Fracture toughness, hysteresis and stretchability of dielectric elastomers under equibiaxial and biaxial loading

Polymer Testing 79 (2019) 106038

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Test Method

Fracture toughness, hysteresis and stretchability of dielectric elastomers under equibiaxial and biaxial loading Dilshad Ahmad, Sujit Kumar Sahu, Karali Patra

T

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Department of Mechanical Engineering, Indian Institute of Technology Patna, Bihta, 801103, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Dielectric elastomers Fracture toughness Biaxial loading Stretchability Hysteresis Drawing ratio

With the emergence of different dielectric elastomer transducers, the characterizations of dielectric elastomers are essential aspects for the design purpose. In this work, two potential dielectric elastomers, acrylic-based VHB and silicone-based Ecoflex, are tested and characterized under common loading conditions called equibiaxial and biaxial loading. Critical mechanical properties like hysteresis, fracture toughness, stretchability, and failure stress are obtained under equibiaxial and biaxial loading and compared with the same obtained under uniaxial and pure shear loading. It is found that hysteresis loss is almost equal in all three deformation modes. Fracture toughness under biaxial loading is more than that obtained from equibiaxial loading. Also, with increasing drawing ratio (DR), fracture toughness and failure stress decrease under biaxial loading condition. Stretchability is highest for uniaxial and followed by pure shear and equibiaxial loading cases. Stretchability is least for biaxial and with increasing drawing ratio, it further decreases. Fracture toughness, stretchability and failure stress are always more for VHB than Ecoflex under all deformation modes. However, hysteresis loss is more in case of VHB than Ecoflex. The present work successfully established the fact that for biaxial loading, fracture toughness and stretchability decreases drastically with drawing ratio. These results will provide the base of designing DEs transducers under various modes of deformation and more particularly for equibiaxial and biaxial deformation modes.

1. Introduction

applications which involve uniaxial pre-stretch deformation [16,17]. Though this mode of pre-stretching is more comfortable to implement, it results in less efficient DE transducers. Another method of deformation is the pure shear in which force is applied from one direction, but the lateral side is not free to contract [18,19]. In pure shear deformation, width is kept at least ten times more than that of its length, so that lateral direction is well constrained. This mode of deformation provides a more significant advantage of larger active to passive area ratio and more importantly keeping the actuation strain in one direction [18,20]. Hence, recently, it is shown that pure shear deformation results in increased actuation strain for DE transducers in the range of 500% [21]. Some of the application areas for this kind of deformation are artificial skin and artificial muscles [17,22,23]. Now, biaxial pre-stretching is the most popular method of deformation in which the elastomer is stretched from both longitudinal and lateral direction. Equibiaxial deformation mode has a more significant advantage of its easy prestretching ability and ease in holding the elastomer, which enhances the performance of DE transducers [24]. Therefore, biaxial deformation mode has been adopted by many researchers and scientist to make efficient DE transducers [25]. The applications of this mode of

Dielectric elastomer-based sensors, actuators and energy harvesting devices are commonly called dielectric elastomer transducer [1–5]. The working of dielectric transducers and their performances largely depend upon pre-stretch of the dielectric elastomer. Stretching of the dielectric elastomer before its application is known as ‘pre-stretch’ [6–8]. Pre-stretch enhances the performances of DE transducers by improving its efficiency and actuation strain [9]. Prestretch reduces the electromechanical instability as well as it controls excessive wrinkle formation [10–12]. The pre-stretch is incorporated in DE transducers in different deformation modes that cannot be neglected depending upon its usage as DE transducers [13]. Uniaxial, pure shear and equibiaxial deformations are popular modes of pre-stretching. Uniaxial (simple extension) is the most fundamental way of deformation where the elastomer is stretched in one direction and the lateral direction is free to contract [14]. Generally, height of the sample is taken to be more than 4–5 times than width of the sample to enable this mode of deformation [15]. Wearable electronics like smart shirts, life shirts, and sensorized sleeves and linear actuators are some of the

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Corresponding author. E-mail addresses: [email protected] (D. Ahmad), [email protected] (S.K. Sahu), [email protected] (K. Patra).

https://doi.org/10.1016/j.polymertesting.2019.106038 Received 28 July 2019; Received in revised form 9 August 2019; Accepted 12 August 2019 Available online 14 August 2019 0142-9418/ © 2019 Published by Elsevier Ltd.

