi eld magnitude data showing the resonant electromagnetic features associated with the gyroid photonic crystal structure with an initial
material volume fraction of 40% and lattice constant of 9 mm using transverse magnetic linearly polarized incident radiation.
[ 40 ] The structure was com-
pressed by 0%, 5.6%, 11.1% 16.7%, and 22.2%, from left to right in (B) and (C), across the [100] direction. A reduced frequency regime was employed,
normalized by the initial lattice constant value of a = 9 mm and c , the speed of light in free space. The sample was rotated over a polar angle range of
45°
θ
45° at an azimuthal angle of
φ
= 0° for each compressed state.
[ 40 ] The labels “P,” “Q,” and “R” (shown only in the central graph of Figure 4 B)
refer to individual dispersion features that originate from resonances in the [101], [001], and [011] directions, respectively, through the gyroid.
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gyroid system
[ 28 ] but suitable for electromagnetic characterization using
microwave radiation. The models were then fabricated using a Stratasys
Connex500 3D printer from a rubber-like UV cross-linkable material
(TangoBlack+). The model was fabricated using a 32 µm z-step height,
which resulted in a high quality smooth surface fi nish without any
visible layers (a common problem for thermoplastic fi lament-based 3D
printing methods). The fabrication process lasted several hours. Based
on established techniques,
[ 47,48 ] the material permittivity was measured
to be
ε
= 2.85 + 0.15i in the frequency regime used for our experiments.
The key geometrical parameter that was replicated from the P. sesostris
gyroid was the material fi lling fraction, which was 40%.
[ 28 ] The remaining
volume was air, which was easily displaced throughout the system upon
compression due to the bicontinuous nature of the gyroid. Gyroids were
fabricated with 5×5×5 and 10×10×10 unit cells dimensions in order to
explore the high- and low-resolution response of this material under
different loading regimes. For the microwave studies, a 10×10×10 unit
cell structure was fabricated such that the incident face was parallel to
the (001) set of periodic planes of its photonic structure.
Microcomputed Tomography Studies : For micro-CT studies, the gyroid
model was scaled up by a factor of two and the 3D model was reprinted
in a 5×5×5 geometry in order to obtain better X-ray transmission
and a more detailed 3D reconstruction during the various stages of
deformation. In order to visualize the gyroid under compression at the
specifi c strain levels of interest, the specimen was immobilized using
a fi xture made of acrylic plates, nylon bolts/nuts and 2.5 cm thick rigid
closed-cell foam plates placed between the specimen and the fi xture (see
Figure S2, Supporting Information). The foam plates were used as low-
electron-density spacers that would be nearly invisible in the acquired
X-ray transmission images and thus not interfere with volume rendering
of the higher-electron-density gyroid. The gyroid/fi xture assembly was
then placed into a XRA-002 X-Tek micro-CT system for image data
collection. The 3D reconstructions were performed using CT-Pro (Nikon
Metrology) and the surface renderings were generated using VGStudio
Max.
Gyroid Modeling for Finite Element Analysis Compression Studies :
Static nonlinear FEA of the gyroid structure was performed using the
commercial fi nite element software Abaqus/Standard. The material was
modeled using a nearly incompressible neo-Hookean model, whose
energy is given by
WI KJ
μ
()
=−+−
2(3)
21
1
2
where µ and K are the initial shear and bulk moduli, respectively.
Moreover, J = det F and FFFFIJ TT
1
2
3
()
= where F is the deformation
gradient. Note that in all our simulations, we assumed that K =
10 000, so that the material response is nearly incompressible. The
mesh was built using linear hybrid solid elements (Abaqus element type
C3D4H). Models comprising 3×3×3, 5×5×5, and 7×7×7 unit cells were
compressed uniaxially by applying a vertical displacement to the top
face, while leaving all lateral faces free to expand. During the analysis,
the maximum lateral expansion was monitored as a function of the
applied compression. The results obtained from the FEA compression
simulations agreed well with the compression results obtained from the
experimental micro-CT studies and were thus used as a basis for the
corresponding microwave simulations.
Experimental and Simulated Electromagnetic Studies : For the
experimental electromagnetic characterization, the compliant 10×10×10
gyroid was placed inside a custom-designed compression device
(Figure 2 C), which was centered between aligned source and detector
microwave broadband horns (Flann model DP241-AB; dual-polarized
horn; option 10–50 GHz). These were connected to an Anritsu Vector
Star 70 kHz to 70 GHz vector network analyzer (VNA) (Figure 2 C). The
source horn emitted a Gaussian microwave beam with a full-width half
maximum of approximately 5 cm measured at a distance of 22 cm away
from the source, which corresponded to the relative sample position
in the experimental set-up.
