P. KOUDELKA et al.: COMPRESSIVE PROPERTIES OF AUXETIC STRUCTURES PRODUCED WITH ...
311–317
COMPRESSIVE PROPERTIES OF AUXETIC STRUCTURES
PRODUCED WITH DIRECT 3D PRINTING
STISKANJE STRUKTUR MATERIALOV Z NEGATIVNIM
POISSONOVIM RAZMERJEM, PROIZVEDENIH Z NEPOSREDNIM
TRIDIMENZIONALNIM TISKANJEM
Petr Koudelka1,2, Ondøej Jirou{ek2, Tomá{ Fíla1,2, Tomá{ Doktor1,2
1Institute of Theoretical and Applied Mechanics, Academy of Sciences of the Czech Republic, Prosecká 76, 190 00 Prague, Czech Republic
2Czech Technical University in Prague, Faculty of Transportation Sciences, Konviktská 20, 110 00 Prague 1, Czech Republic
jirousek@fd.cvut.cz
Prejem rokopisa – received: 2014-08-19; sprejem za objavo – accepted for publication: 2015-04-24
doi:10.17222/mit.2014.204
In the presented paper, three types of auxetic structures were produced with direct 3D printing and their compressive mechanical
properties were tested. Samples were prepared from acrylic material suitable for high-resolution direct printing. Three different
structures exhibiting in-plane and volumetric negative strain-dependent Poisson’s ratio were selected for the analysis:
two-dimensional missing-rib cut, two-dimensional inverted (re-entrant) honeycomb and three-dimensional inverted (re-entrant)
honeycomb. The samples were subjected to quasi-static compression, from which stress-strain relationships were established.
For a proper strain evaluation, digital-image correlation was applied to measure full-field displacements on the sample surfaces.
From the displacement fields, true strain/true stress curves were derived for each sample. Furthermore, for each structure a
three-dimensional FE model was developed using beam elements and subjected to identical loading conditions. Then,
experimentally obtained stress-strain relationships were compared with numerically obtained results. For all the tested auxetic
structures, the compressive behaviour was predicted well by the FE models. This demonstrates that parametric FE models can
be used to tune the design parameters of the structures with a negative Poisson’s ratio to optimize their overall properties.
Keywords: auxetics, cellular materials, quasi-static testing, finite-element method
V prispevku so predstavljene tri vrste struktur materialov z negativnim Poissonovim razmerjem, ki so proizvedene z
neposrednim tridimenzionelnim tiskanjem. Preizku{ene so bile njihove mehanske lastnosti pri stiskanju. Vzorci so bili
pripravljeni iz akrilnih materialov, ki so primerni za visoko resolucijsko neposredno tiskanje. Za analizo so bile izbrane tri
razli~ne strukture, ki prikazujejo negativno odvisno Poissonovo razmerje v ravnini in v prostoru: dvodimenzionalni prerez z
manjkajo~im rebrom, dvodimenzionalni obrnjeni (navznoter usmerjeni) vzorec satovja in tridimenzionalni obrnjeni (navznoter
usmerjeni) vzorec satovja. Vzorci so bili izpostavljeni kvazi-stati~nem stiskanju pri katerem smo ugotavljali razmerja sile –
raztezek. Za primerno oceno sile obremenitve je bila uporabljena metoda korelacije digitalne slike in s tem izmerjeni odmiki na
povr{ini vzorcev. Glede na te odmike so bile za vsak vzorec izpeljane dejanske obremenitvene krivulje. Nadalje je bil za vsako
strukturo izdelan tridimenzionalni FE model, z uporabo matemati~nega modela podpornih struktur in izpostavljen identi~nim
pogojem obremenitve. Nato smo primerjali eksperimentalno pridobljena razmerja med silo in obremenitvijo, z ra~unsko
pridobljenimi rezultati. S pomo~jo primerjalnih diagramov sile in raztezka lahko ugotovimo, da FE modeli dobro napovedujejo
obna{anje pri stiskanju vseh preizku{enih struktur z negativnim Poissonovim razmerjem. To prikazuje mo`nost uporabe
parametri~nih FE modelov za prilagoditev zasnovnih parametrov struktur z negativnim Poissonovim razmerjem za optimiziranje
njihovih splo{nih lastnosti.
