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Behavior of auxetic structures under compression
and impact forces
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Smart Materials and Structures
Smart Mater. Struct. 27 (2018) 025012 (12pp)
https://doi.org/10.1088/1361-665X/aaa3cf
Behavior of auxetic structures under
compression and impact forces
Chulho Yang , Hitesh D Vora
and Young Chang
Mechanical Engineering Technology, Oklahoma State University, Stillwater, OK 74078, United States of
America
E-mail: chulho.yang@okstate.edu
Received 16 October 2017, revised 16 December 2017
Accepted for publication 22 December 2017
Published 17 January 2018
Abstract
In recent years, various auxetic material structures have been designed and fabricated for diverse
applications that utilize normal materials that follow Hooke’s law but still show the properties of
negative Poisson’s ratios (NPR). One potential application is body protection pads that are
comfortable to wear and effective in protecting body parts by reducing impact force and
preventing injuries in high-risk individuals such as elderly people, industrial workers, law
enforcement and military personnel, and athletes. This paper reports an integrated theoretical,
computational, and experimental investigation conducted for typical auxetic materials that
exhibit NPR properties. Parametric 3D CAD models of auxetic structures such as re-entrant
hexagonal cells and arrowheads were developed. Then, key structural characteristics of
protection pads were evaluated through static analyses of FEA models. Finally, impact analyses
were conducted through dynamic simulations of FEA models to validate the results obtained
from the static analyses. Efforts were also made to relate the individual and/or combined effect
of auxetic structures and materials to the overall stiffness and shock-absorption performance of
the protection pads. An advanced additive manufacturing (3D printing) technique was used to
build prototypes of the auxetic structures. Three different materials typically used for fused
deposition modeling technology, namely polylactic acid (PLA) and thermoplastic polyurethane
material (NinjaFlex® and SemiFlex®), were used for different stiffness and shock-absorption
properties. The 3D printed prototypes were then tested and the results were compared to the
computational predictions. The results showed that the auxetic material could be effective in
reducing the shock forces. Each structure and material combination demonstrated unique
structural properties such as stiffness, Poisson’s ratio, and efficiency in shock absorption.
Auxetic structures showed better shock absorption performance than non-auxetic ones. The
mechanism for ideal input force distribution or shunting could be suggested for designing
protectors using various shapes, thicknesses, and materials of auxetic materials to reduce the risk
of injury.
Keywords: protection, impact, negative Poisson’s ratio, 3D printing, additive manufacturing,
finite element analysis, auxetic material
(Some figures may appear in colour only in the online journal)
1. Introduction
directions when placed under tension and becomes thinner
when compressed.
An early work on functionally graded beams where the
cell structure gradually changes from re-entrant to hexagonal
structures under bending load has been reported by Lim et al
[1]. Lira et al carried out work on two types of honeycombs;
re-entrant and hexagonal cell geometry, such that the rib
During the past decades, various geometric structures and
models possessing auxetic effects have been proposed and
investigated for their mechanical properties. An auxetic
material possesses a negative Poisson’s ratio (NPR), which
means it becomes thicker in one or more perpendicular
0964-1726/18/025012+12$33.00
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Smart Mater. Struct. 27 (2018) 025012
C Yang et al
thickness gradually changed from very thick to very thin [2].
Following this work, Lira et al studied the dynamic response
of such honeycombs, with varying internal cell angles, for
application as aeroengine fan blades [3]. The same group then
expanded to work on bending and failure of sandwich
structures where the re-entrant geometry gradually changes
from one end to the other [4]. Hou et al manufactured such
honeycombs, with combined hexagonal and re-entrant geometries, for experimental investigation by flatwise compression [5]. Also, Boldrin et al investigated the dynamic
behavior of graded re-entrant gradient composite honeycombs
[6], while Lim explored the behavior of 3D structures with
graded geometry from arrowhead to rhombus [7]. Jiang and
Hu then studied low-velocity impact response of multilayer
composite structures with auxetic effect [8]. Finally, Hou et al
looked at designing energy-dissipating structures with functionally graded auxetic cellular material [9].