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grooved clamps provided almost perfect clamping. Furthermore, stretchability, which is quantified by the maximum stretching of DEs, commonly known failure stretch [18,37,41] is of greater importance because it drastically affects the performance and efficiency of DE transducers. In other words, stretchability can be defined as the maximum attainable stretch of the material before its failure [37]. The stretchability of dielectric elastomer is markedly decreased down when there is a notch in the elastomer. Notches may present in the dielectric elastomer while operating as DE transducers or during the fabrication process. Some of the researchers specifically addressed the stretchability of dielectric elastomers in details. Chen et al. [35] investigated the stretchability variations of VHB and Polyurethane with different cut lengths under uniaxial loading, and it has been found that stretchability will remain constant around 9 for pristine samples and it decreases with notch lengths. Pharr et al. [37] conducted several experiments under pure shear loading and concluded that stretchability of VHB remains almost constant with strain rate, and its values are around 9 and 3.5 for pristine and larger notched specimens, respectively. But stretchability decreases with sample height and remains constant with stretch rate. Schmidt et al. [41] experimentally found that stretchability of VHB was coming around 9 when equibiaxially stretched using bubble inflation technique. Till now, very few researchers have experimentally studied the effect of biaxial stretching on the mechanical properties like hysteresis, fracture toughness and stretchability of dielectric elastomers. Caimmi et al. [42] investigated strain-induced molecular orientation effect on the fracture toughness of natural rubber-based compounds that were studied under biaxial loading conditions, using non-linear elastic fracture mechanics. The J-integral at fracture was evaluated using the finite element method. Marano et al. [43] studied the effect of molecular orientation on the fracture behavior of carbon black filled with natural rubber. They used a fracture mechanics approach to find the fracture toughness as a function of the drawing ratio applied in the drawing step. Drawing ratio can be defined as the ratio of stretch in drawing direction to the stretch in the loading direction. Their work aimed to evaluate the fracture resistance of filled natural rubber compounds as a function of molecular orientation, using biaxially loaded notched specimens. Helal et al. [44] conducted biaxial tensile experimental evaluations of VHB to illustrate transversely isotropic mechanical behaviors of DEs. They also carried out equibiaxial hysteresis experiments under varying strain rate, but their maximum stretch was limited to 1.8 only. As there are very few experimental works on DEs under biaxial loading in spite of its utmost advantages and applications, it is crucial to present a detailed, innovative work on DEs under equibiaxial and biaxial loading and to compare the results with those of other modes like uniaxial and pure shear. The complexity of the biaxial setup and associated cost may be the possible reasons why this method has not experimentally tried much till date. Therefore, in the current work, we applied an in-house developed biaxial planar tensile testing device to conduct all the experiments. To the best of the authors knowledge, this is the first extensive experimental work illustrating and comparing important mechanical properties like fracture toughness, hysteresis, and stretchability of two DEs under biaxial loading. These aforementioned mechanical properties of these two DEs obtained in equibiaxial and biaxial loading are also compared with those obtained in different other modes of deformation. The current paper is organized as follows: In Section 2, we elaborated the experimental procedure. Materials and specimen geometry along with testing machines and its working, are also discussed in this section. Section 3 consists of results and discussions. Therein, theories of hysteresis and fracture toughness are presented under different loading conditions. Comparison of hysteresis and its correlation with fracture toughness are also investigated. In Section 3, a comparison of stretchability and fracture toughness under both biaxial and equibiaxial conditions are illustrated. A detailed conclusion of the current work is