Klju~ne besede: materiali z negativnim Poissonovim razmerjem, celi~ni materiali, kvazi-stati~no preizku{anje, metoda kon~nih
elementov
1 INTRODUCTION
Porous solids (i.e., open- or closed-cell foams) are
materials suitable for applications requiring a significant
mass reduction and a simultaneous high-impact energy
absorption. This is provided by the foams’ low specific
weight and thus high specific stiffness. However, for
certain applications (including blast protection), it may
be necessary to use materials with a relatively high
compressive strength, which disqualifies the usage of
most foam types including metallic foams.1 To improve
the strength and energy absorption capacity without
increasing the mass of constructional elements, a new
type of material had to be found. One of the possible
approaches to dealing with the absorption of enormous
amounts of deformation energy during blast and impact
loading of structures is to produce a highly optimized
porous structure, taking advantage of the negative
Poisson’s ratio of its skeleton.2
Historically, a structure with a negative Poisson’s
ratio was first reported for single crystals of iron pyrites
and was attributed to crystal twinning.3 This initial
finding was followed only by isolated reports in the
1970s and 1980s showing that negative Poisson’s ratio is
a rather unique phenomenon among natural constructs.
First artificially prepared auxetic polymeric foam was
reported in 1987 by Lakes4 when commercially available
foam was modified in a process involving 30 % volu-
metric compression and heating of the samples to the
polymer’s softening temperature followed by cooling
Materiali in tehnologije / Materials and technology 50 (2016) 3, 311–317 311
UDK 620.192.47:66.069.852:519.61/.64 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 50(3)311(2016)
whilst remaining under compression. Although research
of the microstructures prepared with various similar
techniques from the existing materials continued, the
investigation of the auxetic-based materials capable of
deformation-energy absorption closely followed the
advances in additive manufacturing (i.e., selective laser
sintering, direct 3D printing, etc.).
The reported auxetic topologies are mostly based on
re-entrant, chiral, double-arrow-head and rotating-rigid
unit cells.5–8 Deformation behaviour (both elastic and
plastic) of such a porous construct is determined by
concurrent effects of intrinsic behaviour of the material
used for the scaffold production, cell topology and
connectivity. To optimize its microstructure to suit the
intended application and to achieve a stable negative
Poisson’s ratio up to high strains, a control over the pore
structure is required. Here, the usage of additive manu-
facturing is favourable as all the intended geometrical
characteristics can be attained deterministically, satis-
fying the need for a high mechanical integrity of the
construct during deformation and the need for precise
tuning of the overall stiffness and plastic properties.
Several unit-cell models having a well-defined
Poisson’s function (strain-dependent Poisson’s ratio)
described analytically have already been proposed.9–12 In
this study, samples of three microstructures utilizing both
the in-plane and volumetric negative Poisson’s ratio were
produced with direct 3D printing to evaluate their
compressive-deformation behaviour in both elastic and
plastic regime up to the densification. Deformation of the
microstructures during quasi-static uni-axial com-
pression tests was optically observed using a CCD
camera and the digital-image-correlation (DIC) method
was used for the strain evaluation. Moreover, mechanical
behaviour of the structures was investigated numerically
with virtual experiments (i.e., simulations of the
compression tests) using finite element (FE) method.
The simulations were carried out using identical loading
and boundary conditions and the numerically obtained
stress-strain curves were compared to the experimental
ones to test the proposed material model for the base
material.
2 EXPERIMENTAL PART
2.1 Specimen geometry
In this study, three different types of unit-cell geo-
metry were used: a) two-dimensional missing-rib cut, b)
two-dimensional inverted (re-entrant) honeycomb and c)
three-dimensional inverted honeycomb. These unit cells
were arranged so that predictable (determinate) in-plane
or volumetric negative strain-dependent Poisson’s ratio
was achieved in the cases of two-dimensional and three-
dimensional geometries, respectively. Constructs of
two-dimensional geometries were generated by extrud-
ing a planar (single-layer) arrangement of the unit cells
whereas a three-dimensional construct was created by
copying a fully three-dimensional unit cell along all the
spatial directions.
The missing-rib-cut model was formed by removing
selected ribs (the elements forming a unit cell) from the
periodical arrangement of squares and by rotating the
construct by 45° to the direction of loading.13 Auxetic
behaviour of such a construct depends on the unit-cell
dimensions and the angles between individual ribs. The
geometry of a unit cell with the dimensions used in this
work and a visualisation of the specimen are depicted in
Figure 1. The dimensions of the produced construct
were 25.05 mm × 25.40 mm × 37.75 mm (width, depth,
height), the overall porosity was 72.8 % and the con-
struct consisted of 10 × 15 cells.
