SOFT ROBOTICS
Volume 2, Number 2, 2015ª Mary Ann Liebert, Inc.
DOI: 10.1089/soro.2015.0002

ORIGINAL ARTICLE

Downloaded by YALE UNIVERSITY from online.liebertpub.com at 08/14/17. For personal use only.

Soft Material Characterization for Robotic Applications
Jennifer C. Case, Edward L. White, and Rebecca K. Kramer

Abstract

In this article we present mechanical measurements of three representative elastomers used in soft robotic
systems: Sylgard 184, Smooth-Sil 950, and EcoFlex 00-30. Our aim is to demonstrate the effects of thenonlinear, time-dependent properties of these materials to facilitate improved dynamic modeling of soft robotic
components. We employ uniaxial pull-to-failure tests, cyclic loading tests, and stress relaxation tests to provide
a qualitative assessment of nonlinear behavior, batch-to-batch repeatability, and effects of prestraining, cyclicloading, and viscoelastic stress relaxation. Strain gauges composed of the elastomers embedded with a microchannel of conductive liquid (eutectic gallium–indium) are also tested to quantify the interaction between
material behaviors and measured strain output. It is found that all of the materials tested exhibit the Mullins
effect, where the material properties in the first loading cycle differ from the properties in all subsequent cycles,
as well as response sensitivity to loading rate and production variations. Although the materials tested show
stress relaxation effects, the measured output from embedded resistive strain gauges is found to be uncoupledfrom the changes to the material properties and is only a function of strain.
address this deficiency by investigating soft strain sensors
undergoing large deformations.29 However, the prior work did
not include measurements or consideration of the timedependent properties of soft materials. To our knowledge, thiseffect has not been rigorously evaluated in the soft robotics
literature. To develop models that predict the response of soft
materials over extended time scales, measurements of timedependent material responses are required.
Furthermore, elastomers of the type commonly used in soft
robots typically exhibit variability in material properties between nominally equivalent batches (batch-to-batch variability), which further complicates the modeling of material
properties. This effect is particularly acute when developing
control algorithms for soft robots, where variability in material properties will drive variability in plant dynamics.
Control systems must be robust to this variability in order toachieve effective control.
In this article, we present our studies on the mechanicaland resistive properties of three elastomers we have used tocreate soft robotic devices: Sylgard 184,5,20 Smooth-Sil 950,
and EcoFlex 00-30.1,2 From these materials, we created two
different types of test samples. The first type of sample isa homogeneous elastomeric ‘‘dog bone’’ used in stress–
strain testing. The second type of sample is a liquid-metalembedded elastomeric strain gauge, used to determine theinteraction between the material properties and the output of

IntroductionS

oft robots have the potential to change the way weconstruct intelligent systems. By using highly deformableand stretchable materials, we can build robots that safely interact
with human operators and function in unstructured environments
such as debris fields or within the human body. To date, various
types of soft robotic components have been demonstrated, including resistance-based sensors,1–4 capacitance-based sensors,5–7 ionic actuators,8–10 pneumatic actuators,11–14 anddielectric actuators.15–17 Recent work on soft sensing technologies has employed liquid-metal-embedded elastomers to measure surface strain,1,2,18 joint angles,19,20 and applied pressure.4,21
These sensor devices rely on deformations of elastomers, including two of the elastomers we analyze in this work, to produce
a change in resistance in embedded liquid metal.
In order to advance the field of soft robotics, additional
knowledge of material behavior is needed. This knowledge
will facilitate the design of soft robotic structures and will
provide the basis for control of soft-bodied systems. It should
be noted that our work does not set out to rigorously characterize and model non-linear and viscoelastic elastomers,22–28
but rather provides a practical guide to material selection forthe soft robotics community. Linear and time-invariant material models do not account for many of the dynamics observedin soft systems. Recent work by Overveld et al. has started to

Department of Mechanical Engineering, Purdue University, West Lafayette, Indiana.

80

Downloaded by YALE UNIVERSITY from online.liebertpub.com at 08/14/17. For personal use only.

SOFT MATERIAL CHARACTERIZATION

81

a soft resistive sensor. Our experiments are designed toprovide a qualitative assessment on five critical areas: nonlinear behavior, batch-to-batch repeatability, effects of prestraining, cyclic loading, and viscoelastic stress relaxation.

where A is the resulting cross-sectional area, and d represents
the contraction normal to the direction of stretching. Notethat DL is the corrected length with correction factor applied
described later, not the applied extension.

