Adaptive control of stiffness by electroactive polyurethane

Seediscussions,stats,andauthorprofilesforthispublicationat:https://www.researchgate.net/publication/257346867

Adaptivecontrolofstiffnessbyelectroactivepolyurethane

ArticleinSensorsandActuatorsAPhysical·January2013

DOI:10.1016/j.sna.2012.09.032

CITATIONS

4

READS

38

6authors,including:

KaoriYuse

InstitutNationaldesSciencesAppliquéesdeLy…

43PUBLICATIONS182CITATIONS

SEEPROFILE

DanielGuyomar

InstitutNationaldesSciencesAppliquéesdeLy…

414PUBLICATIONS6,704CITATIONS

SEEPROFILE

M.mounirMeddad

UniversitéMohamedElBachirElIbrahimideB…

32PUBLICATIONS81CITATIONS

SEEPROFILE

YahiaBoughaleb

UniversitéHassanII,Casablanca

168PUBLICATIONS494CITATIONS

SEEPROFILE

AllcontentfollowingthispagewasuploadedbyYahiaBoughalebon01December2016.

Theuserhasrequestedenhancementofthedownloadedfile.Allin-textreferencesunderlinedinbluearelinkedtopublicationsonResearchGate,lettingyouaccessandreadthemimmediately.

Accepted Manuscript

Title: Adaptive control of stiffness by electroactivepolyurethane

Author: Kaori Yuse Daniel Guyomar David Audigier AdilEddiai Mounir Meddad Yahia Boughaleb

PII: S0924-4247(12)00608-5DOI: doi:10.1016/j.sna.2012.09.032Reference: SNA 8025

To appear in: Sensors and Actuators A

Received date: 24-3-2012Revised date: 11-9-2012Accepted date: 11-9-2012

Please cite this article as: K. Yuse, D. Guyomar, D. Audigier, A. Eddiai, M. Meddad,Y. Boughaleb, Adaptive control of stiffness by electroactive polyurethane, Sensors andActuators: A Physical (2010), doi:10.1016/j.sna.2012.09.032

This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

Page 1 of 14

Accep

ted

Man

uscr

ipt

-1/1-

Adaptive control of stiffness by electroactive polyurethane

Kaori Yuse1*, Daniel Guyomar1, David Audigier1, Adil Eddiai1,3, Mounir Meddad2 and

Yahia Boughaleb3

1) Université de Lyon, INSA-LGEF, 8 rue de la Physique, 69621 Villeurbanne, France

2) Departement of electrotechnic, Laboratoire Dosage Analyse et Caractérisation, Université Ferhat

Abbas, 19000, Sétif, Algerie

3) Departement of Physique, Faculty of Sciences, Laboratoire de Physique de la Matiere Condensee

(LPMC), 24000 El Jadida, Morocco

*) [email protected]

Abstract

For applications concerning vehicle suspension or the membranes of acoustic loud

speakers, a conventional stiffness control method is both useful and desired. However,

without total replacement of the material itself or its structure, modification of the

stiffness is no easy matter. Besides, the technology of Electro Active Polymers (EAPs)

is a fast-moving topic. The high electro-induced strain level of these materials is an

attractive advantage compared to many other mechanical/electrical converging

sensor/actuator materials such as piezo devices. This paper presents an easy and

innovative method to control the stiffness of EAPs. First, a polyurethane (PU) sample

was pre-stretched in the 1-direction, and clamped at both ends. Then, an electrical field

was induced in the 3-direction. The positive elongation in the 1-direction created a force

opposite that of the pre-stretching since the specimen was clamped. From the equation

of force valence, a simple stiffness equation was obtained with the ratio between the

pre-stretching force and the force created by the electrical stimuli. Concerning the

electrical saturation in the EAP material, the variation in stiffness could be expressed by

the equation of electrical field. With a simple experimental viewing, more than 30 % of

stiffness variation could be obtained with a moderate electrical induction, < 32 V/μm.

