Received November 16, 2021, accepted December 4, 2021, date of publication December 27, 2021,
date of current version January 4, 2022.
Digital Object Identifier 10.1109/ACCESS.2021.3138890

Built-in Sensor System for Monitoring Internal
Shear Strain and Stress Distribution inSoft Materials
FENGYU LI 1 , YASUHIRO AKIYAMA 1 , (Member, IEEE), XIANGLONG WAN 2 , (Member, IEEE),SHOGO OKAMOTO 3 , (Member, IEEE), AND YOJI YAMADA1 , (Member, IEEE)
1 Department of Mechanical Systems Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
2 School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
3 Department of Computer Science, Graduate School of Systems Design, Tokyo Metropolitan University, Tokyo 192-0397, Japan

Corresponding author: Fengyu Li (li.fengyu@k.mbox.nagoya-u.ac.jp)
This work was supported by the Grants-in-Aid for Scientific Research (KAKENHI) of the Japan Society for the Promotion of Science
under Grant 16H03134.

ABSTRACT Soft robotics require flexible sensors that can realize sensitive measurements for which rigid
sensors are not viable. Precise and quantitative measurement of the mechanical phenomena is necessary
in all the sensors; however, in the field of soft robotics, the complex structure and physical properties ofcomposite materials complicate the construction of a precise sensing model. In this study, a built-in sensor
system for internal shear strain and stress distribution measurement is developed by embedding piezoelectric
polyvinylidene fluoride polymer films within the objective soft material. Shear-strain sensing models are
established by relating the piezoelectricity and cantilever bending mechanics. For validation, experiments
are conducted in which the deflection of the embedded film sensors is monitored and digitized using avideo camera. The shear-strain sensing model is validated by evaluating the agreement between the modeled
and measured physical variations, and a high coefficient of determination of 0.974 is obtained. In addition,
based on the linear relation of the arithmetic expression of each sensing model, calibrated results for internal
shear strain and stress sensing are successfully obtained. Furthermore, the measurement effect of this typeof flexible sensor and its potential applications are discussed.
INDEX TERMS Built-in flexible sensor, multilayer elastic material, PVDF polymer film, shear strain
distribution, soft robotics.
I. INTRODUCTION

Research on elastomeric and soft robotics has been extensive
and significant in a wide range of areas, such as safe wearable
soft sensors [1] and soft-bodied robots [2]. The flexibilityof soft robotics allows them to be applied to unique cases,
where rigid robots are not a viable option. In addition, they aresafer for human interaction and internal deployment within
the human body. Drastic changes in the shape and size arepossible for adapting to various environments. Technological advancements have enabled the usage of such sensors
in vital applications, such as in wearable assistive healthcare devices [1], [3], medical robotics [4], [5], and tactile
sensors [6], [7].
In the field of stress and strain measurement, internal
physical measurements are a well-known topic. Electrical
The associate editor coordinating the review of this manuscript andapproving it for publication was Laxmisha Rai
VOLUME 10, 2022.

strain gauges and optical strain sensors are generally applied
for concrete structures [8]. However, for soft materials withhigh elasticity or viscoelasticity, direct measurement methods
are rare. The general use of ultrasound images [9], [10]or tomographic particle image velocimetry [11] to monitor
internal tissue displacement involves limited measurement
environments and optical devices. Moreover, the realizationof stringent and real-time measurement is difficult.
To solve this problem, sensitized electronic skin is used tosynthesize the soft-substrate and built-in sensors [12]–[14].
Research on the installation of conventional transducers
within the objective material has been limited owing to challenges in the architecture, manufacturing technology architecture, and manufacturing technology, and the difficulties inguaranteeing measurement accuracy [15].
Additionally, soft materials such as skin tissue are multilayered complex structures with different characteristics foreach layer [16]. As the trend of reproducing the mechanicalThis work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/319

