**Folded dielectric elastomer actuators**

**Federico Carpi, Claudio Salaris and Danilo De Rossi**

Interdepartmental Research Centre "E. Piaggio", School of Engineering,
University of Pisa,

via Diotisalvi, 2 -- 56100 Pisa, Italy.

E-mail: <f.carpi@ing.unipi.it>

**Abstract**

Polymer-based linear actuators with contractile ability are currently
demanded for several types of applications. Within the class of
dielectric elastomer actuators, two basic configurations are today
available for such a purpose: the multi-layer stack and the helical
structure. The first consists of several layers of elementary planar
actuators stacked in mechanical series and electrical parallel. The
second configuration relies on a couple of helical compliant electrodes
alternated to a couple of helical dielectrics. The fabrication of both
these configurations presents today some specific drawbacks, arising
from the peculiarity of each structure. Accordingly, the availability of
simpler solutions may boost the short-term use of contractile actuators
in practical applications. For this purpose, a new configuration is here
described. It consists of a monolithic structure made of an electroded
sheet, which is folded up and compacted. The resulting device is
functionally equivalent to a multi-layer stack with interdigited
electrodes. However, with respect to a stack the new configuration is
advantageously not discontinuous and can be manufactured in one single
phase, avoiding layer-by-layer multi-step procedures. The development
and preliminary testing of prototype samples of this new actuator made
of a silicone elastomer are here presented.

*Keywords:* actuator, contractile, dielectric elastomer, electroactive
polymer, folded, linear.

**1. Introduction**

Several types of polymers present intrinsic high compliance, lightness,
high processability and usual low cost. These properties, in addition to
different types of active functionalities they can show, are frequently
regarded as advantageous for a use of such materials for specific
actuation tasks. In particular, actuators based on electroactive
polymers (EAP) offer attractive performances in these and other respects
\[1,2\]. They are being studied for a very broad spectrum of potential
fields of application, such as robotics, biomedical engineering,
automotive, aerospace, etc. However, at present a large number of such
ambits of application would benefit from new reliable actuators having
linear contractile properties. For instance, they may find challenging
uses as 'artificial muscles' \[1,2\]. Prosthetics, orthotics, robotics
and bio-robotics are just few examples of general areas of potential
application for such devices.

Within the broad EAP family, actuators based on dielectric elastomers
represent one of the most performing technologies. They consist of
insulating soft elastomers subjected to high electric fields, applied
via compliant electrodes \[3-5\]. With respect to different EAP
actuators, they can exhibit very large deformations at medium-high
stresses. The electromechanical response is mainly due to an
electrostatic compression, which arises from interactions among the
electrode free charges (Maxwell stress effect). In particular, when a
thin film of a dielectric elastomer is sandwiched between two compliant
electrodes charged by a high voltage difference, a squeezing of the
material at constant volume is achieved \[3-5\].

Several research efforts are today being focused on dielectric elastomer
actuation. Accordingly, a quick widening of the affordable range of
applications is expected in the next few years. A large number of
different types of dielectric elastomer actuators have been demonstrated
so far. Most notable examples include planar devices, rolls, tubes,
stacks, diaphragms, extenders, bimorph and unimorph benders, etc.
\[3-12\]. Nevertheless, despite such a variety of devices, very few
solutions are currently available to obtain linear contractile
actuators. A first type of approach adopts auxiliary external mechanical
components, used to transfer motion towards privileged directions.
Except for such solutions, just two basic actuating configurations at
present intrinsically enable macroscopic linear contractions. They are
the multi-layer stack (Fig. 1a) \[4,11\] and the helical structure (Fig.
1b) \[13\].

A stack-like actuator consists of a multi-layer of elementary planar
actuators connected in mechanical series and electrical parallel (Fig.
1a). The electrically activated thickness compression of each layer
generates a resulting contraction of the device along its main axis
\[4,11\].

A helical dielectric elastomer actuator comprehends two helical
compliant electrodes alternated to two helical layers of elastomer (Fig.
1b). The electrically activated squeezing of each helical elastomer
causes the axial contraction of the entire structure \[13\].

![](media/image1.png){width="3.1875in" height="1.90625in"}

**Figure 1.** State-of-the-art contractile linear devices made of
dielectric elastomers: (a) multi-layer stack; (b) helical actuator.

Despite the utility of both these configurations, their fabrication
presents some specific delicate issues, which basically arise from the
peculiarity of each structure.

In particular, the realisation of an elastomeric stack is typically made
onerous by its structural discontinuity. In fact, it requires multi-step
depositions of several layers of dielectric elastomer, alternated to
layers of electrode material. Moreover, it needs an electrical shorting
of the two resulting series of electrodes \[11\].