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312 Materiali in tehnologije / Materials and technology 50 (2016) 3, 311–317
Figure 2: a) 2D re-entrant structure – unit cell geometry, b) visu-
alisation of the whole sample, c) 3D re-entrant structure – unit cell
geometry and d) visualisation of the whole sample
Slika 2: a) dvodimenzionalna navznoter usmerjena struktura – geo-
metrija celice, b) vizualizacija celotnega vzorca, c) tridimenzionalna
navznoter usmerjena struktura – geometrija celice in d) vizualizacija
celotnega vzorca
Figure 1: Missing-rib-cut structure: a) unit cell geometry and b) visu-
alisation of the whole sample
Slika 1: Struktura prereza z manjkajo~im rebrom: a) geometrija celice
in b) vizualizacija celotnega vzorca
The re-entrant mesh is generated by changing the
four side angles between the ribs in a six-sided honey-
comb.14 The magnitude of Poisson’s ratio at a given
strain is here primarily given with the length ratio of
individual ribs forming the unit cell. Both two-dimen-
sional and three-dimensional arrangements of the
re-entrant unit cells together with visualisations of the
specimens are shown in Figure 2. Dimensions of the
produced two-dimensional construct were 25.65 mm ×
25.40 mm × 58.89 mm (width, depth, height), the overall
porosity was 73.2 % and the construct consisted of 10 ×
15 cells; dimensions of the produced three-dimensional
construct were 7.87 mm × 7.87 mm × 18 mm (width,
depth, height), the overall porosity was 91.7 % and the
construct consisted of three cells in every spatial direc-
tion.
2.2 Specimen preparation
The specimens were manufactured from VisiJet
EX200 (3D Systems, USA) UV curable acrylic material
suitable for high-resolution 3D printing. The physical
properties of the material are summarised in Table 1.
For the specimen production, a Pro Jet HD3000 (3D
Systems, USA) 3D printer in the high-definition mode
was used. The manufacturing principle is based on a
multi-jet modelling technology where a special printing
head covers the whole working area of 198 mm × 185
mm × 203 mm and builds up the model by adding indivi-
dual layers of the produced geometry. Simultaneously,
while modelling the material, a supporting wax material
is automatically added to the construct to enable a pro-
duction of very complex geometries.
Thanks to its low melting point (approximately
55–65 °C) all the supporting material can be simply
removed from the products by heating it in a water bath
to approximately 80 °C without a potential mechanical
damage to the products. A SolidWorks (Dassault Sys-
tèmes SolidWorks Corp., France) parametric modeller
was used to design the sample geometry that was
exported to the STL format for the 3D printing. The final
samples were produced with a resolution of (328 × 328 ×
606) DPI (x, y, z direction) with a layer thickness of
0.036 mm. In this mode, the accuracy of printing was
approximately 0.025–0.05 mm and the production
process took approximately 11 h.
Table 1: Properties of the VisiJet EX200 material
Tabela 1: Lastnosti materiala VisiJet EX200
Mass density 1.02 g/cm3
Tensile modulus 1.283 GPa
Tensile strength 42.4 MPa
Flexural modulus 1.159 GPa
Glass transition temp. 52.5 °C
2.3 Experimental set-up
The experiments were carried out using an in-house
designed loading set-up based on a novel modular
compression/tension loading device suitable for both
optical and X-ray observation of deformation processes15
equipped with a U9b force transducer (HBM, Germany)
with a nominal force capacity of 2 kN. The signal from
the load cell was read out using an OM502T (Orbit
Merret, CZ) load-cell indicator at a sampling rate of 50
Hz.
Imaging was performed using a Manta G504B
monochromatic GigE vision camera (AVT, Germany).
The camera was equipped with an ICX655 CCD sensor
and its maximum frame rate was 9 fps, achieved at a
resolution of 2452 px × 2056 px. In order to guarantee a
high reliability of the correlation procedure and an
accuracy of the computed strains, the camera was
equipped with a TCZR 072 bi-telecentric zoom lens
(Opto Engineering, Italy). The lens used a stepper-
motor-controlled zoom revolver to set four different
magnifications of the scene in the range of 0.125–1.000,
with a very high image-centre stability, parfocality and
no need for a re-calibration after the zooming. The
specimens were illuminated using a KL2500 high-power
white-light LED source (Schott, Germany).
A detailed description of the loading set-up is shown
in Figure 3.