deformation are micro-pumps disk drives, pneumatic valves, loudspeakers, motor, etc. [17,26,27]. Henceforth, firstly, Pelrine et al. [28] used acrylic elastomer as a Dielectric elastomer and achieved actuation strain up to 158% when the DE membrane is biaxially pre-stretched and fixed to a rigid frame. Kollosche et al. [29] observed actuation strain up to 260% when the biaxial pre-stretched membrane is clamped under two rigid structures. Further, Huang et al. [30] achieved actuation strains up to 488% when dead loads are introduced in biaxial stretching. Keplinger et al. [31] attained a much larger biaxial actuation strain up to 1689% by mounting pre-stretched membrane on a cylindrical chamber of compressed air. This biaxial mode of pre-stretching provides greater actuation strain as compared to uniaxial and pure shear because biaxial mode deformation reduces the thickness of the membrane to a greater extent resulting in increased actuation [28]. It is essential to investigate the effects of different modes of deformations on the mechanical properties like hysteresis, fracture toughness, stretchability, etc., of DE membranes so that performances of pre-stretched DE transducers can be better analyzed and their operating ranges can be decided. State of the art of mechanical characterization in different modes of deformations of DE membranes and the research gaps are identified in this area and are described below. Besides significant nonlinear hyperelastic behavior, dielectric elastomer also exhibits some inelastic effect like hysteresis. Hysteresis effect in DE is a phenomenon which indicates the amount of energy dissipated as thermal energy in a cycle of loading and unloading [32]. In other words, stress-induced in the material while loading will be more than the stress-induced when unloading at a particular strain [14]. This effect is an important aspect while designing sensors and energy harvesting devices using DEs because often the DEs deform in cyclic motion to get the required power [3]. Some researchers conducted experiments emphasizing the hysteresis of DEs. Earlier, Sahu et al. [14] carried out hysteresis experiments under uniaxial loading and established that there was little increase in hysteresis losses with increasing strain rate. Rey et al. [33] also conducted experiments on filled silicone rubber, and it was found that the magnitude of hysteresis increased with temperature under uniaxial load. In recent time, Wang et al. [34] developed a new kind of material to be used for soft robotics that shows high toughness and low hysteresis using a pure shear mode of deformation. Generally, the hysteresis of DE is related to both fracture toughness and stretchability. It is because high energy dissipation is the main reason for substantial fracture toughness and hysteresis for elastomers under different conditions. Moreover, energy dissipation is directly dependent upon the number of polymer networks in the material [34], and higher fracture toughness is correlated with higher stretchability because of higher strain energy density stored in the material due to large polymer networks [35]. Hence, high hysteresis is meant for higher fracture toughness and higher stretchability [34,35]. However, hysteresis in various modes of deformation has not been compared so far. Fracture toughness is another property of DEs that describes the ability of the material to resist the growth of a crack and it is one of the most important properties to decide the design of DE transducers [19,26,36]. Firstly, Pharr et al. [37] carried out an experimental investigation to measure the fracture toughness of the most popular dielectric material, VHB. They used pure shear specimen with and without cracks to measure fracture energies at different stretch rates. Further, Kaltseis et al. [38] chose natural rubber and VHB as dielectric materials and compared their compatibility as an energy harvesting device. They calculated fracture toughness under pure shear loading and found that fracture toughness of natural rubber was almost double than that of VHB. Ahmad and Patra [39] also experimentally investigated that fracture toughness of VHB under pure shear deformation increases with strain rate. Bernardi et al. [40] selected three different kinds of gripping systems under pure shear loading and compared fracture toughness in all types of grip. It is observed that 2

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2.2. Testing devices

summarized in section 4.

2.2.1. Universal testing machine (UTM) for uniaxial and pure shear test For doing pure shear and uniaxial experiments, universal testing machine (UTM) is used to conduct all the tests as shown in Fig. 3. A 2.5 kN load cell, which is fixed with the crosshead, is used to carry out all the tests. The thickness for both the materials is 1 mm. The required sample is set into the fixtures, and the upper part moves with the crosshead while the lower part is completely fixed. A controller is attached with a computer to collect force and displacement data at a fixed strain rate of 0.3 per second. Here, we have chosen a strain rate of 0.3/s to compare the results with the existing work done by Helal et al. [44]. For conducting uniaxial and pure shear tests, two different kinds of fixtures are used, which are shown in Fig. 4. Fig. 4a shows a springloaded uniaxial fixture which is having an excellent gripping ability for extensive stretching in case of uniaxial tests. Fig. 4b shows a specially designed in-house fixture, which is used for pure shear tests.