[ 40 ] The compression device applied a force
to the gyroid in a direction orthogonal to that of the incident beam as
shown in Figure 2 C. The gyroid was rotated over a polar angle range of
45°
θ
45° at each compressed state and the transmitted magnitude
was recorded. Due to the number of unit cells across the sample and
the signal attenuation by the constituent material, absorption occurred,
particularly at the edges of resonant electromagnetic features and at
higher frequencies. As a result, transmitted microwave magnitude was
used in all graphical plots to clearly illustrate the presence and frequency
change of the electromagnetic features. The sample was compressed
by 0%, 5.6%, 11.1%, 16.7%, and 22.2% of the initial array size and the
resulting transmitted magnitude data was recorded.
In order to perform analogous numerical modeling of the
transmission, the fi nite element method software HFSS was used
(Ansoft HFSS, Version 13.0.0, ANSYS, Inc.). When building the model,
the sample was assumed to expand uniformly in directions orthogonal
to that of compression, an assumption that was validated by the FEA
deformation analysis and experiments. The expansion value was taken
as the measured maximum expansion across the mid-plane of the
structure since the Gaussian beam used in the experiments centers
most of its power in this region. The electromagnetic simulation was
performed on a gyroid array comprising 5 unit cells in the comparable
z -direction, and infi nite in the x- and y- directions for computing
effi ciency. The same real and imaginary values of permittivity were used
to defi ne material properties in the simulations. Using fewer unit cells
along this z -direction results in a reduction of signal attenuation by the
constituent materials, compared to the fabricated sample. An incident
plane wave was used for excitation in the model and the transmitted
electromagnetic fi eld magnitude was measured over a range of angle
and compression values. The initial lattice constant, fi lling fraction, and
refractive indices used in the modeling were identical to those of the
sample used in the electromagnetic experiments.
Supporting Information
Supporting Information is available from the Wiley Online Library or
from the author.
Acknowledgements
The authors thank Nick Cole for construction of the custom-made
compression device used in the microwave spectroscopy experiments
and Dr. Maik Scherer for providing a customized MATLAB code for
the rendering of virtual gyroid models. C.P. acknowledges fi nancial
support from The University of Exeter EPSRC DTA. M.K. acknowledges
nancial support from the Alexander von Humboldt Foundation in the
form of a Feodor-Lynen Postdoctoral Research Fellowship. P.V. and J.A.
acknowledge fi nancial support from AFOSR Multidisciplinary University
Research Initiative under FA9550-10-1-0020 and FA9550-09-1-0669-
DOD35CAP. This work was performed in part at Harvard University’s
Center for Nanoscale Systems (CNS), a member of the National
Nanotechnology Infrastructure Network (NNIN), which is supported by
the National Science Foundation under NSF award no. ECS-0335765.
Received: August 5, 2015
Published online:
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CopyrightWILEYVCHVerlagGmbH&Co.KGaA,69469Weinheim,Germany,2015.
SupportingInformation
forAdvancedOpticalMaterials,DOI:10.1002/adom. 201500436
Characterization of a Mechanically Tunable Gyroid Photonic
Crystal Inspired by the Butterfl y Parides Sesostris
Caroline Pouya,* Johannes T. B. Overvelde, Mathias Kolle,
Joanna Aizenberg, Katia Bertoldi, James C. Weaver, and Pete
Vukusic*
1
Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2015.
Supporting Information
Characterization of a Mechanically Tunable Gyroid Photonic Crystal Inspired by the
Butterfly Parides sesostris
Caroline Pouya*, Johannes T. B. Overvelde, Mathias Kolle, Joanna Aizenberg, Katia
Bertoldi, James C. Weaver, and Pete Vukusic*
Figure S1.
The arrangement of time-averaged electric fields over either the material or air labyrinths of
the gyroid at the associated band edges of the transmission features P, Q, and R in figure 4b.
Field plots were obtained from either the air or material band-edge of each observed ‘stop-
band’ using the finite element method modeling software HFSS (Ansoft HFSS, Version
13.0.0, ANSYS, Inc.). The images show 5 unit cells in the depth of the structure (z) and a
section one unit cell in size in all other dimensions. The orientation of the gyroid sections
shown here are such that one side of the structure is in view in each case. For instance, the
electric field arrangement labelled ‘Q’ appears to be a repeated high and low electric field
distribution directed along the [101] direction (i.e. in the x-z plane). The compressive force
applied to the structure was in the x-direction and expansions occurred in the y- and z-
directions and the materials used possessed the same real and imaginary permittivity as the
printed experimental sample.