Previous work

Material relaxation models

Elastomers have been well studied and many of the uniqueproperties of the materials are well known.30,31 Although no
general theory exists to predict complete viscoelastic elastomeric behavior a priori, progress has been made describing
certain aspects of elastomeric behavior. Beginning in the
1940s, Mullins identified an effect in natural rubber whereby
straining the rubber resulted in a weakening.32 Later groups
have extended this to other rubber-like materials, suggestingthat it is in fact a common effect among all cross-linked
elastomers, as summarized in the review by Diani et al.33 In
addition to nonlinear behaviors, elastomers are also susceptible to viscoelastic creep and stress relaxation. Many models
have been proposed to capture the effects of viscoelastic
materials, including the two-element Maxwell and Kelvinmodels, and the serial combination of the two called the
Burgers model.34 The Zener model is a modified Kelvinmodel with an additional spring.35
Further complicating matters, actual properties differ fromnominal properties due to variations in material processing,such as the cure temperature and base elastomer-to-curing
agent ratio.31 As a result of these complexities, there is a wide
range of material properties reported in the literature. One
reference lists values for the Young’s modulus of polydimethylsiloxane, of which Sylgard 184 is one formulation,
spanning a full order of magnitude (360–3000 kPa).36
Of the three materials we are studying, Sylgard 184 is
by far the most represented in the literature. For example,
Schneider et al. published a study of the stress–strain relationship of Sylgard 184 under different temperature conditions and with different compositions.30 They limited theiranalysis mostly to the linear region of the stress–strain curve,
which is generally below 40% strain. The two other materials
we considered have not yet been described to this extent in
the literature. Additionally, the available soft robotics literature does not address the time-dependent nature of theseelastomeric materials.

The Maxwell, Zener, and Burgers models of viscoelastic
relaxation are shown in Figure 1. The Maxwell model estimates the time evolution of the stress in a relaxing viscoelastic material. The model is presented below in Equation
2.27
r ¼ eRe  Rt=g(2)

where r is stress, e is strain, R is the spring constant, g is thedamping coefficient, and t is time. The Zener model is presented below in Equation 3.28

 R2 (R1 þ R2 Þt
r ¼ e R1 þ R2 e R1 g

(3)

where R1 is the parallel spring constant, R2 is the serial spring
constant, and g is the damping coefficient. The Burgers
model is presented below in Equation 4.27
r¼e

(q1  q2 r1 )e  r1 t  (q1  q2 r2 )e  r2 t
A

(4a)

g1
g
g
gg
þ 1 þ 2 , p2 ¼ 1 2
R1 R2 R2
R1 R2

(4b)

p1 ¼

g1 g2
R2

(4c)

p1  A2p2(4d)

q1 ¼ g1 , q2 ¼

r1 , r2 ¼

A¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
p21  4p2

(4e)Material deformation model

In the following sections, we develop the analytical models
used in this work. Due to the large strains present in our elastomeric samples, our results are presented in terms of truestress, rather than engineering stress. This difference takes into
account the reduction in cross-sectional area during the test. We
assume a Poisson’s ratio v = 0.5 in all of our calculations, as is
generally done with rubber-like materials. This assumption is
identical to assuming conservation of volume during the test.
Assuming that the material is isotropic, and using the differential form of Poisson’s ratio with no assumptions on linearity,
we find the cross-sectional area as a function of extension to be
A ¼ WT(1  2d þ d2 )DL  vd¼1 1þ
L

where g1 is the serial damping coefficient, g2 is the parallel
damping coefficient, R1 is the serial spring constant, R2 is theparallel spring constant, and p1 , p2 , q1 , q2 , r1 , r2 , and A are

(1a)



(1b)

FIG. 1. Models of viscoelastic creep.

82

CASE ET AL.

intermediate variables. As we noted above in the discussionof nonlinear properties, there is no model to predict the coefficients of the models without resorting to experiments.
Equations 2–4 were used to model the time-dependent viscoelastic creep of the elastomers as described below.

Downloaded by YALE UNIVERSITY from online.liebertpub.com at 08/14/17. For personal use only.