Such problems are not typical of a helical actuator, owing to its
structural continuity, which enables monolithic devices. Nevertheless,
the geometry of the helical structure itself determines different kinds
of problems. Custom fabrication techniques adopted so far still present
some drawbacks. These actually complicate the manufacturing procedure
and, in some cases, limit the reliability of samples \[13\].

Accordingly, the availability of simpler configurations may boost the
short-term use of contractile actuators in practical applications. For
this purpose, this paper presents a new structure for a linear
contractile actuator. The concept of the device, the assembling of
prototype samples and their preliminary characterisation are reported in
the following.

#### 2. Actuator concept

The new configuration is here referred to as a 'folded' dielectric
elastomer actuator. It was conceived \[14\] to concentrate in a single
device different advantageous properties: 1) a functionality equivalent
to that of a multi-layer stack; 2) a continuity of the electrodes,
typical of a helical actuator; 3) a structure of easy fabrication. In
order to satisfy such needs, a folded actuator simply consists of a
monolithic strip of an electroded elastomer which is folded up, with a
resulting structure similar to that sketched in Fig. 2.

The application of a high voltage difference between the electrodes
induces a thickness squeezing (at constant volume) of the entire
elastomeric layer. Accordingly, an axial contraction of the device with
related lateral expansions are obtained (Fig. 3).

This simple configuration can be implemented with different kinds of
cross-sections, beyond the rectangular/square one. This can be done by
opportunely shaping the starting strip, prior to its folding. As an
example, Fig. 4 depicts a device with a resulting cylindrical structure.

![](media/image2.png){width="3.1847222222222222in" height="2.6125in"}

**Figure 2.** Steps to obtain a folded dielectric elastomer actuator:
(a) strip of elastomer; (b) strip with a couple of electrodes; (c)
folding; (d) assembled device.

![](media/image3.png){width="3.1868055555555554in"
height="1.7583333333333333in"}

**Figure 3.** Schematic drawing of the working principle of a folded
dielectric elastomer actuator: (a) rest state; (b) electrical
activation.

#### 3. Materials and methods

*3.1 Elastomer*

A soft commercial silicone rubber (TC-5005 A/B-C, BJB Enterprises Inc.,
U.S.A.), consisting of poly(dimethylsiloxane), was chosen as a
dielectric elastomer to fabricate prototype actuators. According to
previous investigations, this material enables high active strains at
relatively low fields \[13,15\]. It consists of a three-component
product, whose elastic modulus can be modulated by varying the amount of
a plasticizer (softener). In order to obtain very soft samples, a 45 wt%
of softener was used in this study. Following a degassing phase, the
material was cured at room temperature for one day.

![](media/image4.png){width="3.1618055555555555in"
height="1.2354166666666666in"}

**Figure 4.** Folded dielectric elastomer actuator with circular
cross-section: (a) starting strip; (b) assembled device.

*3.2 Electrical and mechanical testing of the elastomer*

In order to investigate the effects of eventual actuator
pre-compressions on the electromechanical response, basic material
properties were studied for different compressions. In particular, both
the dielectric spectrum and the stress-strain characteristic were
measured, at a room temperature of about 23 °C, for thickness strains
down to --40 and --50 %, respectively.

The real and imaginary parts of the complex relative permittivity
*ε~r~*\*(*ω*) of the material were measured in the range 10 -- 10^8^ Hz.
For this purpose, discs of the elastomer having a thickness of 1 mm and
a diameter of 11 mm were used. Measurements were performed with a
coaxial cylindrical capacitor cell connected to a vector network
analyser (ZVRE, Rohde & Schwarz, Germany).

For the mechanical tests, cylindrical samples of material with a height
of 22 mm and a diameter of 25.5 mm were subjected to axial compressions
at a constant deformation rate of 12 mm/min. For this type of test, a
two-columns dynamometer (5500R, Instron, U.S.A.) was used.

*3.3 Fabrication of prototype actuators*

Prototype samples of the new type of actuator were fabricated according
to the following procedure.

As a first step, a continuous strip of the elastomer having the desired
shape was obtained by mould-casting. It was successively coated with a
couple of continuous compliant electrodes, made of a
silicone/carbon-black mixture (CAF 4, Rhodorsil, France / Vulcan XC 72
R, Carbocrom, Italy). As an example, Fig. 5 shows a strip employed for
prototype cylindrical actuators.

![](media/image5.png){width="3.1819444444444445in"
height="1.0756944444444445in"}

**Figure 5.** Left side: electroded strip used to assemble a folded
actuator with circular cross-section. In order to reduce the encumbrance
of the mould, the arrangement sketched in the right side was used.

![](media/image6.png){width="3.1868055555555554in"
height="2.8159722222222223in"}

**Figure 6.** Prototype samples of folded actuators with rectangular or
circular cross-sections and different sizes.

![](media/image7.png){width="3.183333333333333in"
height="1.6263888888888889in"}

**Figure 7.** Force-length diagram representing the cyclic tests
performed to investigate electromechanical performances of the
actuators.