2
Figure S2.
Schematic illustration of the experimental set up for microCT scanning of the flexible 3D-
printed gyroid, showing the X-ray transparent closed cell foam plates and the surrounding
support structure composed of acrylic plates held in place by nylon bolts and nuts.
... Nature has resolved the problem of low weight accompanied by high surface area and curvature with creating specific micro-geometries known as triply minimally periodic surface (TPMS). TPMS structures can be found in butterfly wings (Pouya et al., 2016), sea urchin (Lai et al., 2007), block copolymers (Matsen and Bates, 1996), and soap films (Schoen, 1970). The unit cells inspired by the noted natural structures, which are also the most favorable structures among the researchers in the field (Soyarslan et al., 2019;du Plessis et al., 2020;Abueidda et al., 2017), will be implemented in this study for constructing shape-memory TPMS-based metamaterials (Fig. 1). ...
... The top row demonstrates the macro-scale visualization of the natural creature, the mid-row demonstrates the micro-or nano-scale visualization of the natural creatures, and the bottom row depicts the nature-inspired unit cells. First column: a) butterfly wings (Pouya et al., 2016), (b) micro-structure of butterfly wing (Pouya et al., 2016), and (c) gyroid TPMS-based unit cell. Second column: (d) The sea urchin, (e) micro-structure of a cross-section through a sea urchin skeletal plate (Lai et al., 2007), and (f) primitive TPMS-based unit cell. ...
... The top row demonstrates the macro-scale visualization of the natural creature, the mid-row demonstrates the micro-or nano-scale visualization of the natural creatures, and the bottom row depicts the nature-inspired unit cells. First column: a) butterfly wings (Pouya et al., 2016), (b) micro-structure of butterfly wing (Pouya et al., 2016), and (c) gyroid TPMS-based unit cell. Second column: (d) The sea urchin, (e) micro-structure of a cross-section through a sea urchin skeletal plate (Lai et al., 2007), and (f) primitive TPMS-based unit cell. ...
Article
Full-text available
Triply periodic minimal surfaces (TPMS) metamaterials and shape-memory polymer (SMP) smart materials are known for their beneficial attributes in novel scientific and industrial fields. Through TPMS designs, low weight accompanied by high surface area are achievable, which are known as crucial parameters in many fields, such as tissue engineering. Moreover, SMPs are well-suited to generate force or to recover their permanent shape by means of an external stimulus. Combining these properties is possible by fabricating TPMS-based metamaterials made out of SMPs, which can be applicable in numerous applications. By considering different level volume fraction of four types of TPMS-based lattices (diamond, gyroid, IWP, and primitive), we focus on the effect of micro-architecture on shape-memory characteristics (i.e., shape recovery, shape fixity, and force recovery) as well as mechanical properties (elastic modulus and Poisson's ratio) of these smart metamaterials. For this purpose, shape-memory effect (SME) is simulated employing thermo-visco-hyperelastic constitutive equations coupled with the time-temperature superposition principle. It is observed that by increasing the level volume fraction of each lattice type, the elastic modulus, shape fixity, and force recovery increase, while the shape recovery diminishes. Such behaviors can be attributed to different deformation modes (flexural or uniaxial) in SMP metamaterial TPMS-based structures. Furthermore, it is shown that the Poisson's ratio has a nonlinear behavior in these structures. The smart metamaterials introduced in this study have the advantage of providing the possibility of designing implants, especially in bone defects tailored with different micro-architectures depending on each patient's specific need.
... Furthermore, the wave energy will be weakened after multiple reflections in the internal architectures of TPMS porous structures. Hence, TPMS structures are also ideal choices for sound absorbers [64,65], electromagnetic microwave absorption [66], photonic crystal [67], as shown in figure 1. ...
... Copyright 2017, American Chemical Society [66]. Copyright 2021, Elsevier [67]. Copyright 2015, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim [56]. ...
... Larger phononic bandgaps can even be obtained by higher density contrast between the material components of the structures. Electromagnetic radiation with specific frequencies can be reflected by the photonic crystals [67]. However, for photonic crystals with stable geometries, the frequency of the electromagnetic radiation which can be reflected is also unchangeable. ...