F. Li et al.: Built-in Sensor System for Monitoring Internal Shear Strain and Stress Distribution in Soft Materials

characteristics of human skin has also facilitated the improvement of artificial skin [17], the study of sensor development will not be limited to homogeneous materials alone.
The properties of the composite materials in embedded or
multilayered structures should be carefully considered [18].
Most of the proposed soft sensing techniques have been tested
only through simulation and are not yet ready for practicaluse. The improvement of soft sensors from the simulation
stage to practical use is a significant challenge because theactual process dynamics are more complicated than the conditions considered in simulation experiments [19]. Therefore,
to provide a more precise explanation of the proposed sensor
system, the sensing model should be fully considered andvalidated.
In a previous study, Li et al. had developed a sensor system
for measuring the internal shear strain distribution in soft
materials by embedding an array of polyvinylidene fluoride (PVDF) films [20], [21]. PVDF, which is a thin film-type
piezoelectric polymer [22], has attracted considerable interest
because of its enhanced mechanical and thermal strengthand piezoelectric properties [23]. In the field of robotics,
it has been applied for pressure measurement [24], motion
and vibration monitoring [25], [26], and slip detection for
robot hand grasping [27]. The high mechanical flexibility of
PVDF film sensors renders them suitable for establishing asoft-material built-in sensor system.
In this study, to realize the internal measurement of theshear strain and shear stress distribution in soft materials,
a flexible PVDF film sensor is built in a bilayer substrate.
Sensing models are proposed and validated through experiments in which the charge output and deflection of the embedded sensors are monitored through a transparent material.
To clarify the sensing mechanism, the relation between the
charge generation of the sensor and the deflection is mathematically presented, based on the piezoelectricity and themechanics of the composite structure. Moreover, an artificial
skin substrate with a bilayer structure is developed to tentatively observe the possible application of the sensor system
to more complex structures.
II. SENSOR STRUCTURE AND SENSING MODELS
A. STRUCTURE OF THE EMBEDDED SENSOR SYSTEM

The uniqueness of the proposed sensor system is that the sensing elements are structured within the substrate soft material as an integrated system. The embedded flexible PVDF
films are expected to reflect the mechanical properties ofthe deformed soft substrate material. In this study, the shear
direction is set to take advantage of the high flexibility of the
PVDF film. To improve the shear strain and stress component
measurements, as illustrated in Fig. 1, the PVDF polymer
films were fixed perpendicularly to the surface in the initialstate. The physical variations in the soft material can be
explained by the output charge induced through piezoelectricity. To measure the distribution, different embedded lengthsof sensor elements were arranged in the depth direction at a
position.
320

FIGURE 1. Schematic of the sensor system structure.

B. SHEAR STRAIN SENSING MODEL

The relationship between the output electrical charge fromthe PVDF polymer films and the physical information of
the substrate material is mathematically described in order
to explain the shear sensing mechanism. The measurement
function is divided into shear strain and shear stress sensing
models. The shear strain sensing model is first introduced. For
perpendicularly embedded film sensors under shear deformation of the substrate, the deformation includes bending
motion in the poling direction and stretching motion in thelongitudinal direction. Therefore, the output of the PVDF
sensor qc during measurement is the combined result of thebending effect qb and stretching effect qs as follows:
qc = qb + qs .

(1)

Each sensing model is explained below.
1) BENDING MODEL

A bending model was established based on the piezoelectricity and mechanical behavior of a bending cantilever beam.
The charge generation under deflection of the PVDF film
was calculated based on two main constitutive equations:the direct piezoelectricity equation of the PVDF and thebending curvature differential equation. According to theconstitutive governing equation of piezoelectricity for sheet
PVDF [28], the accumulated electric charge qb induced bybending motion can be calculated asR
qb = e31 A3 S1 dA3 ,(2)
where e31 is the piezoelectric coefficient (75 mC/m2 , measured using the forced oscillation technique and resonancemethod), S1 is the bending strain, and A3 is the electrodearea of the PVDF surface. Subscripts 1 and 3 indicate thelongitudinal direction and poling direction, respectively, corresponding to the l and n axes defined in Fig. 2. To obtain theexpression for the bending strain S1 of a cantilever beam fromthe curvature differential equation, the geometric deflectionof the cantilever-based PVDF film in the O − ln coordinate
is shown schematically in Fig. 2. The origin O was set at theVOLUME 10, 2022

F. Li et al.: Built-in Sensor System for Monitoring Internal Shear Strain and Stress Distribution in Soft Materials

midpoint of the fixed end. The l axis is in the longitudinal
direction of the neutral surface in the undeformed configuration, whereas the m axis is in the plane of the structure perpendicular to the l axis. The bending strain is expressed in termsof the geometric dimension and deflection as follows [29]:S1 (l) = −n00
k · hc= −kh 3 ,
ρ(l)1 + (n0 )2 2

(3)

where ρ is the curvature radius of the neutral layer, hc is the
distance from the center of the PVDF layer to the neutral axis,
kh is the coefficient of dimension revised by the correction
factor k, and n is the deflection of the cantilever beam atany section in terms of l. n0 and n00 represent the first andsecond derivatives of the deflected shape with respect to l,respectively.
Substituting S1 with equation (3), the charge generation in(2) can be expressed as follows:
Z L
n00
(4)
qb = −kh · e31 · b 3 dl,0
1 + (n0 )2 2
establishing the relation between the charge and geometricdeflection. The range of integration is the length from the rootto the free-tip of the sensor film. L is the entire length of thesensor in the longitudinal direction.
The integral part of equation (4) is evaluated as follows:
Z n0 (L)10
qb = −kh · e31 · bp
 3 dn
0
2 2
n (0)
0
1 + (n )n0n0 (L)(5)= −kh · e31 · bp q
2 n0 (0)0
1 + (n )As the PVDF film sensor is perpendicularly fixed, the angleof deflection at the origin position is zero. The output charge
generated by the PVDF film corresponds only to the gradientof the tip of the free-end of the film n0 (L), as follows:
n0 (L)
qb = −e31 · kh · bp q.
1 + [n0 (L)]2
Therefore, n0 (L) can be expressed asqbn0 (L) = q.
(e31 kh bp )2 − q2b