2. Experimental procedure 2.1. Materials and geometry Two dielectric elastomers, VHB and Ecoflex, are used in this work to test their biaxial properties. VHB is a commercially available acrylicbased dielectric elastomer manufactured by 3 M company, USA. This elastomer is available in a roll form. The thickness of the sheet for VHB is 1 mm. On the other hand, Ecoflex, a silicone-based dielectric elastomer, is prepared in the laboratory by mixing two parts A and B (supplied by Smooth-On, USA) together in equal proportion by weight. The Ecoflex is available in different hardness classified as Shore 00 10, Shore 00 20, Shore 00 30, etc. with varying curing time according to its hardness [45]. Here, we have used Ecoflex with Shore 00 30, whose curing time is 4 h. Therefore, the mixture is then stirred continuously and allowed to spread in a mold to cure in a room environment to cool properly for about 4 h at room temperature of 23°c. Curing time will drastically reduce with temperature. The thickness of the sheet is measured at different positions by using a digital thickness gauge to confirm a uniform thickness of 1 mm ± 0.05 μm. The pristine specimens used for uniaxial, pure shear and equibiaxial loading are shown in Fig. 1. The uniaxial specimen used in the current work is shown in Fig. 1a where length is 52 mm and width is 6.5 mm to get the height to width ratio is 8:1. In some earlier works, 10:1 ratio is used in order to confirm uniaxial homogeneous state [46,47] but the recent study shows that even shorter length samples can be used that may not obey 10:1 ratio [48], therefore in the current work 8:1 ratio is used which is leading to homogeneous state of deformation. The pure shear specimen is having 320 mm width and 15 mm length as shown in Fig. 1b. The biaxial specimen is shown in Fig. 1c where a square-shaped sample is fixed under four grips and grip to grip distances are kept to be 60 mm from both lateral sides. To calculate fracture energy of the DEs, a deliberate notch is introduced in the specimens as shown in Fig. 2. In the earlier works [37], to calculate the fracture toughness of rubber under pure shear loading, generally, a notch of 20% width is created and then fracture experiment is conducted. In the same line, a straight notch of 64 mm (20% of the width) is introduced in the pure shear specimen, as shown in Fig. 2a. The horizontally notched specimen is used for biaxial fracture testing where it is first loaded in direction 2 to be fixed at a specific load and then elongation takes place in direction one as shown in Fig. 2b. The diagonally notched specimen as shown in Fig. 2c is used for equibiaxial fracture test where the load is applied from all four directions equally. Hence, it enables homogeneous deformation of dielectric elastomers.

2.2.2. Biaxial planar tensile testing device To do the biaxial tensile tests, a testing device is developed at IIT Patna [49] in our laboratory as shown in Fig. 5. The operations for biaxial and equibiaxial deformation modes are achieved by providing manual inputs using a selection switch. One load cell is attached to one of the racks to measure the force required to pull the DE samples. Only one load cell is used here because the DEs used in this work are isotropic materials i.e., the stress-stretch diagram is the same for both lateral directions [44]. Only one load cell is enough to capture load in the biaxial case because only stretching is required and load data is not necessary when the specimen is drawn in the 2nd direction as shown in Fig. 8 and Fig. 10. When it starts stretching in a 1st direction, then the load cell is required in 1st direction to plot the stress-stretch curve for different drawing ratio, as shown in Fig. 12. The load and displacement data are acquired from the load cell and multi-turn potentiometer position sensors, respectively. After receiving load and displacement data from the machines for uniaxial (UX), pure shear (PS) and equibiaxial (EB) deformation modes, the load data is converted in to engineering stress by dividing initial area of both the specimens (VHB and Ecoflex) used which are (6.5 × 1) 6.5 mm2, (320 × 1) 320 mm2 and (30 × 1) 30 mm2 for UX, PS and EB deformation modes, respectively. Displacement data can be converted into engineering strain subtracting each final displacement data with initial displacement and then divided by initial displacement. The engineering strain is then changed into the stretch by adding 1. True stress is obtained by multiplying stretch with engineering stress and hence true stress-stretch graphs may be obtained for each deformation case. Since all the modes of deformation are homogeneous, earlier researchers have analytically studied their comparison [40,50–52] in terms of true stress. Hence, in the next section, an experimental study is conducted on VHB and Ecoflex comparing true stress-stretch graphs for

Fig. 1. Geometry of pristine specimen for (a) uniaxial (b) pure shear and (c) equibiaxial loading. 3

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Fig. 2. Notched specimen used for determining fracture toughness for (a) pure shear (b) biaxial (c) equibiaxial deformation modes.