Keyword: Stiffness control, Polyurethane [PU], Electrostrictive, Electrical property,

Pre-strain

1. Introduction

Ranging from vehicle suspensions to membranes for acoustic speakers, the

application fields of EAPs are vast if the stiffness of the material can be easily modified.

Page 2 of 14

Accep

ted

Man

uscr

ipt

-2/2-

In general, there are only two ways to alter the stiffness; a total change of the material or

of its structure. The stiffness of a vehicle tire can be changed by a surface treatment with

an adhesive spray. This exists commercially and it is called stiffness control entrainment.

It is an easy and reasonable method compared to a case where the entire material has to

be replaced. The reverse change is, however, not considered.

As the result of research on adaptive stiffness control, there exists a method

that fixes the limitation of deformation of a spring [1]. If a spring is covered by ER fluid,

a magnetic induction is enough to limit its maximum deformation, and thereby is

stiffness. This is a quite conventional adaptive control method. Its use is however

limited since the structure must be totally covered with the fluid. Moreover, applying

the technique to another type of structure is difficult. Based on these points, the adaptive

stiffness is an interesting open issue.

Electroactive polymers (EAPs) have attracted much attention during the last

decades as electric/mechanical conversion sensor and actuator materials. Not only is the

fabrication easy and cheap, giving several variations of materials, but a specific

advantage lies in their high electrostrictive strain level. Polyurethane (PU), one of the

dielectric elastomers, generates more than 30 % of strain under a moderate electrical

field < 20 V/μm, and carbon black (CB)/PU composite films can create more than 50 %

under the same electrical condition, < 20 V/μm, according to a study carried out in our

laboratory [2-3].

This paper proposes an innovative method to adaptively control material

stiffness using EAPs. It demonstrates that it is possible to change the stiffness of a

pre-stretched PU film by simple electrical stimuli. The stiffness of a wide surface area

of the material can be modified. The electrical induction was limited to a low level so

that a wearable device can be targeted later on. After the model, an experimental

procedure with a small dimension specimen is presented.

2. Theory

2.1 Change of stiffness by induced electrical field after pre-stretching

When a PU thin film is stretched in the 1-direction, the corresponding stress

creates an elongation that can be written τmech. = cS. Here, c and S are mechanical

factors corresponding to the elastic compliance and the strain in the 1-direction,

respectively. When the electrical field is induced in the 3-direction of the film, there

occurs an elongation in the 1-direction since the electrostrictive coefficient of PU is

negative. Under natural conditions, without clamping, these two elongations have the

same direction.

Page 3 of 14

Accep

ted

Man

uscr

ipt

-3/3-

Now, we consider a model for a fixed condition. A PU thin film, clamped at

both ends, is stretched in the 1-direction, after which an electrical field is induced in the

3-direction using the specific experimental setup system shown in Figure 1. After the

fixation with the pre-strain S0, no elongation could occur, and the electrical induction

thus led to another stress in the 1-direction according to τele. = αP2. Here, α and P are

electrical factors, i.e., the electrical coefficient and the polarization created by electrical

induction, respectively. Both α and P2 are positive values.

Figure 1: Experimental setup

If there is no clamping, the total stress τt in 1-direction under mechanical and

electrical stimuli can be expressed from the well known electrostrictive constitutive

equations as follows:

τt = τmech. + τele. = cS0 + αP2 (1)

Here, the polymer ends are fixed before the electrical induction. The

mechanical stress and the stress caused by electrics have the opposite direction, and thus

create the total stress according to

τt = cS0 - αP2 (2)

Multiplying this equation by the surface A, the equation of the force F is obtained with

the stiffness K = cA / L as

Ft = cA u0 / L - αAP2 = Ku0 - αAP2 (3)

Here, L is the length of the specimen and u0 is the initial deformation by the pre-strain,

u0 = S0 L.