(6)

(7)

According to the properties of the sensor system, thedeflection n(l) of the PVDF film is assumed to coincidewith the internal deformation of the soft substrate. Therefore,n0 (L) represents the shear strain of the substrate at the tipof the free-end of the PVDF film. A series of mathematicalequations for the piezoelectric-polymer-film bending motion
can explain the application of this sensor system for shear
strain monitoring.
Additionally, a remaining parameter that must be determined is kh in equation (6), as shown in Fig.2. This is thedimensional coefficient of the PVDF sensor and is a constant.
VOLUME 10, 2022

FIGURE 2. Orientation and geometric deflection of the PVDF polymer film.

For the qb model, equation (6) can be factored as two parts:
constant parameters and geometrical terms.
qb = K · H ,(8)

K = e31 · kh · bp ,(9)n0n0 (L)
H = −q| 0.
n (0)1 + (n0 )2

(10)

where

and

The constant parameter K , including kh , can be calibrated
based on the proportional relation of the charge generation
qb and geometrical term H .
2) STRETCHING MODEL

The composite structure necessitates the consideration of theinteraction between the embedded sensor element and thesubstrate in the sensing mechanism. Because built-in films
do not perfectly follow the deformation of the substrate anda stretching press occurs in the longitudinal direction undershear deformation, a stretching model is additionally combined with the sensing model. The stress effect along thelongitudinal direction of the sensor is defined as τ1 , anddepicted in Fig. 3.
The small triangle in the figure represents a unit in theelastic substrate used to calculate the interface press of σ3and τ1 . σ3 on the two sides of the film is considered to bein equilibrium and does not apply an additional press in thepoling direction. Therefore, the charge qs , which is affectedby the surrounding stress distribution, can be expressed asZ
qs = d31 τ1 dA
A
Z L= d31 · bp
τ1 dl,(11)0
τ1 = τxz sin2 θ − cos2 θ + (σz − σx ) sin θ cos θ, (12) dl
= arccot n0 ,(13)
θ = arctandn321

F. Li et al.: Built-in Sensor System for Monitoring Internal Shear Strain and Stress Distribution in Soft Materials

FIGURE 4. Composite material unit composed of sensor film andsubstrate.
FIGURE 3. Schematic illustration of the stress effect from the substrate to
the film sensor.

where d31 is the piezoelectric coefficient with a value of
25 pC/N, which is also measured using the forced oscillation
technique and resonance method.
Because there is no direct measurement method to obtain
the internal stress, the modeling function must be expressedusing deformation variables. The stress components weretransformed into a strain expression using Hook’s law asfollows:
σx = 2Gεx + λ (εx + εz )σz = 2Gεz + λ (εx + εz )
τxz = Gγxz ,(14)where G is the shear modulus of the substrate. Thus, τ1 inequation (11) can be expressed using deformation parametersalone:
τ1 = Gγxz sin2 θ − cos2 θ + 2G (εz − εx ) sin θ cos θ= G εy − εx sin 2θ − γxz cos 2θ





∂u ∂v
∂v ∂u
−
sin 2θ −−cos 2θ . (15)
=G
∂z ∂x
∂z
∂x

Another measurement function is the shear stress sensing
mode. The shear stress can be directly obtained from theresult of the shear strain model if the physical characteristicsof the applied substrate material have been preliminarily
obtained. Based on the mechanics of the materials, the shear
stress component τxz is calculated by multiplying the shear
strain γxz with the shear modulus G of the local substratematerial using the following equation:(16)

However, as an integrated system, the composite materialof the substrate material as well as the embedded sensor
elements should be considered to clarify the mechanicalproperties. Although it is assumed that the highly flexible
film sensor element complies with the deformation of thesubstrate, as a discontinuous material, new variables need to
be defined for the composite material.
As illustrated in Fig. 4, the measurement position, whichis the tip of the free-end of the film, is the focused upon. The
deformed material unit is extracted as a composite material
322

X
,
(17)
h
where h is the thickness of a single layer of the substrate.
As mentioned in the introduction, this study uses a substrate with two material layers, leading to the following
transformation:
τxz = G ·

τxz = Gi · γiX2
i=1hi · γi = X ,(18)

where subscript i refers to each layer.
In consequence, the shear stress sensing model is given as