Fig. 5. Biaxial planar testing device.

100.8 mm and 100.76 mm respectively when stretched. Grip to grip distance is 60 mm from one side and 61 mm from another diagonal side, which becomes 643 mm and 648 mm, respectively after stretching, as shown in Fig. 6 (b). The ratio of final grip to grip distance to the initial grip to grip distance is 10.66 and 10.62 for both pairs of grippers respectively. In the same way ratios of final elongated length to the initial length at the middle of the specimen are 10.66 and 10.66 respectively for both perpendicular directions. Hence, a real equibiaxial and biaxial deformation are possible with this kind of gripper arrangement. These results confirm that the deformation is isotropic in nature at the middle of the specimen, which is the region of equibiaxial and biaxial deformation.

Fig. 3. Schematic diagram of the experimental setup with Universal Testing Machine (UTM) for conducting uniaxial and pure shear tests.

3. Results and discussions 3.1. Comparison of hysteresis behavior of dielectric elastomers under uniaxial (UX), pure shear (PS) and equibiaxial (EB) deformation modes

Fig. 4. Two types of fixtures (a) uniaxial and (b) pure shear are used to conduct tests.

The hysteresis loss can be calculated using the following equation (1):

uniaxial, pure shear, and equibiaxial modes of deformation. Finally, the mechanical properties of the elastomer at different equibiaxial and biaxial loading conditions are obtained. Slippage of the sample from the gripper and stress concentration while loading is the most common phenomena in testing the soft materials like elastomers [40]. Hence, during equibiaxial loading, we designed a special kind of gripper with very sticky VHB tape fixed inside it to hold the specimen tightly, as shown in Fig. 6. This arrangement prevents the material from any possible slippage while the load is applied. This soft VHB tape also provides negligible stress concentration in the specimen, which generally arises due to sharp contact with grippers [41]. To ensure a real equibiaxial deformation at the middle of the specimen, a mark has been applied at the center of the specimen, as shown in Fig. 6 (a). An initial square mark with a side of length 7.45 mm is shown in the middle of the specimen which becomes

Hysteresis (%) Area under the loading curve − Area under the unloading curve = ⎜⎛ Area under the loading curve ⎝ ⎞ × 100 ⎠

⎟

(1)

Here, areas under the loading curve and unloading curves for uniaxial, pure shear, and equibiaxial can be obtained from Fig. 7. Hysteresis curves shown in Fig. 7 are obtained for a maximum stretch of 3.5 under all possible deformation modes, i.e., uniaxial, pure shear, and equibiaxial at a strain rate of 0.3/s. Equibiaxial data from current work is compared with the existing work by Helal et al. [44] at the same strain rate of 0.3/s, which are in quite good agreement. Also, uniaxial data is compared with Sahu et al. [14]. However, Helal et al. 4

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Fig. 6. (a) Initial position of the gripper before stretching (b) Final position of the grippers after stretching with dimensions.

same strain rate for both the elastomers. Hence, the behavior of dielectric elastomers under various deformation modes are different based on the stretching constrained of chains and consequently, their properties like stretchabilities, failure stresses are observed differently. Also, from Table 1, it is observed that the hysteresis loss for VHB under equibiaxial, pure shear and uniaxial modes are almost similar around 35% which is quite high as compared to that for Ecoflex which is around 11%.