Lakes discovered that isotropic auxetic foams could be
easily manufactured from conventional open-cell foam,
identified the microstructural features associated with NPR
materials, and presented several structural models that exhibit
those features in isolation [10, 11]. Bowick et al estimated the
Poisson ratio of physical self-avoiding fixed-connectivity
membranes using Monte Carlo simulations [12]. They
showed that auxetic materials have desirable mechanical
properties such as higher in-plane indentation resistance,
transverse shear modulus, and bending stiffness. They suggested that these materials could be applied to many areas
such as sealants, gaskets, fasteners, and artificial arteries. Liu
and Hu reviewed auxetic polymeric materials, focusing on the
geometric structures which can produce auxetic effects and
their applications [13]. Sanami et al reported FE simulations
of a new cylinder-ligament honeycomb displaying auxetic
behavior in both uniaxial in-plane and out-of-plane bending
loading [14]. Bowick et al determined the Poisson’s ratio of
self-avoiding fixed-connectivity membranes modeled as
impenetrable plaquettes was in good agreement with that of
phantom fixed-connectivity membranes [12]. Underhill discussed some of the unique physical properties of auxetic
materials and claimed that there are promising new areas for
exploitation of these materials in defense applications [15].
Finite-element analyses by Photiou et al showed that the
resistance to conical indentation on auxetic materials dramatically increased with the magnitude of Poisson’s ratio when it
was above 0.5 [16]. Some researchers found auxetic foam
sheets to be very effective in reducing the peak force caused
by a hammer impact [17, 18], while others reported an
increase in the peak force [19]. A computational analysis
showed that auxetic composite panels could be effective
barriers against blast waves [20]. Lim et al examined the level
of damage to auxetic polyurethane foams subjected to an
impact by a wedge-shaped indenter. When the approaching
speed of the indenter exceeded a certain limit, auxetic foams
tended to be damaged more severely than conventional
counterparts made of the same raw material. They proposed a
hexagonal-based missing-rib model to explain the test results
[21]. Brighenti et al presented the possibility of developing
layered plates that will behave linearly over a large range of
deformation [22]. A potential application of such plates is
precision pressure transducers. Finite-element analyses by
Kocer et al showed that a material composed of alternating
layers of positive and NPR behave like a material with a
larger value of modulus of elasticity when subjected to a
tensile load. In their study model, the load is applied
perpendicular to the bonded surfaces [23]. Over the last few
years, the effect of an impact on the behavior of the
mechanical metamaterial as well as wave propagation in such
systems has been the subject of numerous studies. The work
of Ruzzene et al and Scarpa et al is highly commendable in
this regard [24, 25].
Study of the behavior of auxetic materials subjected to
quasi-static indentation or impact has many applications. The
resistance of auxetic materials to quasi-static indentation or
impact increases with the magnitude of the Poisson’s ratio,
and the resistance also increases with the friction between the
indenter and the auxetic material [26]. An extensive summary
of various topics of auxetic materials is available [27].
There have been many suggested applications of auxetic
materials but most of them are still not commercially available due to the difficulty of design and manufacturing real
products. One application where auxetic materials can provide a unique solution is body protection pads. Body protection pads made of auxetic materials are comfortable to
wear and effective in protecting body parts by reducing
impact force and preventing injuries in high-risk individuals
such as elderly people, industrial workers, law enforcement
and military personnel, and athletes. Among these populations, blunt impacts such as falls, bullets, and blast waves
reduce the quality of life, increase the possibility of early
death, and incur extremely high medical costs. A Center for
Disease Control and Prevention report revealed that among
the population aged 65 and older, falls reduce quality of life,
increase the possibility of early death, and are the leading
cause of injury death [28]. One third of the 65 and older
population falls each year, and the resulting adjusted medical
costs in 2010 were estimated to be $30 billion. More than
90% of hip fractures are due to falls, and external ‘hip protectors’ (wearable pads or shields typically embedded in the
undergarment) present a promising strategy for reducing
femoral impact force and preventing hip fractures in high-risk
elderly individuals [29]. However, clinical efficacy has been
limited by poor user compliance. The hip protectors currently
available on the market are made of either hard shells or thick
soft pads. Even though people understand that they can protect their bodies, most are reluctant to wear bulky garments or
ones with rigid shells. Therefore, it is important to develop
new body protectors that best combine comfort (flexible,
lightweight), ease of fitting (customized), ensured protection,
and cost-effectiveness.