C. SHEAR STRESS SENSING MODELτxz = G · γxz .

unit, whose mechanical properties are determined by both thesubstrate and sensor stiffness. The shear modulus is definedas Gcom . This inherent property parameter is generally calibrated before measurement using a series of stress-strain
data. Under simple shear deformation, the shear strain γxz
is obtained based on the previous shear strain model. Shearstress τxz can be applied as the surface shear stress because
it is translated evenly within the sensor system in the depth
direction [30].
In addition, when the shear deformation induced from thesurface is in displacement control, shear stress τxz is transformed from the surface displacement X as follows:τxz =G1 · X= Gcom · γxz .
G2 · h1 + G1 · h2

(19)III. EXPERIMENT AND DATA PROCESSING METHOD
A. EXPERIMENTAL SETUP

Experiments were conducted to validate the sensing modelsof the proposed sensor system and clarify the measurement
effect. For sensor testing, as depicted in Fig. 5, a bilayer
structure with two types of artificial skin (HITOHADA GEL,EXSEAL Co., Ltd., Mino, Japan) is utilized as the soft
substrate material. The upper-layer (blue colored) has an
ASKER-C hardness of seven, whereas the lower layer (yellow colored) has an ASKER-C hardness of zero; the shear
moduli of the upper and lower layers are 1.35 × 105 and0.54 × 105 Pa, respectively. Thicknesses h1 and h2 shownin equation(19) are both 6 mm. Within the bilayer substrate,
six PVDF films (KUREHA Co.,Ltd, Japan) are arranged at
the central position beneath the substrate material without the
influence of the periphery. The six PVDF films are aligned
and embedded at various depths, corresponding to measured
VOLUME 10, 2022

F. Li et al.: Built-in Sensor System for Monitoring Internal Shear Strain and Stress Distribution in Soft Materials

FIGURE 6. Experimental system [20].
FIGURE 5. PVDF arrangement in the bilayer model.

heights of 0.5, 2.5, 4.5, 6.5, 8.5, and 10.5 mm, respectively,from left-to-right. The measured height refers to the length of
the free-end of the sensor from a fixed position, as explainedin the sensing model.
A plastic testbed with inlaid clamps matching the film
thickness was manufactured as a PVDF film supporter usinga three-dimensional printer. For signal transmission, electric
wiring from the solder tabs was performed below the testbed.
The experimental setup is shown in Fig. 6. External
stress was applied using a manipulator (MOTOMAN-MH5F,
Yaskawa Electric Co., Ltd., Kitakyushu, Japan). Dynamic
simple shear deformation was provided by a 2-Hz sinusoidal
waveform in the horizontal direction. The low-frequency
region was focused upon because investigation of skin contact
safety showed that the frequency range of skin vibration
was up to 10-Hz [31]. The part that contacted the substratesurface was designed as a large, square acrylic board tocover the entire device. Note that the contact part did notslip on the substrate, and the surface motion strictly agreed
with the contact plate. A signal conditioning method wasdeveloped using a suitable charge amplifier circuit to achievea real-time charge output with high signal-to-noise ratio [20].
The amplifier provided stable signal amplification in a wide
frequency range up to 100-Hz such that the influence of thephase shift induced by vibration could be neglected.
1) SHEAR STRAIN MODEL VALIDATION TESTThe shear strain sensing model was validated by comparing
the calculated result with the measured charge generation.
Calculation of qb and qs according to equations (6)–(11)requires the measurement of the film sensor deflection.
Taking advantage of the transparent substrate material, theembedded sensor wass clearly filmed using a video camera
VOLUME 10, 2022

from the lateral-side. The shear deformation condition witha surface displacement amplitude of 2.5 mm was selected as
the analysis target.
To capture the quantitative position n − l of the films in
the coordination, the images recorded by the video camera
were processed. Pictures of the film deflection under maximum shear deformation were extracted using GetData Graph
Digitizer(Version 2.26.0.20, S. Fedorov, Russia), as shown in
Fig. 7a. The lines of the film profile were then extracted in thedefined coordinate, and the deflection was digitized. Further,
the curves were fitted to each series of points through polynomial curve fitting. The polynomial degree was set to three andsix for the three shorter and longer films each, respectively,
because the longer one had more complex deflection. Finally,
the specific information of the optimized film curve can beobtained, as shown in Fig. 7b. Therefore, the modeled charge
generation qc , including qb and qs , can be calculated from thedeflection data.
Note that the initial state of the film might not be perfectly
vertical to the horizontal line. The variation in deflection isdefined based on the initial arrangement condition of eachsensor film. Moreover, the calibration result K was obtained
from the proportional relation of qb and the geometric term
according to equations (13).
2) SHEAR STRESS MODEL VALIDATION TEST

Sequentially, the function of the shear stress sensing model
was tested based on equation (19). To validate the linear relation between the shear stress and strain, a seriesof data were measured under different shear deformation
amplitudes A from 0.5–5.5 mm. The shear stress τxz was
obtained by substituting X with A according to the left-sideof equation (19), and the shear strain γxz was obtainedby substituting the measured charge in the strain-sensing
model.
323

F. Li et al.: Built-in Sensor System for Monitoring Internal Shear Strain and Stress Distribution in Soft Materials

FIGURE 8. Charge output amplitude distribution measurement result
from each sensor.