[44] had taken a 10 mm square specimen for an equibiaxial test, and Sahu et al. [14] had used a sample with a width of 25 mm and height of 30 mm for uniaxial hysteresis test. Uniaxial, pure shear, and equibiaxial modes of deformation for viscoelastic materials like VHB and Ecoflex are isotropic in nature when observed individually [53]. But when different deformation modes are compared with each other, their constant like elastic modulus will be different from each other depending upon different ways of stretching of chains and crosslinks inside the material [54]. In summary, the chains and crosslinks are free to contract in width direction under a uniaxial pull, on the contrary, the chains and cross-links are constrained and not free to contract in width direction for a pure shear loading. For an equibiaxial deformation, the chains and crosslinks are equally stretched simultaneously from two perpendicular directions [42]. Based on different modes of deformation their application areas as a dielectric elastomer in transducers are extensive. Some of the examples are the development of weight machines and sensorized sleeves utilizing uniaxial mode [55], human motion energy harvester and artificial muscles using pure shear mode [56,57] and ocean wave energy harvester deform in an equibiaxial manner [55]. Hence, their comparison is worth reasonable in terms of properties like failure, stress, fracture toughness, and stretchability. It is seen that true stress at a particular stretch is always more for equibiaxial and less for uniaxial. For pure shear, true stress is always seen to lie in between uniaxial and equibiaxial. From Fig. 7 a-b and Table 1, it is shown that maximum true stress for VHB under equibiaxial stretching at a strain rate of 0.3/s is 0.95 MPa while it is 0.81 MPa for Ecoflex. For Pure shear, the maximum stress is 0.73 MPa for VHB and 0.47 MPa for Ecoflex. Again, under uniaxial loading, the maximum stress has come out to be 0.58 MPa for VHB and 0.35 MPa for Ecoflex. It shows that true stress is decreasing from equibiaxial to uniaxial at the

3.2. Characterization of DEs under biaxial conditions Fracture toughness of the elastomers under biaxial as well as equibiaxial loading can be calculated as follows [18,58]:

Jc =

σT (πa)2 × 103 E

(kJ/m2)

(2)

where, σT = True Stress at failure (MPa).

E = Elastic modulus (MPa). 2a = Crack length (4 mm). Fracture toughness of the dielectric elastomers under pure shear loading can be given as follows [59]:

Jc =

Uc B (W − a)

(kJ/m2)

(3)

where, Uc = Area under Force-displacement curve (MPa)

B = Thickness of the specimen (mm). a = Length of notch in the specimen (mm)

Fig. 7. (a) Comparison of UX, PS and EB hysteresis for VHB at astrain rate of 0.3/s (b) Comparison of UX, PS and EB hysteresis for Ecoflex at a strain rate of 0.3/s. 5

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Fig. 8. Different drawing ratio starting from (a) DR = 1 (b) DR = 2 (c) DR = 3 for VHB.

experimentally investigated that stress at a particular stretch increases with increasing drawing ratio (DR) from DR = 1 to DR = 3. From Fig. 13a and b, it can be observed that both failure stretch and failure stress decreases as DR increases. Here, failure stretch at DR = 1 is approximately 4.46 and 3.9; at DR = 2, it is 3.45 and 2.8; and at DR = 3, it is 2.34 and 2.19 for VHB and Ecoflex, respectively. Whereas, failure stress at DR = 1 is approximately 0.85 MPa and 0.38 MPa; at DR = 2, it is 0.66 MPa and 0.14 MPa; and at DR = 3, it is 0.47 MPa and 0.10 MPa for VHB and Ecoflex, respectively. Failure stretch and failure stress decrease with DR because fracture toughness ( Jc ) decreases with increasing DR, as shown in Fig. 14c. For DR = 1, Jc = 6 kJ/m2 and 5 kJ/ m2; DR = 2, Jc = 3.6 kJ/m2 and 0.56 kJ/m2; DR = 3, Jc = 2 kJ/m2 and 0.4 kJ/m2, respectively, for VHB and Ecoflex. In the current work, experiments are repeated three times in each case for both VHB and Ecoflex, and one of them is used to represent the true stress-stretch behavior for all types of tests similar to the practice followed in earlier papers [18,35,37,41,47,57]. Earlier, Pharr et al. [37] conducted experiments on the same VHB material with a repeatability of at least three and maximum of five, wherein, standard deviations for failure stretch were 1.05 and 0.45 for pristine sample and pre-cut sample, respectively. However, with three times repeatability, we obtained lesser values of standard deviation which varies from 0.13 to 0.31 for failure stretch as shown by the error bars in Fig. 13 (a). Similarly, the standard deviations for failure stress and fracture toughness lie in the range of 0.2–0.3 and 0.2–0.6 as shown in Fig. 13b and c, respectively. It is experimentally studied earlier that with an increase in stretching the hysteresis loss decreases [26] that leads to the decrease in the fracture toughness because fracture toughness directly depends upon hysteresis. This is because fracture toughness under equibiaxial and pure shear conditions are less for materials with low hysteresis loss. This is a typical characteristic of an unfilled polymer in which at the front of the crack the polymer chain is highly stretched and its breaking dissipates the energy in the entire chain. On the other hand, higher viscous material like VHB has high hysteresis and high toughness because the stress from the front of a crack transmits into the bulk of the network, breaking many covalent bonds and crosslinks and dissipates a large amount of energy [34,35]. Further, it can be observed that the failure stretch, failure stress, and fracture toughness under biaxial loading condition for VHB are always more than those of Ecoflex at a particular strain rate and drawing ratio. Higher hysteresis loss may be the leading cause for the higher fracture toughness, fracture stretch and stress for VHB among these two dielectric elastomers.