Besides, the electrical induced stress can be also written as τele.= c’Sele. The

elastic compliance is no longer the constant coefficient c but the variable coefficient c’

because the strain, Sele, is fixed at the pre-strain, Sele= S0, under the variable stress caused

by electrical induction τele. The second term of the equation (3) thus becomes

αAP2= A c’Sele = K’uele (4)

To clearly differentiate it from the stiffness of the specimen without the electrical

Page 4 of 14

Accep

ted

Man

uscr

ipt

-4/4-

induction, K = F / u0, the varied stiffness was expressed as K’ here. It depends purely on

the electrical induction, so that K’ = f(E).

With this variable stiffness, the total force in equation (3) is rewritten as

Ft = Ku0 – K’uele (5)

Since the experimental condition involved two fixed ends, u0 = uele. This gives

Ft = u0 (K– K’) (6)

Now we have clearly and simply obtained the varied total stiffness under the electrical

induction after pre-stretching,

Kt = K– K’ (7)

A comparison of stiffness with and without the electrical induction can be simply made

by comparing the total force and the pre-strain force, Fm, as follows.

Kt / K=(Ft / u0)/ (Fm / u0)= Ft / Fm (8)

2.2 Saturating polarization

The relation between the polarization and the induced electrical field is linear

when the induced electrical field E is small. In this case, P = εE, is supposed to be

nonlinear when E is increased in the polymeric material, as shown in Figure 2 (a) [4,5].

-2 -1 0 1 2

x 107

-1

-0.5

0

0.5

1

Electrical field [M V/m ]

Normalized polarization

0 5 10 15 200

5

10

15

20

25

Electric field [MV/m]

Strain [%]

ExperimentSimulation

(a) (b)

Figure 2: (a) Saturating polarization, and (b) saturating strain in the polymeric material.

Experimental data and simulation for (b).

This nonlinearity appears also in the S(E) relation. For some time, we have

considered the strain saturation of a polymeric material to be caused by the electrical

saturation. However, numerous approaches might be used to express such saturation.

Among them, we propose an equation that takes into account the polarization saturation

[4]:

P = εEsattanh(E / Esat) (9)

where ε and Esat correspond to the relative permittivity and the coefficient related to the

Page 5 of 14

Accep

ted

Man

uscr

ipt

-5/5-

electrical field, respectively. From our recent work, we know that Esat = 1.53Econ where

Econ is the electrical field value and where d2S / dE2 = 0 [4].

The strain created by electrical stimuli is thus,

Sele = QP2 = Q * (εEsattanh(E / Esat))2 (10)

With this equation, the nonlinearity of the strain in a high electric field would be well

expressed as shown in Figure 2 (b).

2.3 Change in stiffness by the function of the electrical stimuli

In 2.1, it was mentioned that the variable stiffness can be expressed purely by

the equation of the electrical field, K’ = f(E). The total stiffness, under mechanical and

electrical stimuli, Kt, is thus also the equation of the electrical field, Kt = f(E).

Combining equation (9) and (7), the stiffness comparison with and without the electrical

induction, already expressed in equation (8), Kt /K, can be rewritten with the equation of

the electrical field.

Kt / K = Ft / Fm = 1- Fe / Fm = 1 - Aτele./ Fm = 1 - AαP2 / Fm

= 1-(Aα/Fm) * (εEsattanh(E / Esat))2 (11)

3. Experimental setup

Pure polyurethane (PU) elastomer samples, prepared by solution casting, were

used for the present investigation. The specimens were cut into samples of two shapes.

One was a disk with a diameter of 20 mm for electrostrictive strain measurements, and

the other was a rectangle with a shape of 40*16 mm2 for the electrically created force

measurement with pre-strain. The thickness of all the specimens was around 60 μm.

Gold electrodes were sputtered on both sides of both specimen types. A more detailed

fabrication procedure has been given elsewhere [3].

To obtain the strain-electrical field relationship, a linearly increased electrical

field was applied up to 30 V/μm. Disk-shaped specimens were horizontally set between

a steel and a brass disk in order to avoid a flexure motion. The electrical field-induced

strain was precisely measured with a beam laser interferometer (Agilent 10889B) with a

precision on the order of 5 nm. The current was measured using a high sensitive current

amplifier.