FIGURE 7. Film deflection in the defined coordinate.

IV. RESULT
A. VALIDATION RESULT OF THE SHEAR STRAIN SENSINGMODEL

The modeled charge generation of the PVDF was comparedwith the directly measured charge output to validate the established shear strain sensing model. Fig. 8 shows the measured
charge generation amplitude distribution qm from each sensor
for 15 measurement trials. The horizontal axis is the embedded length of the sensing area L of six sensors. Under sinusoidally varied shear deformation, the results of the maximum
deformation states in two opposite directions are plotted in
the same figure. To better observe the symmetry, the verticalaxis (orange colored) denoting the negative output under theminus shear direction is reversed. Both results present an
inflection in the distribution tendency at the interlamination
boundary, which is marked by a broken line. The output signal
initially increases from the bottom in the softer layer and thendecreases incessantly up to the contact surface. The output
between the two shear directions shows an approximately
symmetrical distribution.
Further, using the digitized deflection of each PVDF film,
the modeled charge from the bending model qb and stretchingmodel qs is obtained; however, compared to the measured
output result qm , the result of the stretching model qs ismore than two orders of magnitude smaller. Hence, for shear
strain sensing, the bending model is sufficiently sensitive torepresent the mechanism.
For calibration, Fig. 9 plots the linear relation of geometricterm H and qb according to equations (8)–(10). The verticalaxis qb is obtained by subtracting the measured result on
stretching the model part, qm − qs . The constant parameter
represented by K is summarized from the slope as 783.57.
324

FIGURE 9. Proportional relation to summarize coefficient K .

FIGURE 10. PVDF arrangement in the bilayer model.

The modeling result qc from equation (1) is compared withthe measurement result qm under the maximum deformationin Fig. 10. The results under each of the two shear directions
VOLUME 10, 2022

F. Li et al.: Built-in Sensor System for Monitoring Internal Shear Strain and Stress Distribution in Soft Materials

TABLE 1. Calibration result of the shear stress measurement.

FIGURE 11. Measured local shear strain result at different deformations
under 2 Hz.

FIGURE 13. Gradient distribution of each film.

FIGURE 12. Linear relation to obtain the composite shear modulus.

are plotted. The twelve pairs of results from six PVDF films in
Fig. 10 were used to reach an agreement. The agreement of qc
and qm is evaluated based on the coefficient of determination
R2 = 0.974, indicating the significance of the prediction of
the established model. Furthermore, the root mean squared
error in 26.06 pC and the mean absolute percentage error of
19.8% of qc based on qm additionally confirm the excellent
agreement.
B. VALIDATION RESULT OF THE SHEAR STRESS SENSINGMODEL

The linear relation between the shear stress conditions andthe measured strain was evaluated to validate the establishedshear stress model. Fig. 11 shows the measured shear strain
distributions of the six PVDF films. The different strain
distribution lines correspond to different maximum deformations A.
Further, using the above data, the relationship between theshear strain γxz of each PVDF film and the corresponding
shear stress τxz is plotted in Fig. 12. The different lines correspond to different PVDF films. The linear variation validates
the shear stress sensing model, and the reciprocal slope of theregression line represents the composite shear modulus Gcom
based on equation (19), whose calibration results are listed inTable 1.
V. DISCUSSION
A. SHEAR STRAIN SENSING MODEL

Initially, in the shear strain sensing model, the piezoelectriccharge was modeled by the bending and stretching motions
VOLUME 10, 2022of the PVDF film sensor; however, as explained in the shear
strain sensing model validation results in Section IV, theeffect of the stretching model was relatively limited. From
another point of view, because the stretching effect always
generates a positive piezoelectric charge under both opposite
shear states, a small qs agrees with the fact that the output
charge generation between the two opposite shear directions
has high symmetry, as shown in Fig. 8. The limited effect of
the stretching model can be explained by the small piezoelectric coefficient d31 by orders of magnitude.
In comparison, the bending model is sufficiently sensitive to represent the sensing mechanism. Therefore, for thistype of piezoelectric film sensor, the effect of the deflection
dominates the output signal. As derived in equation (5), theinduced charge is directly related to the deflection differentialof the free-end tip of the sensor film.
B. SHEAR STRAIN DISTRIBUTION

