0-7803-7454-1/02/$17.00 ©2002 IEEE

23.4: Novel Senso r Technolog y for Shear and Norma l StrainDetectio n wit h Generali zed Elect rostriction

Torrey R. Filanc-BowenMechanical Engineering

University of Wisconsin - MadisonMadison, WI, USA

tfilancbowen@students.wisc.edu

Geun Hyung KimMechanical Engineering

University of Wisconsin - MadisonMadison, WI, USA

gkim@cae.wisc.edu

Yuri M. Shkel∗

Mechanical EngineeringUniversity of Wisconsin - Madison

Madison, WI, USAyshkel@engr.wisc.edu

AbstractWe present a novel technology for stress and strain sens-ing. As a fundamental property of any dielectric ma-terial, electrostriction determines the effect of elasticdeformation on dielectric properties. An electrostric-tion sensor detects the dielectric changes due to defor-mation in the media with data acquisition approach,which resembles well-known capacitance sensing tech-niques. Electrostriction sensing technology does notrely on mechanical contact between the sensor elec-trodes and the sensing media, nor does it require phys-ical displacement of the electrodes. Thus, detection ofnormal and shear loads can be implemented in a singleplate configuration with no moving parts. Electrostric-tion sensor design is robust and has high tolerance tooverloads—a critical issue for tactile sensing in roboticapplications. With many materials available for sens-ing media, we discuss electrostriction phenomenon inisotropic and anisotropic polymer composites and pro-vide guidance for selection of a material for a given ap-plication.

KeywordsTactile, stress and strain sensors; capacitance sensing;electrostriction; solid-state sensor.

INTRODUCTIONDeformation and displacement measurements are re-quired for stress, strain, pressure, and tactile sensing.Tactile sensors are widely used in manipulation tasks,automatic grasping, and compliance control (see [5]for a review). Many of the tactile sensors in existenceuse capacitance arrays [2, 5] of pressure-sensitive ele-ments which, when in contact with an object, can pro-vide information on the location of the contact and adistribution of normal stresses in the contact area. Tra-ditional design of capacitance sensors with a vacuumor air-gap capacitor cannot withstand large loads. It isalso a challenging task to design a simple and reliablecapacitor sensor arrays for shear deformations.An entirely new concept of capacitor sensors—singleplate solid-state device is proposed. Single plate tech-nology offers a simple and reliable way to manufac-∗Author to whom all correspondence should be addressed.

ture sensor arrays for stress and strain mapping. Inthis article we discuss the design, modeling and testingof novel single-plate capacitance sensor that incorpo-rates an elastic dielectric material on top of the elec-trodes. Electrostriction properties of the material areemployed to detect deformations. Thus, the dynamicresponse of the sensor is determined by properties of thedielectric material rather than properties of the elec-trodes and no physical displacement of electrodes isneeded. This technology overcomes shortcomings ofair-gap or vacuum-gap capacitors such as lack of ro-bustness, fragility, rigid backing, cost, manufacturabil-ity, but retains the benefits of a capacitor sensing so-lution. Proper selection of dielectric material and elec-trode configuration could make such a device capableto resolve normal or shear deformation.

To illustrate advantages of electrostriction sensing webriefly consider operation of a parallel plate capacitorsensor. Such systems have been traditionally employedin sensor applications and implemented with micro-machining designs (see, for example, [7] and referenceswithin). Pressure or stress loads transmitted to the ca-pacitor electrodes deform them and alter capacitance ofthe sensing element. The capacitance can be measuredby a number of well established methods [1, 3].

A single-plate capacitor sensor for pressure, stress andstrain measurements has no moving parts and detectsdeformations via change in properties of the dielectricmaterial attached to the electrodes. An electrode pat-tern on the surface can be easily manufactured by pho-tolithographic process. With proper selection of elec-trode orientations and dielectric material structure, anarray of single-plate sensors is capable to resolve a dis-tribution of normal and shear stress components overthe surface. We deliberately do not limit the choiceof materials attached to the sensor electrodes—any ex-isting dielectric material can be utilized. For example,material used as a construction element of any designsuch as manipulator or transducer, can be a sensing me-dia, thus, avoiding excessive “interface layers” betweendevice and the sensing mechanism. Although not ad-dressed in this paper, future investigations may be fo-cused on the engineering materials tailored for specificsensor applications.