In this paper, the auxetic effects of three different structures (honeycomb, re-entrant hexagon, and arrowhead) are
investigated and potential application to body protection is
discussed in terms of shock energy absorption and comfort.
This paper also focuses on the behavior of structures that
utilize more than one form of materials subjected to static and
dynamic loads. CAD modeling and finite element analyses
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Figure 1. Normal and auxetic structures and their dimensions (in inches) for tensile loading: (a) honeycomb, (b) re-entrant hexagon, and (c)
arrowhead.
were conducted to explore the possibility of using auxetic
materials in protective devices. Efforts were made to relate the
individual and/or combined effect of auxetic structures and
materials to the overall stiffness and shock-absorption performance of the body protection pads. Preliminary results of
this study were presented and published at two separate
conferences and their proceedings [30, 31]. However, the
present article combines the findings of these studies and the
results are more conclusive. It is important to note that the
systems chosen in this article have been studied previously
and their potential to exhibit a particular value of the Poisson’s ratio is already known [32, 33]. However, the novelty of
this work corresponds to the variation in the magnitude of the
applied tensile force leading to different deformation patterns.
Table 1. Material properties
Material
PLA
TPU1
TPU2
Density
(Kg m−3)
Young’s modulus (Pa)
Poisson’s
ratio
1250
1200
1200
3.5000×109
1.5306×107
2.4821×107
0.36
0.48
0.48
loading are 101.6×101.6×5.1 mm3 (4×4×0.2 inch3).
The geometric parameters of each cell are also shown in
figure 1. The pads are modeled using SolidWorks 2016.
Finite element analyses with tensile loading conditions
were performed on all three geometric structures using the
ANSYS FE package, version 15.0. Table 1 shows the material
properties used for three different materials; (i) polylactic acid
(PLA), (ii) thermoplastic polyurethane (TPU1, Ninjaflex®),
and (iii) thermoplastic polyurethane (TPU2, Semiflex®)
[34, 35].
For each pad, the bottom surface was fixed to a rigid
structure and the top surface was pulled with various input
forces to calculate elongation in the axial direction, transverse
deformation, and Poisson’s ratio. Figure 2 shows the typical
shape of deformation under the tensile load for all materials. It
is clear that the honeycomb structure (figure 2(a)) shrinks in
the transverse direction when pulled and displays typical nonauxetic behavior. However, the other two structures, reentrant hexagon (figure 2(b)) and arrowhead (figure 2(c)),
2. Pad design and validation
2.1. Design and finite element analysis—tensile loading
Auxetic materials attract interest due to their unusual
mechanical properties such as enhanced indentation resistance, fracture toughness, vibration damping, and porosity
variation that cannot be easily achieved with conventional
materials. Particularly, the auxetic effect of two different
geometric structures including re-entrant hexagon and
arrowhead were examined along with a non-auxetic honeycomb structure. The geometries of each structure are shown in
figure 1. The dimensions of the pads investigated by tensile
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Figure 2. Typical deformation shape under tension. (a) Honeycomb, (b) re-entrant hexagon, and (c) arrowhead.
expand in the transverse direction as predicted. This confirms
their auxetic behavior (NPR).