The electroded strip, having a typical thickness of 0.5-0.8 mm, was then
folded up and finally 'sealed' with a thin coating (about 0.1 mm) made
of the dielectric silicone itself.

Pictures of prototype actuators with rectangular and circular
cross-sections are presented in Fig. 6.

*3.4 Electromechanical testing of prototype actuators*

Electromechanical performances of prototype cylindrical actuators were
preliminarily assessed by measuring both the blocking force and the free
stroke due to different applied fields. Samples had a length of 85 mm
and a diameter of 25 mm. Each actuator was placed in vertical position
and connected to the same dynamometer employed for the mechanical tests.
This instrumentation was used, in combination with a dc high-voltage
generator (HV-DC 205A-30P, Bertan, U.S.A.), to perform the cyclic tests
described below with reference to Fig. 7.

As a first step, the mobile crossbar of the machine was held fixed, so
that to constrain the actuator in isometric condition (point A of Fig.
7). A step-wise high voltage ∆V was then applied to the actuator and the
resulting force (point B) was measured. The force variation between
points A and B represented the blocking (i.e. isometric) force of the
actuator for that voltage. After this, while keeping the voltage fixed,
the crossbar was pulled down to compress the actuator at a constant
speed (1 mm/min), until the force was reduced to the same value of point
A (point C). The difference in length between points A and C
corresponded to the free stroke of the actuator (i.e. the displacement
due to an eventual free contraction). Then, the crossbar was fixed again
and the voltage was removed, so that the actuator exhibited a recovery
force (point D). Finally, the crossbar and the actuator were brought
back to their initial position (point A). For each actuator, this cycle
was repeated for increasing voltages up to the dielectric breakdown of
the material. Therefore, such a procedure enabled combined measurements
of free stroke and blocking force on the same sample (up to its
breaking). This permitted to obtain truly comparable data, immune from
possible deviations due to eventual separate tests on different samples.

Moreover, in order to assess the actuator behaviour due to an eventual
pre-compression, the same type of cyclic tests was performed for some
samples by adopting a 10% axial pre-compression.

#### 4. Results

*4.1 Electrical and mechanical properties of the elastomer*

The frequency dependence of both the real and imaginary parts of the
relative permittivity, respectively *ε~r~'*(*ω*) and *ε~r~''*(*ω*), is
reported in Fig. 8 for different values of compression.

> ![](media/image8.png){width="3.188888888888889in"
> height="4.209722222222222in"}

**Figure 8.** Frequency spectrum of (a) real and (b) imaginary parts of
the elastomer relative permittivity at different compressions.

Fig. 9 presents the compression curve of the material.

*4.2 Preliminary electromechanical performances of prototype actuators*

A contraction of a prototype cylindrical actuator used with a purely
demonstrative set-up (lifting of a weight) is presented in Fig. 10.

![](media/image9.wmf)

**Figure 9.** Stress-strain characteristic of the elastomer under
compression.

![](media/image10.png){width="3.1881944444444446in" height="2.25in"}

**Figure 10.** Axial contraction of a prototype folded actuator with
circular cross-section: (a) rest state; (b) activation.

Values of free stroke and blocking force measured with the described
characterisation tests were used to calculate the active strain and
stress generated by the actuators. Fig. 11 shows a quadratic dependence
of these variables on the electric field for three samples: two of them
were not pre-compressed, while the third had a 10% axial
pre-compression.

![](media/image11.png){width="3.188888888888889in"
height="4.309722222222222in"}

**Figure 11.** Electric field dependence of (a) axial strain and (b)
axial stress of prototype folded actuators with circular cross-section
and different pre-compressions (fitting curves are inserted as a guide
for the eye).

**5. Discussion**

The new actuating configuration here described provides a simple means
to obtain an electrically contractile monolithic actuator. Folded
actuators permit to avoid the complexity of fabrication of both stack
actuators (requiring layer-by-layer depositions of dielectric and
conductive layers) and helical actuators (requiring two couples of
helically-shaped dielectric and conductive layers).

It is worth noting that the final compact structure is functionally
equivalent to a multi-layer stack with interdigited electrodes. This
latter solution traditionally offers an efficient transduction of
electrical energy into mechanical work, since the electric field is
aligned with the working direction. However, with respect to the stacked
configuration, a folded device is advantageously not discontinuous and
can be assembled in one single phase. Accordingly, a folded device is
expected to provide the same functionality of a stack, but with a
simpler structure. This permits a reduction of both the complexity and
overall duration of fabrication procedures. Moreover, it may also imply
lower costs of production.