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Figure 1. Capacitance of the system varies due to deforma-tion of the flexible electrodes. The system is very sensitive tooverloads—large forces can damage the electrodes or cause theelectronics to short.

TRADITIONAL CAPACITANCE SENSORA parallel plate capacitor with vacuum or air betweenthe electrodes represents a basic design element of manycapacitance sensors (see Figure 1). This element is typ-ical for most micro-machined pressure and tactile ca-pacitor sensors and can be easily analyzed. The capaci-tance, C, of a parallel plate capacitor with area, A, andgap, h ¿ √

A, between the plates is

C =ε0εA

h[1 + O(log

√A/h)

2√

A/h)], (1)

where ε0 = 8.85× 10−12F/m is the permittivity of freespace and ε is the relative dielectric constant of the ma-terial between the plates. The contribution of the fringeeffect is estimated by the second term in the bracketsand will be ignored in the following analysis. Tradi-tional capacitance sensing detects the variation in thecapacitance with deformation or displacement of thesensor electrodes. The relative change in capacitance,∆C/C, caused by variation in the gap thickness, h, be-tween rigid electrodes is given by

∆C

C=

∆ε

ε− ∆h

h. (2)

This expression assumes that the electrodes are not de-formed (the term ∆A/A is absent). In most capacitancesensor designs the dielectric constant does not change(dielectric between the electrodes can escape withoutdeformation). The change in capacitance can be mea-sured by a variety of well-established methods [1, 3].Sensing response of parallel plate vacuum-gap or air-gap sensors is defined by the elastic properties of theelectrodes (membrane). The system is very sensitiveto overloads—unexpected large deformation can dam-age the membrane or electrically short the electrodes.Micro-machining of the capacitance sensor arrays with alarge-area and small-gap parallel plate design is a chal-lenging manufacturing task. As it has been discussedin Ref. [9], reliability of the parallel plate capacitor sen-sor can be improved by introducing an elastic dielectricmaterial between the plates. The sensor becomes morerobust, because its dynamic response is determined by

Figure 2. Electrodes of equal width are spaced equally apart.The dielectric layer has length, , and separation between lines2a, where (h/a, `/a ¿ 1). Deformation of the dielectric layeraffects the dielectric constant of the material and, therefore, thesensor capacitance.

elastic properties of the material between the plates.In addition, dielectric material between the electrodesincreases the sensor sensitivity due to electrostrictioneffect. It is also much easier to manufacture a devicewith a dielectric film between the plates given a wideselection of technologies for producing uniform films ofdielectric materials.

SINGLE-PLATE CAPACITANCE SENSORAn entirely new concept of capacitor sensors—singleplate solid-state device is proposed. This sensor hasno moving parts and detects deformations via changein properties of the dielectric material attached to elec-trodes. An electrode pattern on the surface can be eas-ily manufactured by photolithographic process. Withproper selection of electrode orientations and structureof dielectric material, an array of single-plate sensors iscapable to resolve a distribution of normal and shearstress components over the surface. Presented in Fig-ure 2 is a single-plate capacitance sensor, which is com-posed of a layer of dielectric material deposited on in-terdigitated electrodes. The electrodes form a patternof equal width lines, which are spaced equally apart.Both thickness of the dielectric layer, h, and length ofthe electrode, `, are much larger than distance betweenthe electrodes, 2a (h/a, `/a ¿ 1). Deformation of thedielectric layer affects the dielectric constant of the ma-terial and, therefore, the sensor capacitance. It is ad-vantageous to combine single-plate sensing elements inan array, where each element has a different structureof the dielectric material and different orientation of theelectrodes. Such arrays, with at least three sensing el-ements, will be capable to resolve a normal and twoshear components of deformation. A larger array maybe required to map a distribution of deformation oversome area. In this study two arrays of four single-platesensing elements were tested. The dielectric material

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was silicon rubber with random and anisotropically dis-tributed alumina particles.