Table 1 Hysteresis (%) and true stress for equibiaxial, pure shear and uniaxial loading. True stress (MPa) at maximum stretch of 3.5

Hysteresis loss (%)

Hysteresis loss (%) in literature

VHB

Ecoflex

VHB

Ecoflex

VHB

Equi-biaxial

0.98

0.83

37.2

11.48

Pure Shear Uniaxial

0.83 0.51

0.4 0.3

40.1 35.1

12 10

50 Helal et al. (42) – 34 Sahu et al. (12)

Modes/Hysteresis Percentage/True Stress

In order to identify the variation of fracture toughness under biaxial loading an equal length (4 mm) notch has been created in both dielectric elastomers and then stretched up to different lengths. The drawing ratio (DR) can be defined as follows:

Drawing Ratio (DR) =

λ2 λ1

(4)

Where, λ2 = Stretch in 2nd direction. λ1 = Stretch in 1st direction. The drawing ratio (DR) under biaxial loading (BX) of VHB and Ecoflex can be understood from Figs. 8 and 10, in direction two whereas the clamps fixed with the specimen in direction one does not move. Alternately, it can be stated that the crack is only stretched, but the fracture itself is not increased. Fig. 8 a-c show VHB samples of 4 mm notch for DR = 1, 8 mm notch for DR = 2 and 12 mm notch for DR = 3, respectively. The similar drawing patterns are obtained for Ecoflex for DR of 1, 2 and 3 as shown in Fig. 10a, b and 10c, respectively. After the specimen is pre-stretched in direction 2 using a biaxial testing machine, loading takes place in direction 1 till the complete fracture of the specimen takes place. The propagations of crack for VHB and Ecoflex for DR = 2 are clearly shown in Fig. 11 and Fig. 13, respectively. The specimen of VHB is stretched in direction 2 to convert a 4 mm notched specimen into 8 mm (DR = 2) as shown in Fig. 11a. This pre-stretched specimen is then allowed to elongate in a direction one by the biaxial planar tensile testing device. The crack is then blunted, and its shape becomes circular, as shown in Fig. 11b. Then initiation of crack from both sides takes place as shown in Fig. 11c and finally the specimen tears into two parts, and complete fracture takes place as shown in Fig. 9 d. Similar fracture behavior is observed by Ecoflex as shown in Fig. 11. As shown in Fig. 12a and b, true stress-stretch curves for VHB and Ecoflex, respectively, have been obtained under three different biaxial loading conditions where the specimens are stretched in the 2nd direction first and then load is applied along direction 1. It is

3.3. Characterization of dielectric elastomers under equibiaxial loading condition To understand the behavior of DE materials (VHB and Ecoflex) under equibiaxial loading, we have conducted equibiaxial fracture test 6

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Fig. 9. Propagation of crack in VHB for DR = 2 starting from a 4 mm crack which turned in to (a) 8 mm crack when stretched in direction 2 (b) then blunted in to circular shape while loading in direction 1 and then (c) initiation of crack from both cut sides starts which eventually results in to (d) complete fracture of specimen.

Fig. 10. Different drawing ratio starting from (a) DR = 1 (b) DR = 2 (c) DR = 3 for Ecoflex. Fig. 11. Propagation of crack in Ecoflex for DR = 2 starting from a 4 mm crack which turned in to (a) 8 mm crack when pre stretched in direction 2 (b) then blunted in to circular shape when stretched in to direction 1 and then (c) initiation of crack from both cut sides starts which eventually results in to (d) complete fracture of specimen.