Resistive strain gauge model

The strain gauges used in this study utilize liquid metal(eutectic gallium–indium)-filled microchannels in an elastomeric substrate.2,37 As the gauge strains, the length and crosssectional area of the microchannels change, resulting in achange in resistance of the liquid metal. Our analytical modelof the liquid-metal-embedded elastomeric strain gauges isbased on several assumptions. First, we assume that all of thestrain in the gauge is parallel to the direction of the microchannels. This assumption is justified since the bulk of thestrain gauge is in the center of the dog-bone sample, wherestress and strain are nearly uniaxial. Second, we neglect all of
the parts of the sensor that are not part of the primary linear
pattern. This includes the channels to the bonding ports andthe semicircles at the top and bottom of the channels. This
assumption is justified since the lengths that we are neglecting are small compared to the ‘‘active’’ length of thedevice. Finally, we assume that the liquid metal contained in
the sensor is incompressible. With this, we can say that thevolume of liquid metal in the strain gauge is
V ¼ 4L0 A0 ¼ 4LA(5)where V is the volume of the liquid metal, L0 is the initiallength, A0 is the initial area, L is a deformed length, A is adeformed area, and the coefficient accounts for the presenceof four parallel channels in the strain gauge. Thus,
A¼

4L0 A0
L0 A0
A0
¼
¼
4L
L0 þ d 1 þ (6)where d is the deformation and  ¼ Ld0 is the strain. Further,
the resistance of the strain gauge is
R¼

qL
A

(7)

ples were spun for 60 s, with 10 s acceleration and deceleration periods. The EcoFlex 00-30 and Sylgard 184 were bothspun at 200 RPM, resulting in thickness of 371.4 – 31.85 lm
and 307.6 – 19.63 lm, respectively. Smooth-Sil 950 was spunat 400 RPM, resulting in a thickness of 643.0 – 40.57 lm. The
thickness measurements were obtained using a Zeta Instruments Zeta-20 True Color 3D Optical Profiler after curing
and patterning, described below.
Samples for material testing and blank slides to be patterned into strain gauges were placed into an incubator set to60C to cure overnight. Once cured, elastomeric films were
patterned using a Universal Laser Systems VLS 230, utilizing
a 10.6 lm CO2 laser. All of the material testing experiments(i.e., all experiments without embedded strain gauges) used
the same material sample geometry, which is shown in Figure
2a. The geometry is specified in inches to maintain compatibility with the laser drivers. Six patterns of this design can be
cut from a single substrate.
In order to fabricate the liquid-metal-embedded strain
gauges, two layers of elastomer were utilized. The fabrication
sequence consists of patterning a bottom layer of elastomer
with microfluidic channels, as seen in Figure 2b, bonding an
upper layer of elastomer to close the channels, injecting
liquid gallium–indium alloy into the channels, inserting wires
into the parts for electrical connectivity, and finally sealing
the wires in place. In the case of Sylgard 184 and Smooth-Sil
950, the first step in the fabrication of a strain gauge was topattern a blank slide of elastomer. These are the same slides
used to fabricate material test samples described above.
To pattern these slides, the same laser system is used, butwith lower power to achieve a controlled partial cut into thematerial. Once patterned and cleaned, another slide with
spin-coated elastomer was partially cured until tacky. The
patterned elastomeric sheet was then pressed into this tacky
layer with the microchannels between the two layers toachieve a bond between the two layers. In the case of EcoFlex
00-30, we utilized an SU-8 mold on a glass slide to pattern thematerial. Once cured, the patterned EcoFlex 00-30 sheet wasbonded to an unpatterned sheet of equal thickness using oxygen plasma in a PlasmaEtch PE-50. Four-terminal measurements were used for these sensors to negate the effect ofcontact and interface resistances.

Combining Equations 6 and 7 results in the ratio of change
in resistance to initial resistance, which is the expression wecompare to experimental results:DR¼ (2 þ )
R0

(8)

Materials and Methods

The three elastomers described in this article were all
prepared using similar processes. All of these elastomers aredelivered as two liquid or paste parts that were mixed together to begin crosslinking. The two liquid parts were
massed using a Brecknell MBS-6000 electronic balance with
0.1 g resolution. These parts were mixed using a THINKY
ARE-310 centrifugal mixer. The uncured liquid elastomer
was spun onto cleaned 3† · 2† glass slides using a Specialty
Coating Systems Spincoat G3-8 spin coater. All of the sam-

FIG. 2. Test sample geometry for (a) elastomeric dog
bones and (b) strain sensors.