As plotted in Fig. 11, the measured shear strain distribution of
the bilayer soft material in the depth direction first increases
to a peak and then decreases. The measurement effect of
substrate deformation reflected on the sensing element should
be assessed. Here, the shear strain of the bilayer substrate in
the experimental condition was calculated for comparison.
According to the linear elasticity expressed in equation (18),when the surface displacement X is 2.5 mm, the shear strain
γ1 and γ2 of each layer are 0.12 and 0.3, respectively [32];however, the distribution measured by the sensor system ineach layer shows a gradually varying value.
To describe the phenomenon intuitively, the gradient of
the film deflection under the above-mentioned conditions isplotted in Fig. 13. The two horizontal dotted lines represent
the actual shear strains γ1 and γ2 of the substrate. Sensor film325

F. Li et al.: Built-in Sensor System for Monitoring Internal Shear Strain and Stress Distribution in Soft Materials

curves with different lengths were deformed in various ways.
As flexible sensors, they are compliant with the deformationof the substrate, and the differential deflection approaches thelinear shear strain of each layer; however, as mentioned in
the stress sensing model, the stiffness of the built-in sensor isdifficult to ignore. Sensor films with considerable stiffness,
especially the shorter ones, tend to have a larger difference
from the actual shear strain value.
C. LIMITATION AND FUTURE WORK

For strain measurement, the accuracy is limited by the stiffness of the embedded sensors and their arrangement relative
to the substrate material. Direct measurement of the shear
strain requires a more ideal flexible sensor, which is expected
in material science. Furthermore, manufacture of the interposition system is also difficult. If a very light and soft sensor isapplied, a manufacturing operation is required to cautiously
construct the soft PVDF film in a flat state. As applied inthis study, a type of urethane resin is recommended as thesubstrate soft material, which can solidify from the liquidstate without influencing the natural state of the sensor.
Based on the above discussions, this sensor system canbe applied to various materials for sensitive measurement ofboth the shear strain and shear stress. To simulate humanexperimentation, anthropometric dummies or substitute animal tissue are often applied. This sensor system can render the biomaterials smarter and provide more informationon the internal physical phenomena. In future, human-bodydummy models equipped with the built-in sensor system will
be developed and used for conducting human contact safety
experiments.
VI. CONCLUSION

For the internal physical measurement of soft materials, a sensor system was developed in this study to measure the internal
shear strain and stress distribution of bilayer artificial skin,using built-in flexible PVDF films. To explain the sensing
mechanism, sensing models were mathematically establishedbased on piezoelectricity and material mechanics. The shear
strain sensing model considers the bending and stretchingmotions of the film sensor. The shear stress sensing model
proposes a definition of the shear modulus for composite
material.
In the validation experiment, the shear strain and stressof the bilayer artificial skin substrate in the depth direction
were measured. The deflection of the embedded PVDF films
was captured by a video camera and digitized through image
processing. Excellent agreement of the charge generation
results between the model and measurement was found witha high R2 coefficient of determination of 0.974. In addition, calibration for both strain and stress measurements wasintroduced. The measured shear strain distribution tendency
indicated the boundary of the multimaterial and provided areasonable mechanical explanation. Adaptable suggestions
on improving the measurement and manufacturing accuracy
were additionally provided.
326