2.4 Loading procedure and strain measurement
The loading of the samples was performed as a
displacement-driven uniaxial compression. The maxi-
mum displacement was set to 8 mm with a loading rate
of 20 μm s–1. The positioning of the camera as well as the
loading were carried out using in-house developed con-
trol software based on the GNU/Linux real-time ope-
rating software and LinuxCNC open-source project.
P. KOUDELKA et al.: COMPRESSIVE PROPERTIES OF AUXETIC STRUCTURES PRODUCED WITH ...
Materiali in tehnologije / Materials and technology 50 (2016) 3, 311–317 313
Figure 3: Loading set-up used in the experiments
Slika 3: Postavitev obremenjevanja, ki je bilo uporabljeno pri preiz-
kusih
The strains were derived from optically measured
displacements using a sequence of the images capturing
a deforming sample. Depending on the sample height,
0.125 or 0.25 magnifications were used and the images
were captured with the maximum resolution of 2452 px
× 2056 px at 2 fps, enabling the identification of a suffi-
cient number of points on the stress-strain curve. The
acquisition of the projections was controlled with
custom-developed software based on the OpenCV library
and Python programming language. The observed faces
of the specimens were sprayed using granite paint to
generate a random pattern for a high reliability of the
optical deformation tracking. A selected loading scene is
depicted in Figure 4.
2.5 Stress-strain diagram evaluation
Displacements were determined from the image
sequences using a custom-developed DIC software tool16
based on the Lucas-Kanade tracking algorithm17 imple-
mented in MATLAB. Two rows of correlation points
(markers) perpendicular to the loading direction were
selected near the upper and lower edges of the observed
surfaces of the specimens. Each marker was in a series of
projections tracked by searching for the highest corre-
lation coefficient between two consequent projections.
Engineering-stress (eng) and strain (
eng) values were
determined from the geometrical properties of the tested
specimens and optically measured displacements of the
markers. Then, true stress (true) and true strain (
true)
were calculated according to Equations (1) and (2):
  
true eng eng= +( )1 (1)

 
true eng= +ln( )1 (2)
3 NUMERICAL PART
Apart from the experimental methods, analytical and
FE models can be used for a description of deformation
behaviour of auxetic constructs, allowing a prediction
and optimization of the effective mechanical characte-
ristics that facilitate the material design for a specific
application.
Most of the analytical models assume small deflec-
tions, neglecting the axial deformation of the struts.19
Thus, analytical approach can be used to prove the con-
cept of negative Poisson’s ratio, optimize the parameters
of a structure (e.g., the re-entrant angle, relative density,
strut thickness) and maximize the effective parameters of
the resulting constructs (i.e., deformation energy per unit
volume, yield strength of the structure, compressive
strength) according to specific requirements. For
instance, using these analytical models, it is possible to
express Poisson’s ratio μ of the re-entrant honeycomb
structure (Figure 2a) with Equation (3):
( )
μ =
− + −
−
sin( / sin(
cos (
90 90
90
2 1
2
 

L L
(3)
where L1 and L2 are the strut lengths and  is the strut
angle (measured in degrees). The value of resulting
Poisson’s ratio is negative and its dependency on the
magnitude of the angle  and the strut length ratio L2/L1
corresponds to the observed experimental results. Using
the Timoshenko beam theory and the elastic-behaviour
assumption, it is possible to express the overall elastic
modulus E and critical-yield compressive force Fm
based on the yield strength y of the bulk solid material.
From the yield compressive force the compressive
strength of the structure can be then expressed.
However, these analytical models are effective only
when simplifying the assumptions such as the small-
deflection theory and linear elastic-material properties
are used. Consequently, these models only give satisfac-
tory results for small deformations and are limited to the
calculation of the overall elastic properties or to the
estimation of the yield point of a structure.
When large strains with non-linear material pro-
perties are to be considered, FE models have to be used
instead. Thus, FE models of the tested auxetic structures
were developed and subjected to the same loading
conditions as during the compression tests. Deformation
behaviour of the tested samples under large strains (up to
10 % or 20 % strain) was then compared with the predic-
tions obtained from the numerical models to verify their
suitability for a representation of such microarchitec-
tures.