Downloaded by YALE UNIVERSITY from online.liebertpub.com at 08/14/17. For personal use only.

SOFT MATERIAL CHARACTERIZATION

83

FIG. 3. Pull-to-failure data for (a) Sylgard 184, (b) Smooth-Sil 950, and (c) EcoFlex 00-30 with 95% confidence interval(shaded region).
Material testing was conducted using an Instron 3345
single-column material tester fitted with a 1 kN load cellusing custom-made material grips. We conducted a preliminary series of tests to determine the extension correction
factor to convert between applied extension and the actual
extension observed within the elastomeric material. In thecase of the material test samples, we applied two small black
ink dots to the elastomeric sample as shown in Figure 2. We
then placed the sample in the Instron and measured the distance between the dots using a digital calipers at approximately 0%, 20%, 40%, 60%, and 80% of the extension
at failure. In the case of the resistive strain gauge samples,
we measured length from 0 to 35 mm extension in 5 mmincrements. We limited the strain in the resistive strain sensors due to electrical failure at higher strains. In both cases,
we assumed a linear relation between extension and gauge
length. For EcoFlex 00-30, these correction factors (for thematerial test dog bone and resistive strain sensor) wereL = 25.4 + 0.538E and L = 24.5 + 0.709E, for Sylgard 184 thefactors were L = 25.4 + 0.515E and L = 25.8 + 0.550E, andfor Smooth-Sil 950 the factors were L = 25.4 + 0.580E and
L = 26.2 + 0.597E, where L is the gauge length, and E is theextension. These correction factors were used for all subsequent tests. Although this method is not as accurate as measuring gauge factors for each test, we believe it is sufficiently

FIG. 4. Pull-to-failure data for each material at 100 mm/
min. Shaded areas represent 95% confidence intervals.

accurate to support our objective of providing qualitative
assessment of material properties.
Our tests included five types of tests using three methods,
which are pull-to-failure tests, cyclic loading tests, and stressrelaxation tests. Within the first method, we conducted three
types of tests: variable strain rate tests, batch-to-batch consistency tests, and prestrain tests. Cyclic loading and stressrelaxation tests were performed on the strain sensors to determine their resistive response in both of these loading
modes. Each test was run three times for each elastomer, withthe exception of the cyclic loading tests. The average and95% confidence interval for the experiment was determinedbased on the data obtained in each of the three runs.
Pull-to-failure: variable strain rate

Our first series of tests involved pulling samples at aconstant rate until failure. We peeled the cured samples off ofthe substrates and placed the samples directly into the sample
holders. We measured the stress and strain of all three elastomer types at strain rates of 1, 10, and 100 mm/min. The
stress–strain curves for various strain rates for Sylgard 184,
Smooth-Sil 950, and EcoFlex 00-30 are shown in Figure 3.
All three elastomers are shown on a common axis for comparison in Figure 4.

FIG. 5. Pull-to-failure data for each material at 100 mm/
min of three separate batches. Shaded areas represent 95%
confidence intervals.

84
Pull-to-failure: batch-to-batch consistency

To determine batch-to-batch consistency between the materials, three batches of each elastomer were made over a 20day period. Samples from all batches were pulled at a strain
rate of 100 mm/min. The results of these tests are shown in
Figure 5. These samples were prepared using common laboratory equipment, and we believe they represent the level ofvariability that would be expected in practice.

Downloaded by YALE UNIVERSITY from online.liebertpub.com at 08/14/17. For personal use only.

Pull-to-failure: effect of prestrain

To determine the effect of prestrain, we removed a sample
from the glass substrate on which it was cured, prestrained thesample to approximately 80% of the failure extension, andthen relaxed it either briefly or overnight. In both cases, we
completely removed the sample from the test fixture. Afterreplacing the sample in the fixture, the sample was pulled to
failure at a rate of 100 mm/min. The results for Sylgard 184,
Smooth-Sil 950, and EcoFlex 00-30 are shown in Figure 6.
Cyclic loading tests