In summary, the application of the proposed sensor system
for internal shear strain and stress sensing in soft materials
was systematically validated. This sensor system is expected
to have immense potential for application in soft material
measurement and soft robotics development.
REFERENCES[1] S. Xu, D. M. Vogt, W.-H. Hsu, J. Osborne, T. Walsh, J. R. Foster,S. K. Sullivan, V. C. Smith, A. W. Rousing, E. C. Goldfield, and
R. J. Wood, ‘‘Biocompatible soft fluidic strain and force sensors for
wearable devices,’’ Adv. Funct. Mater., vol. 29, no. 7, Feb. 2019,
Art. no. 1807058.
[2] L. Viry, A. Levi, M. Totaro, A. Mondini, V. Mattoli, B. Mazzolai, and
L. Beccai, ‘‘Flexible three-axial force sensor for soft and highly sensitive
artificial touch,’’ Adv. Mater., vol. 26, no. 17, pp. 2659–2664, 2014.
[3] Y.-L. Park, B.-R. Chen, N. O. Pérez-Arancibia, D. Young, L. Stirling,
R. J. Wood, E. C. Goldfield, and R. Nagpal, ‘‘Design and control of a
bio-inspired soft wearable robotic device for ankle–foot rehabilitation,’’Bioinspiration Biomimetics, vol. 9, no. 1, 2014, Art. no. 016007.
[4] A. Miriyev, K. Stack, and H. Lipson, ‘‘Soft material for soft actuators,’’
Nature Commun., vol. 8, no. 1, pp. 1–8, Dec. 2017.
[5] Z. T. H. Tse, Y. Chen, S. Hovet, H. Ren, K. Cleary, S. Xu, B. Wood, and
R. Monfaredi, ‘‘Soft robotics in medical applications,’’ J. Med. Robot. Res.,
vol. 3, nos. 3–4, Sep. 2018, Art. no. 1841006.
[6] J. C. Yeo, J. Yu, Z. M. Koh, Z. Wang, and C.-T. Lim, ‘‘Wearable tactile sensor based on flexible microfluidics,’’ Lab Chip, vol. 16, no. 17,
pp. 3244–3250, 2016.
[7] M. Kaltenbrunner T. Sekitani, J. Reeder, T. Yokota, K. Kuribara,
T. Tokuhara, M. Drack, R. Schwödiauer, I. Graz, S. Bauer-Gogonea, S.
Bauer and T. Someya, ‘‘An ultra-lightweight design for imperceptible
plastic electronics,’’ Nature, vol. 499, no. 7459, pp. 458–463, Jul. 2013.
[8] B. Bonfiglioli and G. Pascale, ‘‘Internal strain measurements in concreteelements by fiber optic sensors,’’ J. Mater. Civil Eng., vol. 15, no. 2,
pp. 125–133, Apr. 2003.
[9] K. Holst, H. Liebgott, J. E. Wilhjelm, S. Nikolov, S. T. Torp-Pedersen,
P. Delachartre, and J. A. Jensen, ‘‘Internal strain estimation for quantification of human heel pad elastic modulus: A phantom study,’’ Ultrasonics,
vol. 53, no. 2, pp. 439–446, Feb. 2013.
[10] A. I. Bowler, B. W. Drinkwater, and P. D. Wilcox, ‘‘An investigation into
the feasibility of internal strain measurement in solids by correlation ofultrasonic images,’’ Proc. Roy. Soc. A, Math., Phys. Eng. Sci., vol. 467,
no. 2132, pp. 2247–2270, Aug. 2011.
[11] A. Takahashi, S. Suzuki, Y. Aoyama, M. Umezu, and K. Iwasaki, ‘‘A threedimensional strain measurement method in elastic transparent materials
using tomographic particle image velocimetry,’’ PLoS ONE, vol. 12, no. 9,
Sep. 2017, Art. no. e0184782.
[12] B. Shih, D. Shah, J. Li, T. G. Thuruthel, Y.-L. Park, F. Iida,
Z. Bao, R. Kramer-Bottiglio, and M. T. Tolley, ‘‘Electronic skins andmachine learning for intelligent soft robots,’’ Sci. Robot., vol. 41, 2020,
Art. no. eaaz9239.
[13] C. Majidi, ‘‘Artificial skin,’’ Mech. Eng., vol. 138, no. 3, pp. S17–S21,
2016.
[14] R. Dahiya, N. Yogeswaran, F. Liu, L. Manjakkal, E. Burdet, V. Hayward,
and H. Jorntell, ‘‘Large-area soft e-skin: The challenges beyond sensor
designs,’’ Proc. IEEE, vol. 107, no. 10, pp. 2016–2033, Oct. 2019.
[15] K. Noda, K. Hoshino, K. Matsumoto, and I. Shimoyama, ‘‘A shear stresssensor for tactile sensing with the piezoresistive cantilever standing inelastic material,’’ Sens. Actuators A, Phys., vol. 127, no. 2, pp. 295–301,
Mar. 2006.
[16] H. Joodaki and M. B. Panzer, ‘‘Skin mechanical properties and modeling:
A review,’’ Proc. Inst. Mech. Eng., H, J. Eng. Med., vol. 232, no. 4,
pp. 323–343, Apr. 2018.
[17] Y. Iki, Y. Yamada, Y. Akiyama, S. Okamoto, and J. Liu, ‘‘Designing adummy skin by evaluating contacts between a human hand and a robot end
tip,’’ in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS), Oct. 2020,
pp. 11337–11344.
[18] T.-D. Ngo, ‘‘Introduction to composite materials,’’ in Composite andNanocomposite Materials, T.-D. Ngo, Ed. Rijeka, Croatia: IntechOpen,
2020, ch. 1, doi: 10.5772/intechopen.91285.
[19] C. Abeykoon, ‘‘Design and applications of soft sensors in polymer processing: A review,’’ IEEE Sensors J., vol. 19, no. 8, pp. 2801–2813, Apr. 2019.
VOLUME 10, 2022