Capacitance of Interdigitated ElectrodesThe capacitance of any capacitor is defined by expres-sion

C =Q

V, (3)

where Q is the charge required to produce the poten-tial difference, V . This relationship can be consideredas a definition of capacitance for any system of elec-trodes. At the same time Eq. 3 shows how variation incapacitance can be measured. For example, one couldfix the charge, Q, on the capacitor electrodes then,∆C/C = ∆V/V , since Q = const. Variation in capaci-tance can be registered as a variation in voltage acrossthe capacitor. Or, one could fix the voltage, V , betweenthe electrodes then, ∆C/C = ∆Q/Q, since V = const.Variation in capacitance can be registered as a currentflow across the capacitor.Let us consider the capacitance of an interdigitated sys-tem of electrodes with isotropic dielectric on top. Dueto symmetry of the field distribution near interdigitatedelectrodes, the whole system of interdigitated electrodescan be modeled as just two electrodes of width a andlength, L = `n each with positive surface charge, +σ,and negative surface charge, −σ. The electric field inan isotropic dielectric can be approximated as

E =V

πr, (4)

where r is the radial distance from the point locatedequidistance from either electrode. 1 Electrode chargedensity, σ, can be defined in terms of the electric fieldnear the electrode surface

σ = 2ε0εE, (5)

where ε is dielectric constant of the material. The dif-ferential charge on the surface can be written as

dQ = σL · dr. (6)

Total charge, Q, can be obtained through integratingthe charge over the electrode surface. The capacitanceis determined from the relationship between the chargeon the surface and the potential between the two elec-trodes

C =Q

V=

1V

∫ 2a

a

dQ = ln 4ε0εL

π. (7)

Variation of Capacitance with DeformationDeformation of elastic dielectrics affects its dielectricproperties. Even initially isotropic material becomes1Note, that the relation (4) is correct only for an isotropicdielectric material. It should be corrected for a deformeddielectric material, which becomes anisotropic after deformation.

1

2

3

4

1

2

3

4

Am

plifie

r

Figure 3. The sensor is arranged in an array of four sensingelements: elements1 and 3 have electrodes oriented along theshear direction, and elements2 and 4 are perpendicular to theshear direction.

anisotropic in the direction of deformation. This phe-nomenon, called electrostriction [8, 10, 13], is employedas a sensing mechanism in the single-plate sensor de-sign. Two processes contribute to the variation of ca-pacitance, ∆C/C: (a) change in dielectric propertiesof the material with deformation, ∆ε/ε; (b) change inelectric field near electrodes with deformation, ∆E/E

∆C

C=

∆ε

ε− ∆E

E. (8)

Note, that term ∆E/E in this equation, has same phys-ical meaning as term ∆h/h in Eq. 2.For example, a normal deformation of dielectric layer,∆h/h, affects its dielectric constant

∆ε

ε= Kε

n

∆h

h. (9)

At the same time, compression of the dielectric affectsthe electric field distribution near electrodes, which islinear for small deformations

∆E

E= −KE

n

∆h

h. (10)

The field contribution appears because Eq. 4 should bemodified for anisotropic materials. The total capaci-tance response for a normal deformation is

∆C

C= Kn

∆h

h, (11)

where parameter Kn = Kεn + KE

n is defined by the ma-terial composition and can be theoretically estimatedor directly measured (see Refs. [6, 10, 11, 12]).Similar analysis can be provided for a shear deformationas well. A parallel displacement, U = γh, where thick-ness of the dielectric layer h = const, causes a sheardeformation γ/2. Analysis shows that [6]

∆ε

ε= (Kε

n + Kετ )

γ2

2. (12)

Variation of the electric field near electrodes with sheardeformations can be presented as

∆E

E= −KE

τ

γ2

2. (13)

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Figure 4. Microtailored dielectric composite is obtainable byapplying electric field during curing process: (a) random struc-ture, (b) arch-like structure, (c) chain-like structure.