The experimental setup built in the laboratory, as shown in Figure 1, renders

possible sensitive determinations of the dielectric constant, the Young modulus and the

electrostrictive coefficients of electroded polymer films. The details have already been

reported elsewhere [6].

Using the present setup, a precise pre-strain in the 1-direction was added. This

Page 6 of 14

Accep

ted

Man

uscr

ipt

-6/6-

pre-stretching force Fm was obtained with the help of an XFTC300 linear

tension/compression sensor capture specialized for miniature force detection from the

FGP Company. Its precision is on the order of 0.05 N. Both ends of the specimen were

clamped after which a sinusoidal electrical field of 1 Hz (E = Edc+Eampcos(ωt)) was

applied with a varying DC bias Edc and amplitude Eamp. Here, ω corresponds to the

pulsation of the electrical excitation and t is the time. The deformation mentioned in the

present paper is well within in the viscoelastic range of the material.

4. Results and Discussion

Three coefficients were varied one by one while the other two were kept

constant. Those varied were the pre-stretching force Fm, the electrical DC bias Edc and

the electrical amplitude Eamp.

4.1 Variation of the pre-stretching force Fm

The specimen was stretched in the 1-direction at four levels of the pre-strain

force thus creating a pre-stretching force Fm of 0.72, 0.55, 0.40 and 0.22 N. The

sinusoidal electrical field was then induced in the 3-direction with the bias Edc = 16

V/μm and the amplitude Eamp = 16 V/μm. Under this condition, the electrical field never

dropped below zero, but stayed positive. Figure 3 shows the variation of the total force

as (a) simulated and (b) experimental results. The images of the electrical field have

been added to the figure for the sake of comparison. Upper levels of quasi-sinusoidal

curves correspond to each pre-stretching force level. The influence of the size of

pre-stretching force is not visible with this level of electrical stimuli.

0.5 1 1.5 2 2.5 3 3.50.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tim e [sec]

Force [N]

Im age of EFm = 0.72 NFm = 0.55 NFm = 0.40 NFm = 0.22 N

0 0.5 1 1.5 2 2.5 3 3.50.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tim e [sec]

Force [N]

Im age of EFm = 0.72 NFm = 0.55 NFm = 0.40 NFm = 0.22 N

(a) (b)

Figure 3: Comparison of the force when varying the pre-stretching force Fm; (a) simulated and (b)

experimental results.

Page 7 of 14

Accep

ted

Man

uscr

ipt

-7/7-

With the parameters used above, a change in stiffness was obtained and it is

shown in Figure 4 as (a) simulated and (b) experimental results. It can be clearly seen

that it varied with the pre-stretching force level. When the film was stretched to a very

small pre-strain level, the change in stiffness by the same electrical stimuli became

dramatic. Here, a reduction of more than 30 % was easily obtained with the small level

of electrical induction, < 32 V/μm, as mentioned above.

(a) (b)

Figure 4: Comparison of the stiffness when varying the pre-stretching force Fm; (a) simulated and

(b) experimental results.

4.2 Variation of the electrical DC bias Edc

The films were always stretched with Fm = 0.74 N, after which the input

electrical DC bias was varied at Edc = -16, 0, and 16 V/μm. The electrical amplitude was

fixed at Eamp = 16 V/μm. Figure 5 shows (a) the simulated and (b) the experimental

results.

Compared to the electrical field, shown in the figure as a dotted line for

reference, the entire electrical field had the same sign when Edc = -16 V/μm. This is

expressed by the bold line in Figure 5. In contrast, when Edc = 16 V/μm, corresponding

to the finest line in the figure, there was a phase lag of π between them. The duplicated

frequency can be clearly seen with the result of a null bias, Edc = 0 V/μm. The simulated

and experimental results were in good agreement.