The Poisson’s ratio (ν) for a two-dimensional system is
determined by
- etrans
(1 )
v=
,
eaxial
where, εtrans is the transverse strain and εaxial is the axial
strain.
To determine if the cell size of the structures affects the
Poisson’s ratio, four different cell sizes of a honeycomb
structure were examined for two material types. The material
had a minor effect on the value of Poisson’s ratio (0.69 for
PLA and 0.63 for both polyurethane materials). However, the
cell size had a more noticeable effect on Poisson’s ratio as
shown in figure 3. As cell size decreased the Poisson’s ratio
also decreased, approaching that of a typical solid object.
Being aware of this effect, the authors decided to compare the
behaviors of the structures with the same cell size because the
honeycomb structure showed non-auxetic behavior while the
other two showed auxetic behavior, which would result in
opposite responses to the input force. No direct comparison
would be possible in any cell sizes. The honeycomb structure
with larger cell size had the higher Poisson’s ration, which
meant it would show more obvious behavior in lateral
direction while compressive and impact force were applied in
vertical direction so that the authors could show clearer
conclusion.
The Poisson’s ratio for each structure with PLA (polylactic acid) material is shown in figure 4. The Poisson’s ratio
is constant for each structure regardless of the level of input
force: 1.087 for honeycomb, −1.816 for re-entrant hexagon,
and −0.466 for arrowhead.
The effect of the tensile force on Poisson’s ratio was
examined for different materials and cell structures. The
tensile force was varied between 5 and 50 N. Figure 4(a)
illustrates that Poisson’s ratio is not affected by the tensile
force for honeycomb and re-entrant hexagon structures
regardless of the material used. For the arrowhead structure,
however, the behavior depends on the material. As shown in
figure 4(b), the Poisson’s ratio of the arrowhead structure
Figure 3. Poisson’s ratios for different cell sizes of honeycomb
structure for TPU (thermoplastic polyurethane) material.
Figure 4. Poisson’s ratio for different materials with different
designs: (a) honeycomb and re-entrant hexagon, (b) arrowhead.
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Figure 5. Deformed shapes of the arrowhead pad for various input forces: (a) 20 N, (b) 35 N, and (c) 50 N.
Figure 6. Test setup for tensile test.
Figure 7. Comparison of Poisson’s ratios obtained from test and
finite element analysis.
2.2. 3D printing and test
Additive manufacturing (3D printing) techniques were used
to build prototypes of the auxetic polymeric structures. Three
different materials commonly used for fused deposition
modeling (FDM) were selected for different stiffness and
shock-absorption properties, namely polylactic acid (PLA)
and thermoplastic polyurethane (TPU) material (Ninjaflex®
and Semiflex®). Tensile tests were conducted for thermoplastic polyurethane (Ninjaflex®) samples with the re-entrant
hexagon and arrowhead patterns. Samples were mounted in
the vertical position as shown in figure 6, and gradually
stretched while the tensile force, axial (vertical) deformation,
and lateral deformation were measured. Testing was done
with the axial force within the range of 10 N.
made of polylactic acid does not change with the tensile force.
On the other hand, the Poisson’s ratio of the arrowhead
structure made of polyurethane is affected by the magnitude
of the tensile force. This is especially evident for polyurethane1, which changes from negative to positive as the
tensile force increases. In this case, the transition occurs
between 30 and 35 N. This is due to the geometric deformation of each cell as seen in figure 5. The flipped rib
changes the cell shape from arrowhead to rhombus, then the
lateral dimension starts shrinking as the load increases. For
forces greater than 35 N, the Poisson’s ratio gradually
increases with the input force as the side rib of the cell
approaches a vertical line.
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Figure 8. Auxetic structures for impact loading: (a) honeycomb, (b) re-entrant hexagon, and (c) arrowhead.
Figure 9. Von Mises stress versus time plot on honeycomb structures with various cell sizes for impact loading: (a) top surface and (b) bottom
surface.