The total capacitance response for a shear deformationis

∆C

C= Kτ

γ2

2. (14)

Parameter Kτ = Kεn + Eε

τ + KEτ can be estimated or

directly measured.

SENSOR DESIGN

Sensor ConstructionParticular sensor design discussed here is developed fortesting with a parallel plate rheometer. The rheome-ter provides controllable shear and normal deformationswhich are compared with the sensor response. Pre-sented in Figure 3 is the sensor arranged in an arrayof four sensing elements. Elements 1 and 3 have elec-trodes oriented along the direction of shear, and ele-ments 2 and 4 are oriented perpendicular to the sheardirection. The same polymer composite—silicone rub-ber from (Silicons, Inc.) with alumina particles—is castand cured on the sensing element array. Various areasof the composite (see Figure 4) have a random struc-ture of dispersed particles (a) near elements 1 and 2,and particles arranged in either arch-like (b) or chain-like (c) structures near elements 3 and 4. An electrodepattern is created using photosensitive copper coatedboards (from Kaypro Electronics).

Micro Tailored Structure of Sensing MediaAlumina particles of diameter 63 < d < 90µm and vol-ume fraction φ ≈ 5 vol% were mixed with base pre-polymer of silicon elastomer (from Silicons, Inc.) andde-gazed in vacuum chamber. With added cross-linkingagent, the mixture was evacuated for 10 min and trans-ferred to casting cells 35 mm in diameter and 3 mmthick. A composite with micro tailored particle struc-ture was formed in casting cells by maintaining an elec-tric field during the first two hours of curing time. Thestructure of the sensor media was modified to obtainan array of sensors with a desirable structure. Dur-ing a single process using an electric field in the pre-ferred direction with a specially designed electrode all

W w0sin ( t)

Rheometer

Amplifier10x

Low PassFilter

0-25VDC

Lock-inAmplifierdetecting

2 signalsw, w

Reference

signalw

Figure 5. Power supply provides bias DC electric field; highimpedance AC signal due to sample deformation is measuredby Lock-in-Amplifier and compared with rheometric data.

three structures described in Figure 4 are obtained. Anisotropic structure with a random particle configurationis obtained in the absence of an electric field. Chain-like structures are formed using a parallel plate config-uration. Arch-like structures are formed using a singleplate configuration and an electric field created by volt-age potential between the surface electrodes. To forma arch-like structure, high voltage potential of 1.0 kVhas been applied across the sensor electrodes. Elec-tric potential of 4.0 kV , applied across an additionaltop electrode and one of the sensor’s electrodes forms achain-like structure.Modification of the sensor media structure enhances theshear and normal strain detection. A random struc-ture is most sensitive and provides information rela-tive to volume deformation. The chain-like structure isvery sensitive to normal deformation; while the arch-likestructure has different sensitivity to shear deformationdepending on if deformation is along or perpendicular tothe arch-like structure. Information about normal andshear deformation can be extracted from the measuredresponse of different sensing elements.

SENSOR TESTING

SetupAR 1000 rheometer from TA Instruments with parallelplate configuration was modified for testing and em-ployed for electrostriction and electrorheological char-acterization of a single-plate solid-state sensor. Sen-sitivity to shear and normal detection of the micro-tailored structure was tested for various normal andshear strains. Each sensor is capable of delivering fourdifferent signals, which provide information about de-formation occurring in locally sensitive areas. The volt-age variation due to shear and normal electrostrictionwas registered with an experimental set up (see Fig-ure 5). A voltage produced by the sample has enor-mously high source impedance, which cannot be mea-sured by conventional instrumentation having input im-

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Figure 6. Shear response of random composite for variousnormal pressures and various shear directions.

pedance of 1MΩ. Electrostriction measurements of thesensor resemble a dynamic potential technique imple-mented in capacitance microphones for amplifying de-formation induced potentials [4]. A DC power supplyprovides a constant dielectric displacement D to thesensor. The AC signal due to deformation on the sen-sor media is buffered and amplified by a high impedanceamplifier and measured by Stanford Research SystemsLock-in-Amplifier.