Our cyclic loading tests were designed to analyze the response of elastomers in conditions representative of whatmight be experienced in a robotic application. We extended
the samples at fixed rates of 10 and 100 mm/min to approximately 80% of the failure extension, and then returned at thesame rate to 0 mm extension, repeating this process for 10
cycles. Cyclic loading tests were performed on strain sensors
to capture repeatability. The sensors were cycled between
0 mm to an absolute extension of 32 mm for 10 cycles. The
stress–strain curves of tests for the Sylgard 184, Smooth-Sil
950, and EcoFlex 00-30 are shown in Figure 7a–c. The resistive sensor results of these tests for Sylgard 184, SmoothSil 950, and EcoFlex 00-30 are shown in Figure 7d–f.
Stress relaxation tests

Our final series of tests were designed to capture the longduration stress relaxation behavior of these elastomers. We
applied an extension of approximately 80% of the failure
extension at a rate of 1,000 mm/min, and held the extension
for 3 h. For strain sensors, we applied an absolute extension of
32 mm at a rate of 1,000 mm/min and held for 3 h. Material
stress relaxation curves for each material are shown in Figure
8a. The curves for the resistive sensors’ stress relaxation tests
are shown in Figure 8b.
Results and Discussion
Material properties are dependent on strain rate

Material properties are typically thought of as strain rate
invariant. However, our experiments show that this is not avalid assumption in the case of these elastomers. From Figure
3, we can see that the stress–strain relationship is dependent
on strain rate. In the case of Sylgard 184 (Fig. 3a), we see thatat 100 mm/min, the material becomes softer than at 1 or
10 mm/min. Smooth-Sil 950 (Fig. 3b) shows increasing
stiffness with increasing strain rate, an opposite effect from
Sylgard 184. EcoFlex 00-30 (Fig. 3c) generally shows softening with increasing strain rates, but the wide confidence
intervals prevent any definitive conclusions. We believe thatthe range between 1 and 100 mm/min is representative of soft

CASE ET AL.

robotic applications such as a strain gauge positioned on amanipulator joint for proprioceptive sensing. Without accounting for the effects of strain rate dependence, using anominal Young’s modulus for these elastomers would giveerroneous results.
Material properties are sensitive to production
variations

From a practical standpoint, the soft robotics researcher
should be concerned about the variability of material properties between batches. Our experiments have shown that,even with what we consider practical process control oversmall batches, we see a meaningful difference in material
properties between batches. Figure 5 shows the stress–strain
relationships for three nominally identical batches for each of
our three test materials. Sylgard 184 shows the most variation. For example, at 100% strain, the stress varies from 5.5 to
12.0 MPa. The curves also demonstrate the small confidence
intervals within a batch, suggesting that batches are internallyconsistent, and that samples taken from the same batch exhibit similar material properties. We believe that these variations are a significant contributor to the variation in the
published data. For this reason, we suggest that nominalmaterial values are not sufficient in critical applications. Instead, materials should be measured once fabricated to ensurethat accurate material properties are known.
Initial strain results in irreversible material changes

Another significant finding is that material properties
change irreversibly after initial strain, a confirmation that the
Mullins effect is present in these materials. This is clearly
illustrated in Figure 6. Of the three materials tested, SmoothSil 950 (Fig. 6b) and EcoFlex 00-30 (Fig. 6c) exhibited themost pronounced change in stiffness, while Sylgard 184 (Fig.
6a) exhibited the same effect to a lesser degree. In thesematerials, straining and relaxing the material had the effect of
reducing its stiffness in the middle of the extension regime.
As strain increases to yield, the stiffness of the prestrainedmaterial quickly increases to match that of the native samples. In the most extreme case, Smooth-Sil 950 shows a 40%
reduction in stiffness at 200% strain. There are significant
differences in stiffness in Smooth-Sil 950 from nearly 0%
strain to 250% strain. In Sylgard 184, the effected region isfrom 60% to 120%, and in EcoFlex 00-30, it is from 100% to500% strain. We also note that, in the case of Smooth-Sil 950,
the material becomes considerably more nonlinear once it hasgone through an initial strain cycle. Sylgard 184 and EcoFlex
00-30 are already sufficiently nonlinear that the qualitativechanges in behavior are less pronounced. Since most soft
robotic applications operate in the middle of the elastic strain
regime, where this prestrain effect is most pronounced, weconclude that this is an important effect that needs to beconsidered by soft robotics designers and by those groups
measuring material properties for soft robotics applications.
Cyclic loading tests show an absenceof work hardening

The cyclic loading tests shown in Figures 7a–c show threeeffects. First, they confirm the results of the prestrain tests
discussed above, and show that there is a significant change inDownloaded by YALE UNIVERSITY from online.liebertpub.com at 08/14/17. For personal use only.