Article
Full-text available
Inspired by natural porous architectures, numerous attempts have been made to generate porous structures. Owing to the smooth surfaces, highly interconnected porous architectures, and mathematical controllable geometry features, triply periodic minimal surface (TPMS) is emerging as an outstanding solution to constructing porous structures in recent years. However, many advantages of TPMS are not fully utilized in current research. Critical problems of the process from design, manufacturing to applications need further systematic and integrated discussions. In this work, a comprehensive overview of TPMS porous structures is provided. In order to generate the digital models of TPMS, the geometry design algorithms and performance control strategies are introduced according to diverse requirements. Based on that, precise additive manufacturing methods are summarized for fabricating physical TPMS products. Furthermore, actual multidisciplinary applications are presented to clarify the advantages and further potential of TPMS porous structures. Eventually, the existing problems and further research outlooks are discussed.
... Discovered in 1970 by A. Schoen, a gyroid commonly features a triply periodic surface with a constant mean curvature (CMC) of zero [1]. This unique structural characteristic can endow the peculiar optical properties of matterfrom subwavelength-scale optical metamaterials [2][3][4][5][6][7][8][9][10] to wavelength-scale photonic crystals [11][12][13][14][15][16][17][18][19][20][21]. Specifically, over the last two decades, fruitful theoretical [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and experimental [13,[15][16][17][31][32][33][34][35][36] achievements have been reported regarding this topic. ...
... This unique structural characteristic can endow the peculiar optical properties of matterfrom subwavelength-scale optical metamaterials [2][3][4][5][6][7][8][9][10] to wavelength-scale photonic crystals [11][12][13][14][15][16][17][18][19][20][21]. Specifically, over the last two decades, fruitful theoretical [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and experimental [13,[15][16][17][31][32][33][34][35][36] achievements have been reported regarding this topic. However, the importance of gyroids as an optical structure was not well recognized during the 1970-1990s, because a gyroid had rarely been realized, especially at the nanoscale [37][38][39]. ...
... This unique structural characteristic can endow the peculiar optical properties of matterfrom subwavelength-scale optical metamaterials [2][3][4][5][6][7][8][9][10] to wavelength-scale photonic crystals [11][12][13][14][15][16][17][18][19][20][21]. Specifically, over the last two decades, fruitful theoretical [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] and experimental [13,[15][16][17][31][32][33][34][35][36] achievements have been reported regarding this topic. However, the importance of gyroids as an optical structure was not well recognized during the 1970-1990s, because a gyroid had rarely been realized, especially at the nanoscale [37][38][39]. ...
Article
Full-text available
A gyroid crystal possesses a peculiar structural feature that can be conceptualized as a triply periodic surface with a constant mean curvature of zero. The exotic optical properties such as the photonic bandgap and optical chirality can emerge from this three-dimensional (3D) morphological feature. As such, gyroid crystals have been considered as the promising structures for photonic crystals and optical metamaterials. To date, several methods have been proposed to materialize gyroid crystals, including 3D printing, layer-by-layer stacking, two-photon lithography, interference lithography, and self-assembly. Furthermore, the discovery of Weyl points in gyroid crystals has further stimulated these advancements. Among such methods, the self-assembly of block copolymers (BCPs) is unique, because this soft approach can provide an easy-to-craft gyroid, especially at the nanoscale. The unit-cell scale of a gyroid ranging within 30–300 nm can be effectively addressed by BCP self-assembly, whereas other methods would be challenging to achieve this size range. Therefore, a BCP gyroid has provided a material platform for metamaterials and photonic crystals functioning at optical frequencies. Currently, BCP gyroid nanophotonics is ready to take the next step toward topological photonics beyond the conventional photonic crystals and metamaterials. In particular, the intrinsic lattice transformations occurring during the self-assembly of BCP into a gyroid crystal could promise a compelling advantage for advancing Weyl photonics in the optical regime. Lattice transformations are routinely considered as limitations, but in this review, we argue that it is time to widen the scope of the lattice transformations for the future generation of nanophotonics. Thus, our review provides a comprehensive understanding of the gyroid crystal and its lattice transformations, the relevant optical properties, and the recent progress in BCP gyroid self-assembly.
... A growing range of elastomeric materials have been used within 3D printed lattice structures in recent times, including rubber-like UV crosslinkable TangoBlack+ [22], polydimethylsiloxane (PDMS) silicon rubber [20], tin-catalyzed silicone elastomers [23] 1 and the thermoplastic polyurethanes (TPU) SemiFlex [24], NinjaFlex [25] and most recently Desmopan 3690 [26]. While the ability of such metamaterials to reproduce soft foam-like behaviour has been shown in some of these works, more work is required to determine repeatable structural features and parameters that would enable controlled tuning of the compressive response of such materials for custom cushion applications. ...