Results and DiscussionShear and normal response of the single-plate sensor hasbeen tested for three different structures of the dielectricmaterial presented on Figure 4: (a) - composite with arandom distribution of inclusions, (b) - composite withan arch-like and (c) - composite with a chain-like struc-tures. Each sensor element array has been organizedin such a way that a comparison can be made betweenthe response of random and modified structures, eitherarch-like (b) or chain-like (c). Each testing array haselectrodes of the sensing elements oriented along andperpendicular to the shear direction for each structure.Our goal at this stage is to demonstrate the feasibilityof organizing sensing elements, which are capable of re-solving shear and normal forces applied to the surface.Rheometer was used to apply a normal force in therange 0.5 − 1.0 N , which produces a normal pressure700 Pa. At the same time, an oscillatory shear torquewas applied by rheometer causing up to 6% shear defor-mation of the polymer, which is equivalent to a shearstress up to 1200 Pa. Sensor response, which is pro-portional to a capacitance change with deformation hasbeen registered as a voltage variation across the sensingelement

∆V = −∆C

CV, (15)

where V is a bias voltage across the sample. This ex-pression follows from the capacitance-voltage relation

Figure 7. Oscillatory shear response of random (a), arch-like (b)and chain-like (c) structures with respect of strain magnitude.

V = Q/C when the charge, Q, is constant. Accord-ing to Eq. 12, variation of capacitance is proportionalto square shear rate, γ2, which means that oscillatoryshear deformations occurring at frequency ω producesa voltage signal ∆V with frequency 2ω. Furthermore,the voltage response must be quadratic with the shearmagnitude.

Output of the sensing elements with respect to shear de-formation are plotted on Figures 6 and 7 for sensing el-ements with different orientations of the electrodes anddifferent material structures. Figure 6 presents shearresponses of random composite for various normal pres-sures and various shear directions. Figure 7 comparesshear response of random (a), arch-like (b) and chain-like (c) structures.

Obtained experimental data indicates that the secondharmonic of the voltage response is quadratic with re-spect to shear deformation. The response varies withthe sensing element orientation and the microstructureof the composite. All structures demonstrate differ-ent response for different orientations of the electrodes.Overall analysis of the data suggests that by manipulat-ing the sensing elements we could extract informationabout all three components of a load on the sensingsurface.

In our test we also observe a voltage signal at frequencyω. This signal appears because the dielectric poly-mer material used as a sensing media has viscoelasticproperties. The total deformation, γ, is composed oftwo contributions—elastic deformation, γe, and plas-tic deformation, γp, where γ = γe + γp. Only elas-tic deformation, γe, contributes to the electrostrictioneffect. Thus for oscillatory shear deformations γ =γp + γe0 · sin(ωt) and the voltage response, which isproportional to γ2 will have two harmonic frequenciesof oscillation 2γpγe0sin(ωt) and γ2

e0sin(2ωt).

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CONCLUSIONWe have demonstrated the feasibility of employing elec-trostriction phenomenon for shear stress/strain sensingin a single-plate capacitance setup. Such simple manu-facturing of sensors can be applied in many different ar-eas. There is a potential to combine an array of sensingelements and polymer composites with micro-tailoredstructure to resolve three components of a load distri-bution over the sensing surface. A novel shear elec-trostriction phenomenon requires future investigationand designing materials with optimal sensing response.

ACKNOWLEDGMENTSThe authors thanks Shannon K. Cobb for discussionand help with measurements. This work was supportedin part by the University of Wisconsin I&EDR grant#2002038.

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