SOFT MATERIAL CHARACTERIZATION

85

FIG. 6. Pull-to-failure data for (a) Sylgard 184, (b) Smooth-Sil 950, and (c) EcoFlex 00-30 with prestrained samples.
Shaded areas represent 95% confidence intervals.

FIG. 7. Material cyclic loading tests for (a) Sylgard 184, (b) Smooth-Sil 950, and (c) EcoFlex 00-30 and resistive strain
cyclic loading tests for (d) Sylgard 184, (e) Smooth-Sil 950, and (f) EcoFlex 00-30. Data are for 10 complete cycles. Jumps
in the data are due to slipping of the sample during the course of the test.

FIG. 8. (a) Step extension response for Sylgard 184, Smooth-Sil 950, and EcoFlex 00-30. Shaded areas represent 95%
confidence intervals of the experimental data, the markers represent the averaged experimental data, and the black lines
represent the theoretical models: Maxwell, Zener, and Burgers. (b) Step extension response for Sylgard 184, Smooth-Sil
950, and EcoFlex 00-30 strain sensors. Shaded areas represent 95% confidence intervals.

86

Downloaded by YALE UNIVERSITY from online.liebertpub.com at 08/14/17. For personal use only.

material properties after the first loading cycle. Second, theyshow that no significant changes in material properties takeplace during the subsequent 10 loading cycles, as all of thesubsequent data fall within a narrow band. Third, the figures
show that there is little to no mechanical hysteresis observedin the materials at these loading rates, since the loading andunloading traces fall over one another. In the case of EcoFlex
00-30 (Fig. 7c), the variation in data arises from a lowfrequency noise source. However, the qualitative results from
EcoFlex 00-30 match the other two materials.
Stress relaxation behaviors are well-modeledby the Burgers model

Both the Zener and the Burgers models for viscoelastic
stress relaxation show good agreement with Sylgard 184 andSmooth-Sil 950 experimental data. Figure 8a shows the 95%
confidence intervals for the long-duration creep tests of thethree materials, and the Maxwell, Zener, and Burgers models
fit for Sylgard 184 and Smooth-Sil 950. We were unable to fit
a model to the EcoFlex 00-30 data, due to significant lowfrequency noise. Our hypothesis is that this error is thermal innature, and is either due to time-varying heating of the material, the load cell, or a combination of the two. We fit
Equations 2–4 to the observed stress data using a leastsquares regression. From the data, we can see that a twoelement model (Maxwell) is not sufficient to capture thetransient dynamics of the material. The three-element model(Zener) is better able to capture the ‘‘slow’’ transient dynamics, but still is unable to capture the ‘‘fast’’ transient. The
four-element model (Burgers) captures both the ‘‘fast’’ and‘‘slow’’ transient effects. That behavior can be seen in Figure
8a, which shows a short, fast creep stage (t < 25 min), followed by a slower creep stage.

CASE ET AL.

tests are shown in Figure 8b. This result supports our conclusion that embedded liquid metal sensors are appropriate
for soft robotic proprioception, as they respond to the current
strain state without regard for previous strain states.
Conclusions

Our experiments have examined three elastomers thathave been used in soft robotic applications. Our focus has
been on identifying material properties that are of concern
to the designer of soft robotic systems. Models for theseproperties have been developed by Ogden and Simo andHughes, but require experimental data to determine thecoefficients for a particular material. This work begins tofill the void present in the literature with regard to soft
material properties. The elastomeric materials discussed inthis article are very different from metals, and many of thesimplifying assumptions that can be made with small deformations are no longer applicable when discussing finite
deformations of viscoelastic materials. Instead, richer dynamics must be evaluated, as demonstrated by the experimental results we have presented. We believe that the work
presented here will be useful in the design of conformableelectronics, soft actuators, active wearable systems, sensory skins, and other highly deformable robotic systems.
Our experiments also validated the use of embedded liquid
metal strain sensors in soft robotic applications. These devices
show good correlation between their output and their current
strain state, without significant effect from the material properties of the elastomeric substrate. This is in good agreement withthe simple analytical model developed for these devices. In
actual soft robotic applications, our experimental results demonstrate that strain gauges can be used to provide proprioception.
Acknowledgments