The continuity of the structure may favour possible future developments
of continuous-type processes of manufacturing. They could employ, for
instance, long ribbons of electroded elastomer, to be folded
continuously. In this respect, we are currently working on a
semi-automatic fabrication technique, based on a custom folding machine
at lab-scale. The machine is expected to enable easier handlings of
elastomers with reduced thickness and to provide samples with higher
reliability and shorter production times.

Beyond such general features of the folded configuration, data reported
in this study suggest further observations.

As a first point, the measured axial stresses resulted independent of
the applied pre-compression (Fig. 11b). Furthermore, they were found to
be about 25% lower than expected theoretical values, as shown by the
following evaluations. By applying an electric field (*E~z~*) along the
thickness direction (*z*) of a planar compliant capacitor, the
electrostatic pressure (*p*) along *z* due to the Maxwell stress effect
is \[4\]:

> $p = \varepsilon_{0}\varepsilon_{r}E_{z}^{2} = \varepsilon E_{z}^{2}\text{  }$
> (1)

where *ε~0~* is the free-space dielectric permittivity
(*ε~0~*=8.85×10^-12^ F/m) and *ε~r~* is the relative dielectric constant
of the elastomer. Due to the structure of a folded actuator, the
pressure *p* represents also the theoretical axial stress achievable
from the device. According to Eq. (1), the assessed independence of the
stress from pre-compression (Fig. 11b) is consistent with another
experimental evidence: the real permittivity is substantially
independent from pre-compression as well (Fig. 8a). Assuming at low
frequencies an average value of *ε~r~*'=*ε~r~*=4.5, the theoretical
value of *ε* (Eq. (1)) is *ε~theor~*=39.8 Pa/(V/*μ*m)^2^ (=39.8×10^-12^
F/m). As a comparison, a quadratic fitting of the experimental stresses
provides *ε~exp~*=30.9 Pa/(V/*μ*m)^2^.

Concerning the strain, a modelling should take into account the
non-linear constitutive equations of the material and the effects of the
borders of the structure. In fact, the lateral non-electroded portions
(used as an electrical protection) offer a disadvantageous mechanical
resistance, which limits the deformation of the device. Regardless of
any modelling, the reported experimental data show a reduction of the
achievable strain with an applied pre-compression. This is consistent
with both the constancy of the stress (Fig. 11b) and the increase of the
elastic modulus (Fig. 9). In particular, the latter varies from 30 to 50
kPa by increasing the compression strain from 0 to 10%. Therefore,
according to these data, for the silicone material considered in this
study pre-compressions seem to be not advantageous for actuation.

In order to further develop folded actuators, some particular issues
require additional investigations. As a first point, we are currently
working towards a reduction of the material thickness, and therefore of
the driving voltages. However, the effect of the structural folds with
elastomers of particularly reduced thickness is currently unknown. So
far, no problems were experienced in terms, for instance, of premature
dielectric breakdown of the material. However, this may be reasonably
due to the employed large values of thickness (not lower than 0.5 mm).
Thinner elastomers may behave differently, even in consideration of the
stress experienced by the material around the folds.

As another point, a sort of 'optimisation' of the ratio between the
electroded area of the cross-section with respect to its total extension
is considered of fundamental importance. For a definite geometry of the
cross-section, this implies a reduction of the inactive area to the
limit electrically permitted (in order to avoid lateral electric
discharges). However, if the geometry of the cross-section is not
constrained by the application, the use of a rectangular shape seems to
be preferable. In fact, this permits to limit the inactive portions to a
couple of lateral bands (increasing the above-mentioned areas ratio).
Therefore, for a same value of the active area, a rectangular
cross-section seems to be better than a circular one. As an example,
Fig. 12 presents a contraction of a prototype sample of such an
actuator. The efficacy of this elementary configuration is shown by the
preliminary data reported in Fig. 13. They show that strains greater
than those of a circular actuator can be achieved.

![](media/image12.png){width="3.1881944444444446in"
height="1.8708333333333333in"}

**Figure 12.** Axial contraction of a prototype folded actuator with
rectangular cross-section: (a) rest state; (b) activation.

![](media/image13.wmf)

**Figure 13.** Electric field dependence of the axial strain of a
prototype folded actuator with rectangular cross-section and no
pre-compression (a fitting curve is inserted as a guide for the eye).

These preliminary data encourage further investigations aimed at
identifying optimised dimensional parameters, so that to take the most
from this simple and promising new type of contractile actuators.

#### Conclusions

The concept of a new dielectric elastomer actuator with contractile
linear properties has been described. The proposed configuration permits
to obtain a monolithic compact structure, functionally equivalent to a
multi-layer stack but with continuous electrodes. Silicone-made
prototypes have been demonstrated. The simplicity of fabrication of this
new type of actuator may facilitate the short-term diffusion of
contractile devices, to be readily employed for a broad range of
potential applications.

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