Page 8 of 14

Accep

ted

Man

uscr

ipt

-8/8-

0.5 1 1.5 2 2.5 3 3.5 4

0.58

0.6

0.62

0.64

0.66

0.68

0.7

0.72

0.74

Tim e [sec]

Force [N]

Im age of EEdc = 25 M V/mEdc = 0 M V/mEdc =-25 M V/m

0.5 1 1.5 2 2.5 3 3.5 40.6

0.62

0.64

0.66

0.68

0.7

0.72

Tim e [sec]

Force [N]

Im age of EEdc = 25 M V/mEdc = 0 M V/mEdc =-25 M V/m

(a) (b)

Figure 5: Comparison of the force when varying the DC bias Edc; (a) simulated and (b) experimental

results.

Moreover, the upper levels of the sinusoidal curves were not consistently equal

due to the pre-stretching force being difficult to fix precisely. The simulation took these

slight differences into account.

As can be seen in Figure 6, the change in stiffness gave rise to similar

phenomena. A duplicate of the frequency of the stiffness change also appeared with Edc

= 0 V/μm.

0.5 1 1.5 2 2.5 3 3.5 485

90

95

100

Tim e [sec]

Variation of Stiffness (Kt/K) [%]

Im age of EEdc = 25 M V/mEdc = 0 M V/mEdc =-25 M V/m

0.5 1 1.5 2 2.5 3 3.5 485

90

95

100

Tim e [sec]

Variation of Stiffness (Kt/K) [%]

Im age of EEdc = 25 M V/mEdc = 0 M V/mEdc =-25 M V/m

(a) (b)

Figure 6: Comparison of the stiffness when varying the DC bias Edc; (a) simulated and (b)

experimental results.

4.3 Variation of the electrical amplitude Eamp

The film was stretched with Fm = 0.74 N and then clamped. The amplitude

Eamp was varied from 13.85 to 21.70 V/μm while the bias was consistently held at zero,

Edc = 0 V/μm. Figure 7 shows (a) simulated and (b) the experimental results of this case,

and similarly to Figure 5, where there was also a null bias, all the curves presented a

Page 9 of 14

Accep

ted

Man

uscr

ipt

-9/9-

duplicated frequency. The lower peak level increased with the amplitude of the induced

electrical field. As can be seen, the phenomena were well reproduced in the simulation.

0 0.5 1 1.5 2 2.5 3 3.5 40.64

0.65

0.66

0.67

0.68

0.69

0.7

0.71

0.72

Tim e [sec]

Force [N]

Im age of EEam p = 13.85 M V /mEam p = 16.00 M V /mEam p = 17.75 M V /mEam p = 21.70 M V /m

0.5 1 1.5 2 2.5 3 3.5 40.66

0.67

0.68

0.69

0.7

0.71

0.72

Tim e [sec]

Force [N]

Im age of EEam p = 13.85 M V /mEam p = 16.00 M V /mEam p = 17.75 M V /mEam p = 21.70 M V /m

(a) (b)

Figure 7: Comparison of the force when varying the electrical amplitude Eamp; (a) simulated and (b)

experimental results

Figure 8 (c) shows the change in stiffness. Although the variations in stiffness

were not very remarkable, duplicates of the frequency can be clearly seen.

0.5 1 1.5 2 2.5 3 3.5 491

92

93

94

95

96

97

98

99

100

Tim e [sec]

Variation of Stiffness (Kt/K) [%]

Im age of EEam p = 13.85 M V /mEam p = 16.00 M V /mEam p = 17.75 M V /mEam p = 21.70 M V /m

0.5 1 1.5 2 2.5 3 3.5 494

95

96

97

98

99

100

Tim e [sec]

Variation of Stiffness (Kt/K) [%]

Im age of EEam p = 13.85 M V /mEam p = 16.00 M V /mEam p = 17.75 M V /mEam p = 21.70 M V /m

(a) (b)

Figure 8: Comparison of the stiffness when varying the electrical amplitude Eamp; (a) simulated and (b)

experimental results.