Figure 7 provides a comparison of Poisson’s ratios of reentrant hexagonal and arrowhead structures. Very close
agreement between the test and simulation results were
observed. The test results vary around the calculated value
due to structural defects in the 3D printed test specimens and
measurement error.
boundary probes were assigned to the top and bottom surfaces
to computationally predict the maximum von Mises stress.
To investigate if the cell size of the structure affects the
von Mises stress, the same load conditions were applied to
four different cell sizes (0.16, 0.24, 0.32, 0.40 inch) of a PLA
honeycomb structure. Figure 9 shows the stress on the top and
bottom faces of the four different cell sizes of a honeycomb
structure. It clearly shows that the magnitude of the stress
systematically increases with an increase in cell size for both
top and bottom faces of the structure. However, the magnitude of the stress is greater on the top faces than the bottom
faces of these structures.
The stress versus time plot is shown in figure 10.
Figure 10(d) specifically compares the Von Mises stress on
the bottom surface of all three structures. For each structure,
the stress on the top surface is higher than the bottom surface
during the application of the impact load. After releasing the
impact load, the stresses on the top and bottom surfaces
became almost the same for both the honeycomb and reentrant honeycomb structures. For the arrowhead structure,
however, the stress on the bottom surface is still lower than on
the top surface.
Figure 11 shows the nature of the stress distribution on a
cross-sectional X–Y plane (just above the bottom plane by
1.25 mm) under deformation at 0.025 s. It is clear that the
bottom layer experiences very low load compared to the top
surface of the structure. In addition, the load was evenly
2.3. Finite element analysis on cubes—impact loading
Finite element analyses with impact loading conditions were
performed on thermoplastic polyurethane (TPU1, Ninjaflex®)
materials (table 1) for three different geometric structures
including honeycomb, re-entrant hexagon, and arrowhead
using COMSOL Multiphysics FE package version 5.2. The
dimensions of the pads investigated for impact loading are
101.6×101.6×50.8 mm3 (4×4×2 inch3). The geometric parameters of each cell are also shown in figure 8.
An impact load of 1000 N was applied to the circular area
(radius=12.7 mm or 0.5 inch) on the top surface of the
structure for 0.01 s to simulate typical impact load conditions.
The structure was then allowed to relax for another 0.4 s to
investigate the impact load transfer within the structure. The
goal of this test was to simulate the behavior of auxetic
structures during impact. Therefore, a load of 1000 N was
chosen to avoid a complete collapse of the structure while
maintaining a reasonable amount of deformation. The
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Figure 10. Von Mises stress versus time plot on auxetic structures for impact loading: (a) honeycomb, (b) re-entrant hexagon, and (c)
arrowhead, (d) comparison of Von Mises stresses on the bottom surface of all three structures.
distributed over the surface area for the auxetic structures.
However, the honeycomb structure showed a little higher
stress in the center. These results imply that the auxetic
structures can be more useful for body protection applications
than non-auxetic ones.
were compressed by evenly distributed forces of various
values.
Additional studies were conducted on non-auxetic
structures such as a solid bulk pad and a honeycomb pad with
uniform thickness. Figure 13 shows the uniform deformation
over the width of the solid pad and the honeycomb pad with
constant thickness under the compressive load of 20 N. These
pads offer no benefit of dissipating or shunting the input force
through them. On the other hand, figure 14 shows deformation of the auxetic pads under the same load. It can be
observed that the center portion of the bottom surface is raised
in vertical direction even when it is compressed. This unique
behavior of the structures is due to their NPR and stiffness.