F. Li et al.: Built-in Sensor System for Monitoring Internal Shear Strain and Stress Distribution in Soft Materials[20] F. Li, Y. Akiyama, X. Wan, S. Okamoto, and Y. Yamada, ‘‘Measurementof shear strain field in a soft material using a sensor system consisting of
distributed piezoelectric polymer film,’’ Sensors, vol. 20, no. 12, p. 3484,
Jun. 2020.
[21] F. Li, Y. Akiyama, X. Wan, Y. Yamada, and S. Okamoto, ‘‘Shear stresssensor for soft material with built-in piezoelectric polymer films,’’ inProc. IEEE 8th Global Conf. Consum. Electron. (GCCE), Oct. 2019,
pp. 656–658.
[22] H. Kawai, ‘‘The piezoelectricity of poly (vinylidene fluoride),’’ Jpn.
J. Appl. Phys., vol. 8, no. 7, p. 975, 1969.
[23] S. D. Mahapatra, P. C. Mohapatra, A. I. Aria, G. Christie, Y. K. Mishra,
S. Hofmann, and V. K. Thakur, ‘‘Piezoelectric materials for energy harvesting and sensing applications: Roadmap for future smart materials,’’ Adv.
Sci., vol. 8, no. 17, Sep. 2021, Art. no. 2100864.
[24] A. V. Shirinov and W. K. Schomburg, ‘‘Pressure sensor from a PVDF
film,’’ Sens. Actuators A, Phys., vol. 142, no. 1, pp. 48–55, 2008.
[25] H. Lee, R. Cooper, B. Mika, D. Clayton, R. Garg, J. M. Gonzalez,
S. B. Vinson, S. Khatri, and H. Liang, ‘‘Polymeric sensors to monitor
cockroach locomotion,’’ IEEE Sensors J., vol. 7, no. 12, pp. 1698–1702,
Dec. 2007.
[26] M. Luo, D. Liu, and H. Luo, ‘‘Real-time deflection monitoring for millingof a thin-walled workpiece by using PVDF thin-film sensors with a cantilevered beam as a case study,’’ Sensors, vol. 16, no. 9, p. 1470, Sep. 2016.
[27] B. Choi, H. Ryeol Choi, and S. Kang, ‘‘Development of tactile sensor
for detecting contact force and slip,’’ in Proc. IEEE/RSJ Int. Conf. Intell.
Robots Syst., Aug. 2005, pp. 2638–2643.
[28] J. Sirohi and I. Chopra, ‘‘Fundamental understanding of piezoelectricstrain sensors,’’ J. Intell. Mater. Syst. Struct., vol. 11, no. 4, pp. 246–257,
Apr. 2000.
[29] F. P. Beer, R. Johnston, J. Dewolf, and D. Mazurek, Mechanics of Materials. New York, NY, USA: McGraw-Hill, 1981, pp. 150–233.
[30] P. A. Hassan, G. Verma, and R. Ganguly, ‘‘Soft materials-properties
and applications,’’ in Functional Materials: Preparation, Processing andApplications. Amsterdam, The Netherlands: Elsevier, 2011, p. 1.
[31] Y. Akiyama, Y. Yamada, K. Ito, S. Oda, S. Okamoto, and S. Hara, ‘‘Test
method for contact safety assessment of a wearable robot -analysis of loadcaused by a misalignment of the knee joint,’’ in Proc. IEEE RO-MAN: 21stIEEE Int. Symp. Robot Hum. Interact. Commun., Sep. 2012, pp. 539–544.
[32] K. L. Johnson and K. L. Johnson, Contact Mechanics. Cambridge, U.K.:
Cambridge Univ. Press, 1987.

FENGYU LI was born in Qingdao, Shandong,
China, in 1994. She received the B.S. degree
in engineering from Wuhan University, Hubei,
China, in 2016, and the M.S. degree inengineering from Nagoya University, Nagoya,Japan, in 2020.

VOLUME 10, 2022

YASUHIRO AKIYAMA (Member, IEEE) received
the B.E. degree in engineering from the Tokyo
Institute of Technology, Tokyo, Japan, in 2006, andthe M.S. and Ph.D. degrees in engineering fromThe University of Tokyo, Tokyo, in 2008 and 2011,
respectively. Since 2016, he has been an Assistant Professor with Nagoya University, Japan. His
main research interests include mechanical safety,
human–robot interaction, and biomechanics.

XIANGLONG WAN (Member, IEEE) received
the Ph.D. degree in engineering from Kobe University, Japan. He is currently a Lecturer at the Schoolof Automation and Electrical Engineering, University of Science and Technology Beijing, China. His
main research interests include singular configuration in robotics, rehabilitation robots, gait analysis,
and biomechanics.

SHOGO OKAMOTO (Member, IEEE) received
the Ph.D. degree in information sciences fromTohoku University, in 2010. From 2010 to 2021,
he was with Nagoya University. He is currently
an Associate Professor with the Department ofComputer Science, Tokyo Metropolitan University. His research interests include haptics, assistive robotics, human-centered informatics, andaffective engineering.

YOJI YAMADA (Member, IEEE) received the
Ph.D. degree from the Tokyo Institute of Technology. Since 1983, he has been with the Toyota
Technological Institute, Nagoya, Japan. In 2004,
he joined the Safety Intelligence Research Group,
National Institute of Advanced Industrial Scienceand Technology (AIST), as a Leader. In 2009,
he joined the Department of Mechanical Scienceand Engineering, Graduate School of Engineering,
Nagoya University, as a Professor.

327