Stress-strain curves were inversely assessed from the
FE simulations, i.e., from the reaction forces calculated
at the restrained side of a sample. Using such inverse FE
simulations, it is relatively easy not only to obtain the
stress-strain curves for each considered sample, but also
to establish the stresses and strains arising at individual
P. KOUDELKA et al.: COMPRESSIVE PROPERTIES OF AUXETIC STRUCTURES PRODUCED WITH ...
314 Materiali in tehnologije / Materials and technology 50 (2016) 3, 311–317
Figure 4: Loading scene captured using a CCD camera during the
experiment. Missing-rib specimen with sprayed surface for a DIC
strain evaluation.
Slika 4: Trenutek obremenitve, ki je prikazan na CCD kameri med
preizkusom. Vzorec z manjkajo~im rebrom z napr{eno povr{ino za
oceno DIC sile obremenitve.
struts from the deformation of the structure. Hence, these
strains can be easily compared to the values experimen-
tally obtained from the digital-image correlation at the
same positions (i.e., individual markers).
For all the considered auxetic constructs, the FE
model was created using 3D beam elements with 6° of
freedom (three translational and three rotational ones)
defined at two nodal points. The element is based on
Timoshenko beam theory, which includes shear-defor-
mation effects. The material model set in the simulations
was elasto-plastic, combining von Mises yield criteria
and bilinear isotropic work hardening. The material pro-
perties are summarised in Table 2.
Table 2: Material properties used in the FE simulations
Tabela 2: Lastnosti materiala uporabljenega pri FE simulaciji
Young’s modulus 1.159 GPa
Poisson’s ratio 0.2 –
Yield stress 42.4 MPa
Hardening tangent modulus 12.8 MPa
The loading was prescribed to be done in 100 loading
steps, i.e., in each step a 0.1 % or 0.2 % deformation was
applied.
In the case of such a large-strain analysis, a highly
deformed geometry has an important effect on the strain
and, therefore, geometric nonlinearities must be con-
sidered. To consider the post-buckling behaviour of the
thin beams subjected to a large compression, strain
measures have to account for higher-order terms. Thus,
in our analyses, material stress-strain properties were
input in terms of true stress versus logarithmic strain. In
every loading step, reaction forces originating from the
supports were calculated and the true stresses and strains
were established using Equations (1) and (2). Visuali-
zations of the FE models for individual constructs can be
seen in Figure 5.
4 RESULTS AND DISCUSSION
From both the numerical and experimental quasi-
static compression tests true stress/true strain diagrams
for all three considered auxetic microarchitectures were
plotted.
A comparison of the experimental and numerical
stress-strain diagrams of the missing-rib-structure cut is
depicted in Figure 6.
It can be seen that this type of microstructure exhibits
a similar initial compressive behaviour as a typical
closed-cell porous solid. The initial linear elastic part is
followed by an apparent yield point and a compaction
region with a constant stress plateau. These parts are
then, at an approximately 17.5 % strain, followed by a
region of localized densification due to negative
Poisson’s ratio of the unit cell and repeated decreases of
the stress that can be attributed to the ruptures of beams
due to excessive bending. Good correlation of the
numerical and experimental results was obtained in
terms of stiffness, yield point and plateau stress up to a
20 % strain.
In Figure 7, a comparison of the experimentally and
numerically acquired stress-strain diagrams of the two-
dimensional inverted honeycomb structure is presented.
It is clearly apparent that the microstructure of such a
construct exhibits a significantly different deformation
behavior than the missing-rib-structure cut. After the
initial linear elastic region, a 30 % drop in the stress is
followed by cyclic increases and decreases in the stress
levels in the specimens with an apparent progressive
trend. After a visual inspection of individual projections
during the deformation, the occurrence of the cycles can
P. KOUDELKA et al.: COMPRESSIVE PROPERTIES OF AUXETIC STRUCTURES PRODUCED WITH ...
Materiali in tehnologije / Materials and technology 50 (2016) 3, 311–317 315
Figure 6: Comparison of experimentally and numerically obtained
stress-strain diagrams of the missing-rib-cut structure
Slika 6: Primerjava eksperimentalno in {tevil~no pridobljenih diagra-
mov sile in raztezka za strukturo prereza z manjkajo~im rebrom
Figure 5: Visualization of FE-model elements used in the numerical
simulations: a) missing-rib-structure cut with a detail of the unit cell,
b) 2D re-entrant structure with a detail of the unit cell and c) detail of
3D re-entrant unit cell
Slika 5: Vizualizacija elementov FE modela, ki je bil uporabljen v
{tevil~nih simulacijah: a) struktura prereza z manjkajo~im rebrom s
podrobnostmi enote celice, b) dvodimenzionalna navznoter usmerjena
struktura s podrobnostmi enote celice in c) podrobnosti tridimenzio-
nalna navznoter usmerjene enote celice
be attributed to the collapse of individual layers of the
unit cells in the microstructure. For this type of
microstructure, FE simulations give a good prediction of
the yield point and strain-softening behaviour up to the
densification of the individual layers in the microstruc-
ture.