For the normal structure with positive Poisson’s ratio, the
lateral dimension of the pad increases while it is compressed
in the vertical direction. This causes easier collapse of the cell
structures, eventually reducing stiffness. On the other hand,
the auxetic cell structures become denser under compression
because it shrinks inward in both directions, which causes the
increased stiffness. Obviously, thicker walled structures will
have higher stiffness. This is an interesting and important
property that can be applied to protective pad design. It means
that pads can be designed to avoid direct transmission of
impact force to the most vulnerable body part, the femur head,
by a gap generated between the body and pad surface due to
the uneven deformation. The impact force will be transmitted
2.4. Various constructions of cell structures
The auxetic effect of impact pads with re-entrant hexagon and
arrowhead structures was examined along with the honeycomb structure. The geometries of each structure are shown in
figure 12. The dimensions of the pads are
152.4×50.8×2.54 mm3 (6×2×0.1 inch3) for compressive loading. To reduce the number of finite elements and
calculation time, the simulation was conducted using
2.54 mm thickness and frictionless support was applied on the
front and rear surfaces to simulate a plain strain condition.
The wall thickness of each cell varied from 1 mm at the center
to 2.5 mm at both edges of the pads.
Finite element analyses of compressive loading conditions were performed on honeycomb, re-entrant hexagon,
arrowhead, and combined structures. To investigate the
mechanical behavior of the auxetic structures, the bottom
ends of the pads were supported by an elastic joint with a
stiffness of 1.0×107 Pa while the top surfaces of the pads
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Figure 12. Impact pads with various combination of thicknesses and
structures: (a) combined, (b) honeycomb, (c) re-entrant hexagon, and
(d) arrowhead.
Figure 11. Von Mises stress versus time plot on auxetic structures
for impact loading: (a) honeycomb, (b) re-entrant hexagon, and (c)
arrowhead.
to the surrounding body parts that are less susceptible to
injury.
Figure 15 compares the difference in height of the bottom
surface (highest-lowest) after deformation for two different
polyurethane pads (TPU1 and TPU2). It shows the highest
height difference for the honeycomb pad and the lowest for
the combined pad. The pad with PLA also shows similar
properties but requires much higher input force to get
observable deformation due to its higher stiffness. Due to the
large difference in the amount of deformation and input forces
for PLA versus TPU1 and TPU2, a direct comparison was not
shown in the graph.
To examine if the way of combining different patterns
affects the mechanical behavior of impact pads, three different
layouts of patterns were modeled and analyzed. Figure 16
shows stress distribution and deformation shape of those three
pads. Unlike figure 14, which shows only center portions of
the pad deformed, figure 16 shows that each pad with
Figure 13. Typical deformation shape of non-auxetic structures
under compression: (a) solid bulk pad and (b) honeycomb pad with
uniform thickness.
combined patterns deformed differently. Regardless of its
location in the pad, the non-auxetic honeycomb pattern
always shows the largest deformation. This means the layout
of auxetic structures is also an important parameter for protective pad design.
2.5. Finite element analysis on pads with various construction
—impact loading
The effect of impact loading was investigated for four material structures: (i) combined structure, (ii) honeycomb
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Figure 16. Stress distribution and deformation shape of each pad
with different combination of patterns.
Figure 14. Deformation of auxetic pads under compression: (a)
combined, (b) honeycomb, (c) re-entrant hexagon, and arrowhead.
Figure 17. Assigning impact loading condition.
to the previous cubical structure (figure 8), which also supports the reduction in impact load. The bottom boundary was
constrained in the Z direction but allowed to move in the X
and Y directions. However, the front and rear surfaces were
constrained in the Y direction but allowed to move in the X
and Z directions.
The boundary probes were assigned on the top and bottom surfaces to predict the maximum von Mises stress. In
addition, the domain probe was assigned to the whole geometry to predict the overall maximum stress on the structure.
The stress versus time plots (figures 18–20) show the von
Mises stress distributions while structures are under impact
load conditions.
It was found that the bottom surface experiences significantly lower stresses compared to the top surface under the
impact load. In addition, the stresses on the bottom surface are
evenly distributed over the surface area even when the load
on the top surface is concentrated on a relatively narrow area.
It was also observed that the bottom surfaces of auxetic pads
experienced less stress than a honeycomb pad. This result
supports the possibility of using such auxetic structures for
attenuating large stresses on the body subjected to an impact.