Strain gauge measurements are highly repeatable

Across all of the materials, the resistance response to strain
is highly consistent and repeatable with no visible Mullins
effect. Further, we find that the resistance response of the strain
gauge is well-modeled by the simple analytical model developed in Equation 8. Moreover, since the analytical model
contains no fitting parameters or arbitrary coefficients, we do
not have to fit the model to the experimental data. Although thematerial response in terms of stress versus strain exhibits ahigher-order nonlinearity, the normalized resistance change
versus strain response exhibits only a quadratic effect, as predicted by the model. The results of normalized resistance change
versus strain are shown in Figures 7d–f. We conclude fromthese measurements that embedded liquid-metal-resistive
strain gauges are an appropriate sensing modality for proprioception in soft robotic systems.

E.L.W. is supported under the National Science Foundation
Graduate Research Fellowship program (DGE-1333468).
This work was partially supported by an Early Career Faculty
grant from NASA’s Space Technology Research Grants
Program (NNX14A052G).
Disclaimer

Any opinions, findings, and conclusions or recommendations expressed in this article are those of the authors and do
not necessarily reflect the views of the National Science
Foundation or the National Aeronautics and Space Administration.
Author Disclosure Statement

The authors declare that they have no competing financial
or other interests that present a conflict of interest.

Strain gauges are not susceptible to material
viscoelastic stress relaxation

References

The long-term response of the strain gauge resistancemeasurements shows little to no effect of stress relaxation.
This is predicted by Equation 8, which shows that there
should be no correlation between stress in the material andthe output resistance. Although the stress in the elastomer ischanging over time, the strain remains fixed, and hence theresistance is unchanged. The results of these long-duration

1. Park Y-L, Chen B-R, Wood RJ. Design and fabrication ofsoft artificial skin using embedded microchannels and liquid conductors. IEEE Sens J 2012;12:2711–2718.
2. Chossat JB, Park Y-L, Wood RJ. A soft strain sensor basedon ionic and metal liquids. IEEE Sens J 2013;13:3405–3414.
3. Menguc Y, Park Y-L, Martinez-Villapando E, et al. Soft
wearable motion sensing suit for lower limb biomechanics

Downloaded by YALE UNIVERSITY from online.liebertpub.com at 08/14/17. For personal use only.

SOFT MATERIAL CHARACTERIZATION

measurements. 2013 IEEE International Conference on
Robotics and Automation (ICRA), 2013, pp. 5309–5316.
4. Kramer RK, Majidi C, Wood RJ. Wearable tactile keypad
with stretchable artificial skin. 2011 IEEE International
Conference on Robotics and Automation (ICRA), 2011, pp.
1103–1107.
5. Lee H-K, Chang S-I, Yoon E. Dual-mode capacitive proximity sensor for robot application: implementation of tactile
and proximity sensing capability on a single polymer platformusing shared electrodes. IEEE Sens J 2009;9:1748–1755.
6. Cotton DPJ, Graz IM, Lacour SP. A multifunctional capacitive sensor for stretchable electronic skins. IEEE Sens J
2009;9:2008–2009.
7. Fassler A, Majidi C. Soft-matter capacitors and inductors
for hyperelastic strain sensing and stretchable electronics.
Smart Mater Struct 2013;22:055023.
8. Wei W, Guo S. A novel PDMS diaphragm micropump basedon ICPF actuator. 2010 IEEE International Conference on
Robotics and Biomimetics (ROBIO), 2010, pp. 1577–1583.
9. Cho MS, Seo HJ, Nam JD, et al. An electroactive conducting polymer actuator based on NBR/RTIL solid polymer electrolyte. Smart Mater Struct 2007;16:S237.
10. Bahramzadeh Y, Shahinpoor M. A review of ionic polymericsoft actuators and sensors. Soft Robotics 2014;1:38–52.
11. Shepherd RF, Ilievski F, Choi W, et al. Multigait soft robot.
PNAS 2011;108:20400–20403.
12. Suzumori K, Endo S, Kanda T, et al. A bending pneumatic
rubber actuator realizing soft-bodied manta swimming
robot. 2007 IEEE International Conference on Robotics andAutomation, 2007, pp. 4975–4980.
13. Polygerinos P, Wang Z, Galloway KC, et al. Soft robotic
glove for combined assistance and at-home rehabilitation.
Robotics Auton Syst 2014; in press.
14. Martinez RV, Branch JL, Fish CR, et al. Robotic tentacleswith three-dimensional mobility based on flexible elastomers. Adv Mater 2013;25:205–212.
15. Cianchetti M, Mattoli V, Mazzolai B, et al. A new design
methodology of electrostrictive actuators for bio-inspired
robotics. Sens Actuat B Chem 2009;142:288–297.
16. Pelrine R, Kornbluh RD, Pei Q, et al. Dielectric elastomer
artificial muscle actuators: toward biomimetic motion. SPIE’s
9th Annual International Symposium on Smart Structures andMaterials, 2002, pp. 126–137.
17. Madden JD, Vandesteeg NA, Anquetil PA, et al. Artificial
muscle technology: physical principles and naval prospects.
IEEE J Ocean Eng 2004;29:706–728.
18. Boley JW, White EL, Chiu GTC, Kramer RK. Direct
writing of gallium indium alloy for stretchable electronics.
Adv Funct Mater 2014;24:3501–3507.
19. Majidi C, Kramer R, Wood RJ. A non-differential elastomer curvature sensor for softer-than-skin electronics, Smart
Mater Struct 2011;20:105017.
20. Kramer RK, Majidi C, Sahai R, Wood RJ. Soft curvature
sensors for joint angle proprioception. 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems(IROS), 2011, pp. 1919–1926.