Figure 9 (a) shows the variation of stiffness in function of pre-stretching force,

Fm, for constant electrical amplitude, Eamp, and electrical bias, Edc. Figure 9 (b) shows

that of the electrical amplitude, Eamp, for constant pre-stretching force, Fm, and electrical

bias, Edc. We see that the pre-stretching force play more important role than electrical

amplitude.

Page 10 of 14

Accep

ted

Man

uscr

ipt

-10/10-

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

15

20

25

30

35

40

45

50

pre-stretching force [N]

Change in stiffness ⊿K [%]

Sim ulatedExperim ental

13 14 15 16 17 18 19 20 21 221

2

3

4

5

6

7

8

9

Electric am plitude [M V/m ]

Change in stiffness ⊿K [%]

Sim ulatedExperim ental

(a) (b)

Figure 9: Variation of stiffness in function of (a) pre-stretching force (Fm) and (b) electrical

amplitude (Eamp)

Additionally to say, the electrical saturation, demonstrated by the Equation 11,

was seen quite slightly in Figure 3, but not on the others since the level of electrical

input is not very high in other results.

5. Conclusion

A simple conventional method to modify the stiffness of a polymer material has

been presented. After clamping both ends of a pre-stretched Polyurethane [PU] film, a

sinusoidal electrical signal, E = Edc+Eampcos(ωt), was induced. Three coefficients were

varied one by one – the pre-stretching force Fm, the electrical DC bias Edc and the

electrical amplitude Eamp – while the other two were held constant. Good agreements

were found between simulated and experimental results, thus confirming the theory.

Three main facts were found. First of all, it was shown that the induction of a

moderate electrical field, < 32 V/μm, was enough to change its stiffness more than 30 %.

Second, a duplication of frequency occurred when the electrical DC bias was null.

Finally, the pre-stretching force was more important than the electrical amplitude.

The present method requires only an electrical induction and thus represents a

quite conventional and adaptive method to change the stiffness of a material. PU are

under increasing demand day by day, and their application area might soon expand.

References

[1] M.J. Mahjoob, H.R. Martin, F. Ismail, “Identification of damping and stiffness of smart

structures incorporating ER fluids,” App. Acoustics, vol 45, pp. 211-226 (1995)

[2] K. Yuse, D. Guyomar, M. Kanda, L. Seveyrat, B. Guiffard, “Development of large-strain and

low-powered electro-active polymers (EAPs) using conductive fillers,” Sensors and Actuators A, vol

Page 11 of 14

Accep

ted

Man

uscr

ipt

-11/11-

165, pp. 147-154 (2011)

[3] Daniel Guyomar, Kaori YUSE, Masae Kanda, "Thickness effect on electrostrictive polyurethane

strain performances: a three-layer model" Sensors & Actuators: A. Physical, Vol. 168, Issue 2, pp.

307-312 (2011)

[4] D. Guyomar, K. Yuse, P.-J. Cottinet, M. Kanda, L. Lebrun, “Focus on the electrical

field-induced strain of electroactive polymers and the observed saturation,” J. of App. Phy., Vol.

108, 114910, (2010)

[5] D. Guyomar, P.-J. Cottinet, L. Lebrun, C. Putson, K. Yuse, M. Kanda, Y. Nishi, “The

compressive electrical field electrostrictive coefficient M33 of electroactive polymer composites and

its saturation versus electrical field, polymer thickness, frequency and fillers,” Polym. Adv. Tech.,

DOI: 10.1002, (2011)

[6] D. Guyomar, P-.J. Cottinet, L. Lebrun, G. Sebald, “Characterization of an electroactive polymer

simultaneously driven by an electrical field and a mechanical excitation: An easy means of

measuring the dielectric constant, the Young modulus and the electrostrictive coefficients” Physics

Letters A, Volume 375, Issue 16, p. 1699-1702 (2011)

Page 12 of 14

Accep

ted

Man

uscr

ipt

-12/12-

Kaori Yuse obtained her doctor degree in Ecole Centrale Paris, France. After few

years work in national research center in Tsukuba, Japan, she moved to INSA Lyon,

France in 2003, titled Associate Professor since 2006. She has started working in

the Laboratoire de Génie Electrique et Ferroélectricité (LGEF) since 2006. She is

submitted in varied works in the field of intelligent materials, such as NDT of

composite material, vibration control, and piezo-material characterization. Her

current main research topic is the development of polymeric actuator. Many other

electro-active materials also interest her.