Figure 15. Height of the raised bottom surface under compression
(for two materials: TPU1 and TPU2): combined, honeycomb, reentrant hexagon, and arrowhead.
structure, (iii) re-entrant hexagonal cells structure, and (iv)
arrowhead structure. The main objective of this effort was to
evaluate the individual and/or combined effect of auxetic
structure and materials on the overall stiffness and shockabsorption performance of the body protection pads. FE
analyses were performed only on thermoplastic polyurethane
(TPU1, Ninjaflex®).
An impact load of 250 N was applied to the top rectangular surface of 25.4×2.54 mm2 (1×0.1 inch2) as shown
in figure 17 for a time duration of 0.01 s to simulate a typical
impact load condition. The structure was then allowed to
relax for another 0.4 s to investigate the impact load transfer
within the structure. The goal of this test was to simulate the
behavior of the auxetic structure rather than the magnitude of
the impact load, therefore 250 N was chosen. In addition, the
present auxetic structure (figure 17) is much thinner compared
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Figure 18. Von Mises stress versus time plot on auxetic structures for impact loading: (a) combined, (b) honeycomb, (c) re-entrant hexagon,
and (d) arrowhead.
that depending on the level of force applied and the materials
used, the Poisson’s ratio and deformation pattern could either
stay constant or change with the force. The FEA and test
results showed good agreement in stiffness and Poisson’s
ratios of the auxetic and non-auxetic materials. The structures
studied showed promising performance in shock absorption,
particularly the re-entrant hexagon and arrowhead structures.
Static and dynamic analyses of impact pads with various
combinations of auxetic structures and cell thicknesses were
conducted. Under the evenly distributed compressive load on
the top surface, the impact pads unevenly deformed creating a
gap between the supporting structure (e.g. human body) and
the pad. Protective pads can be designed to shunt the impact
force away to surrounding areas by specifically laying out the
pattern of auxetic structures. When an auxetic material is hit
by the impact force, it dissipates the shock energy in transverse directions. Therefore, the bottom layer experiences
much lower peak stress compared to the top layer. In addition,
the loads were distributed over a large surface area instead of
being concentrated in the region where the impact force was
applied. The computer simulation results showed that auxetic
materials have the potential to be used in a variety of protective devices including body armor, helmets, gloves,
shoulder pads, and hip pads that exploit better conformability
Figure 19. Comparison of Von Mises stresses on the bottom surface
of all four impact blocks.
3. Conclusions and future work
Auxetic materials have unique mechanical properties and
excellent shock absorption capability. It was shown that even
the same material could have different Poisson’s ratios based
on the structures it was manufactured into. It was also shown
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Figure 20. Von Mises stress distribution on auxetic structures for impact loading at 0.007 s: (a) combined, (b) honeycomb, (c) re-entrant
hexagon, and (d) arrowhead.
ORCID iDs
for comfort and support, and enhanced energy absorption for
lighter and thinner components.
A successful design of protective pads requires a proper
selection of both the material and geometry (structure).
Design methods for optimum distribution or shunting of the
impact force need to be developed considering various
shapes, thicknesses, and materials. Fracture of the auxetic
cells will be considered in the case of high impact loading
conditions to verify if the auxetic structures perform better
than the other structures. Detailed design will also be conducted in the near future. During the design process, slimmer
and more realistic structures will be considered and shock
absorption performance under higher impact force will be
examined.
Chulho Yang https://orcid.org/0000-0001-6228-1133
Hitesh D Vora https://orcid.org/0000-0001-8504-0455
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Acknowledgments
Authors would like to acknowledge the Technology Development Center at Oklahoma State University—for TBDP
Phase I Grant (OSU Invention Disclosure No.: 2016.013).
They also would like to thank Mr Landon Thomas, Mr
Clinton Winterroth, and Mr Benjamin Andrews for providing
help in CAD designing and testing.
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