A stress-strain diagram showing the experimentally
and numerically assessed behavior of the three-dimen-
sional inverted honeycomb structure is shown in Figure
8.
The mechanical response is similar to that of the
two-dimensional structure but with a more significant
stress drop after the linear elastic region and a lower
number of the stress cycles, caused by a 20 % lower
overall porosity and a lower number of the cells in the
structure. The performance of the FE model is, in this
case, similar to the two-dimensional re-entrant structure
with a numerically well-determined yield point and
strain-softening characteristics.
Only for the missing-rib cut of the auxetic structure,
it was possible to perform the FE analysis up to a 20 %
strain. Larger strain values could not be calculated as the
elements became extremely distorted, yielding instability
and convergence issues of the simulations. Furthermore,
to capture the stiffening during the compaction, it would
have been necessary to include self-contact between
individual struts, which would have significantly
increased the complexity and computational costs of the
simulations.
The FE simulations of the re-entrant structures pre-
dict a smaller overall stiffness, which is apparent from
the comparison between the experimental stress-strain
curves and the numerically obtained responses. For this
reason, a set of three-point-bending experiments was
carried out using prismatic beams with rectangular
cross-sections that were carefully cut from the printed
specimens. Based on the DIC strain evaluation, a
bending modulus of approximatly 1.5 GPa was calcu-
lated. This value is close to the nominal flexural modulus
of 1.2 GPa provided by the manufacturer that was also
used in the FE simulations. Thus, the discrepancies
between the numerically and experimentally evaluated
stiffness might have been caused by properties that were
different from the predicted properties of the joints
between individual struts, influencing the bending
characteristics of individual layers, which formed the
principal mode of deformation of the re-entrant struc-
tures. Here, a combination of a precise inspection of the
geometry and possibly a nanoindentation measurement
of the joints should be applied to obtain an accurate
material model for the FE simulations.
5 CONCLUSIONS
Mechanical behaviour of three different porous
microarchitectures exhibiting in-plane and volumetric
negative Poisson’s ratios was studied both experimen-
tally and numerically. The specimens prepared with
high-resolution direct 3D printing were compressively
loaded up to the densification regions of their mechani-
cal responses. The true stress/true strain diagrams for the
compression were derived from a high-precision force
measurement and an optical DIC evaluation of the strain
field. Based on the experimental results, numerical FE
models of all the considered microarchitectures were
developed and their ability to predict mechanical
responses of the studied constructs was assessed by
comparing the numerically and experimentally obtained
stress-strain diagrams. It was found that the deformation
response of the missing-rib-cut structure was well cap-
tured by the FE model up to a 20 % strain. Simulations
of the re-entrant honeycomb structures showed good
correlation of the yield point and strain-softening charac-
P. KOUDELKA et al.: COMPRESSIVE PROPERTIES OF AUXETIC STRUCTURES PRODUCED WITH ...
316 Materiali in tehnologije / Materials and technology 50 (2016) 3, 311–317
Figure 7: Comparison of experimentally and numerically obtained
stress-strain diagrams of the 2D inverted honeycomb structure
Slika 7: Primerjava eksperimentalno in {tevil~no pridobljenih diagra-
mov sile in raztezka za dvodimenzionalno obrnjeno strukturo satovja
Figure 8: Comparison of experimentally and numerically obtained
stress-strain diagrams for the 3D inverted honeycomb structure
Slika 8: Primerjava eksperimentalno in {tevil~no pridobljenih diagra-
mov sile in raztezka za tridimenzionalno obrnjeno strukturo satovja
teristics up to a 10 % strain, while the calculated stiffness
of the models was lower than the stiffness of the
measured specimens. Still, the acquired results demon-
strate that parametric FE models can be used to tune the
design parameters of the structures with negative
Poisson’s ratio and numerically optimize their overall
properties. Therefore, we can conclude that such FE
models can be successfully used in material engineering
to design highly optimized structures for a given range of
strain rates, with maximized strain-deformation energy.
Acknowledgements
The research was supported by the Czech Science
Foundation (research project Nos. P105/12/0824 and
15-15480S) and by RVO: 68378297.
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