Daniel Guyomar received a degree in acoustics from Compiègne University,

Compiègne, France, and a PhD degree in physics from Paris VII University, Paris,

France. In 1982–1983, he worked as a research associate in fluid dynamics at the

University of Southern California (USC), Los Angeles. He was a National Research

Council Awardee (1983–1984) detached at the Monterey Naval Postgraduate School,

CA, to develop transient wave propagation modeling. He was hired in 1984 by

Schlumberger to lead several projects dealing with borehole imaging, and then

moved to Thomson Submarine activities in 1987 to manage the research activities

in the field of underwater acoustics. In 1992, Dr. Guyomar co-created the Techsonic

Company, which is involved in research, development and production of

piezoelectric and ultrasonic devices. He is presently a full-time university professor

at Institut National des Sciences Appliquées (INSA) de Lyon, Lyon, France, where

he manages the Laboratoire de Génie Electrique et Ferroélectricité. His present

research interests are in the field of smart materials and their applications to

self-powered systems, vibration damping, energy harvesting from ambient source,

flexible actuators. He has co-authored more than 230 papers.

David Audigier was born in France in 1966. He received the B.S. degree from Lyon I

University, Lyon, France, in 1988, and the M.S. and Ph.D. degrees from the Institut

National des Sciences Appliquées de Lyon (INSA de Lyon), Lyon, France, in 1990

and 1996, respectively, all in electrical engineering. In 1997, he became an Assistant

Professor at the INSA de Lyon, where he joined the Laboratoire de Génie Electrique

et Ferroélectricité. His current research activities include piezoelectric systems,

energy harvesting, vibration control and noise reduction, and characterization and

power applications of piezoelectric materials.

Adil Eddiai was born in Morocco in 1977. He received his master’s degree in

Page 13 of 14

Accep

ted

Man

uscr

ipt

-13/13-

condensed matter physics from Chouaib El Doukkali University in El Jadida, Morocco

in 2008. He is currently a Ph.D. student at Institut National des Sciences Appliquees

(INSA) de Lyon, France and Chouaib El Doukkali University in El Jadida, Morocco and

is working on electroactive polymers and their applications for actuators and energy

harvesting. His work included the development of electroactive polymer composite

exhibiting electromechanical coupling for environmental energy scavenging

applications and large electric field actuation performance.

Mounir Meddad is an associate professor of electrical engineering from 2006. He

received His engineer degree in electrical engineering from the University of setif

Ageria in 1992, and his magister degree in electrical engineering from the University of

Setif in 1999. His current field of interest focuses on vibration damping, energy

harvesting and Structural Health Monitoring using piezoelectric, pyroelectric or

electrostrictive devices, as well as autonomous, self-powered wireless systems.

Yahia Boughaleb is dean of Faculty of Sciences El Jadida, Chouaib Doukkali

University. He received his PhD from Polytechnic School of Paris in 1987 and since

then he is professor of physics. His research is focused on physics of fractals, transport

phenomena in solids, failure of heterogeneous materials and materials for harvesting

energy applications.

Page 14 of 14

Accep

ted

Man

uscr

ipt

-14/14-

Highlights

Control the stiffness of EAPs.

Electrical induction to pre-stretched EAP (Polyurethane (PU)) sample.

From the equation of force valence, a simple stiffness equation obtained with the ratio

between the pre-stretching force and the force created by the electrical stimuli.

More than 30 % of stiffness variation with a moderate electrical induction, < 32 V/μm.