... Spanning materials such as hard plastics (e.g., Polyamide 12, Acrylonitrile Butadiene Styrene (ABS)), and metals (e.g., Al-Si10-Mg, Ti-6Al-4V, stainless steel), the most applicable of these investigations look at the mechanical performance of 3D printed lattices based on shapes derived from differential geometry known as triply periodic minimal surfaces (TPMS) [28]. Such studies have been carried out on TPMS variants such as Schwarz Primitive, Schoen IWP and Neovius [28][29][30][31], and especially the Gyroid TPMS [21,22,[32][33][34][35][36][37][38]. The studies generally vary lattice parameters such as strut/wall thickness, unit cell size, and corresponding solid volume fraction (net density) to investigate their effect on mechanical response including compressive strength, elastic moduli, energy absorption, and other critical measures. ...
Article
Various areas of healthcare utilise custom foam cushioning to treat or mitigate conditions like pressure ulcers, or to provide personalised support structures for patients with specific clinical needs. Polyurethane foams are often used; however, such materials require significant time and expertise to combine different foam types into a device that provides sufficient structural support in some areas, with soft pressure distribution in others. In this paper, flexible 3D printed gyroid based metamaterials are investigated as a tuneable replacement for polyurethane foams. The impact of changing key gyroid structural characteristics on the material’s mechanical response is examined. Samples with six different unit cell geometries for each of two flexible TPU 3D printing filaments (NinjaFlex and Flexion X60) were produced using fused filament fabrication, tested, and compared to three types of conventional polyurethane rehabilitation foam. Compression tests were conducted focussing on compressive stress-strain response, strain rate effect, print layer effect, and cyclic fatigue behaviour. In all tests it was observed that gyroid samples of both filament types were able to produce compressive responses comparable to the foams. Solid volume fraction was determined as the critical gyroid geometric parameter that influenced compressive response, and solid volume fractions capable of reproducing the specific response of each of the three rehab foams were determined. It is shown that 3D printed gyroid materials are a viable replacement for soft polyurethane foams, and the direct control of material response possible with simple geometric changes means such metamaterials may lead to improved optimisation of rehabilitation cushions.
... Due to geometric freedom of the process complex design oriented to behavior can be implemented. One of the structures enabled by additive manufacturing is the gyroid structure, a triply periodic minimal surface structure with high stiffness and strength being suitable for automotive and aerospace industries [1]. Besides the application of lattice structures, the mechanical behavior of these structures still needs to the studied. ...
Article
Full-text available
Triply periodic minimal surfaces such as Gyroid structures have been widely used in additive manufacturing as a strategy to reduce material usage, printing time, and part weight, which are of high interest by the automotive industry. Most Software dedicated to additive manufacturing have lattice tools for infill available, but they usually do not consider the influence of the infill strategy on the part‘s mechanical properties. Therefore, this study analyzed numerically and experimentally the influence of lattices on the compressive behavior of samples manufactured by selective laser melting and developed a procedure to use the finite element method as a tool for mechanical properties evaluation. The procedure employed the software nTopology to generate gyroid structures and Ansys for the structural analyses. Different gyroid densities were numerically analyzed and samples with the best weight/stress ratio were selected for experimental validation with compression tests according to the ASTM E9 standard. The material considered was a carburizing steel DIN 5120 suitable for industrial applications. The results showed that the infill percentage is not associated with a linear relationship between weight and stress. It was observed that besides the infill ratio, the material distribution has a significant effect on the sample performance, which was affected by the stress concentration phenomena. A good representativity was found between the numerical model and experiments, enabling it as a reliable method to evaluate how the infill affects mechanical behavior
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Gyroid (G) and primitive (P) porous structures have multiple application areas, ranging from thermal to mechanical, and fall in the complex triply periodic minimal surface (TPMS) category. Such intricate bioinspired constructs are gaining attention because they meet both biological and mechanical requirements for osseous reconstruction. The study aimed to develop G and P structures with varying porosity levels from 40% to 80% by modulating the strut thickness to proportionally resemble the stiffness of host tissue. The performance characteristics were evaluated using Ti6Al4V and important relationships between feature dimension, strut thickness, porosity, and stiffness were established. Numerical results showed that the studied porous structures could decrease stiffness from 107 GPa (stiffness of Ti6Al4V) to the range between 4.21 GPa to 29.63 GPa of varying porosities, which matches the human bone stiffness range. Furthermore, using this foundation, a subject-specific scaffold (made of P unit cells with an 80% porosity) was developed to reconstruct segmental bone defect (SBD) of the human femur, demonstrating a significant decrease in the stress shielding effect. Stress transfer on the bone surrounded by a P scaffold was compared with a solid implant which showed a net increase of stress transfer of 76% with the use of P scaffold. In the conclusion, future concerns and recommendations are suggested.
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