87

21. Hammond FL, Kramer RK, Wan Q, et al. Soft tactile
sensor arrays for micromanipulation. 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems(IROS), 2012, pp. 25–32.
22. Ogden RW. Non-Linear Elastic Deformations. Dover Publications: 1997.
23. Simo JC, Hughes TJR. Computational Inelasticity. Springer:
2008.
24. Saccomandi G, R. W. Ogden. Mechanics and Thermomechanics of Rubberlike Solids. New York, NY; Springer:
2004.
25. Ogden RW, Saccomandi G, Sgura I. Fitting hyperelastic
models to experimental data. Comput Mech 2004;34:
484–502.
26. Ogden RW. Nonlinear Elasticity with Application toMaterial Modelling. In: AMAS Lecture Notes, Vol. 6,
Warsaw, Poland, 2003.
27. Dorfmann A, Ogden RW. A pseudo-elastic model for loading, partial unloading and reloading of particle-reinforced
rubber. Int J Solids Struct 2003;40:2699–2714.
28. Ogden RW, Holzapfel GA. Mechanics of Biological Tissue. Springer, 2006.
29. Overvelde JT, Menguc Y, Polygerinos P, et al. Numericalmechanical and electrical analysis of soft liquid-embedded
deformation sensors. Extreme Mech Lett 2014;1:42–46.
30. Schneider F, Fellner T, Wilde J, Wallrabe U. Mechanicalproperties of silicones for MEMS. J Micromech Microeng
2008;18:065008.
31. Kim TK, Kim JK, Jeong OC. Measurement of nonlinear
mechanical properties of PDMS elastomer. Microelectron
Eng 2011;88:1982–1985.
32. Mullins L. Effect of stretching on the properties of rubber.
Rubber Chem Technol 1948;21:281–300.
33. Diani J, Fayolle B, Gilormini P. A review on the Mullins
effect. Eur Polym J 2009;45:601–612.
34. Findley WN. Creep and Relaxation of Nonlinear Viscoelastic Materials: With an Introduction to Linear Viscoelasticity. New York: Dover, 1989.
35. McCrum NG, Buckley CP, Bucknall CB. Principles of Polymer Engineering. New York: Oxford University Press, 1997.
36. Meng E, Zhang X, Benard W. Additive Processes for
Polymeric Materials. In: MEMS Materials and Processes
Handbook. New York: Springer, 2011, pp. 198–271.
37. Hyun-Joong K, Son C, Ziaie B. A multiaxial stretchable
interconnect using liquid-alloy-filled elastomeric microchannels. Appl Phys Lett 2008;92.

Address correspondence to:Rebecca K. Kramer
Department of Mechanical Engineering
Purdue University
585 Purdue Mall, ME 2147
West Lafayette, IN 47907
E-mail: rebeccakramer@purdue.edu