Fig. 12. Stress-stretch curve for DR = 1,2 and 3 for (a) VHB (b) Ecoflex at strain rate of 0.3/s.

as shown in Fig. 15c. True stress versus equibiaxial stretch for VHB and Ecoflex are shown in Fig. 16a and b, respectively. In Fig. 16a, pristine sample of VHB is stretched equibiaxially and its failure stretch reaches up to λ f = 4.92 while failure stretch for 4 mm diagonal notched specimen decreases down to λ f = 3.25. On the other hand, for Ecoflex elastomer, the pristine sample is reaches up to failure till λ f = 4.76 as shown in Fig. 16b. For a diagonal notched specimen, the failure stretches reach till λ f = 3.1. The decrease in failure stretch with the introduction of the notch is because fracture toughness decreases appreciably, which causes early failure of the material as it happens in case of pure shear

on VHB by introducing a 4 mm long diagonal notch in the center of the specimen as shown in Fig. 2c. The diagonal notch for VHB is then stretched from both direction 1 and two equally and homogeneously, as shown in Fig. 14a. After a certain amount of equibiaxial stretching, the notch blunts in a circular shape and crack initiation takes place as shown in Fig. 14b. The specimen is then torn into two parts, and complete fracture happens, as shown in Fig. 14c. Similar kinds of crack propagation and fracture of specimen take place for Ecoflex, as shown in Fig. 15. A 4 mm diagonal notch for Ecoflex is shown in Fig. 16a. A blunted crack with crack initiation is shown in Fig. 15b, which finally tears into two parts, 7

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Fig. 13. Variation of mechanical properties (a) failure stretch (b) failure stress and (c) fracture toughness with drawing ratio (DR) for VHB and Ecoflex under biaxial loading.

Fig. 14. Propagation of crack in equibiaxial loading of VHB for a (a) 4 mm diagonal (45°) notch which is (b) equibiaxially stretched in direction 1 and 2 so that the notch blunts and initiation of crack takes place which then (c) bifurcates and resulted in to complete fracture of specimen.

Fig. 15. Propagation of crack in equibiaxial loading of Ecoflex for a (a) 4 mm diagonal (45°) notch which is (b) equibiaxially stretched in direction 1 and 2 so that the notch blunts and initiation of crack takes place which then (c) bifurcates and resulted in to complete fracture of specimen.

diagonal notched specimen is 2.37 MPa, as shown in Fig. 16b. The possible reasons for this discrepancy of failure stress under different loading conditions are due to equal strain energy density stored in the specimen irrespective of different deformation modes. Stress acting at a particular stretch for EB is always maximum, minimum for UX and stress lies between both for PS [41,54]. Also, from Fig. 16a, it is seen that the value of failure stretches for

[37]. The failure stress for VHB under equibiaxial (EB), pure shear (PS) and uniaxial (UX) loading are 1.91 MPa, 6.1 MPa, and 8.52 MPa, respectively, as shown in Fig. 16a. The failure stress for the diagonal notched specimen is 2.04 MPa. On the other hand, failure stress for Ecoflex is 2.37 MPa, 4.63 MPa, and 5.93 MPa, respectively, for EB, PS, and UX loading, as shown in Fig. 16b. The failure stress for Ecoflex for a 8

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Fig. 16. Stress-stretch curve for pristine and notched specimen under equibiaxial loading for (a) VHB comparing with Schmidt et al. (2012) results at 0.0043/s (39) and (b) Ecoflex at strain rate of 0.3/s.

around 3.9 for Ecoflex and DR = 2, DR = 3, the failure stretches will be 2.17. and 2.4, respectively. For equibiaxial loading with a diagonal notch failure stretch for Ecoflex will be around 3.1. Failure stretch at different loading conditions for both VHB and Ecoflex are compared in Fig. 17. It can be observed that failure stress and failure stretch for Ecoflex are always less than those of VHB, because fracture toughness of Ecoflex is less than VHB as shown in Fig. 18. This is because Ecoflex is less viscous than VHB, as discussed in section 3.2. Fig. 18 represents fracture toughness under pure shear (PS), equibiaxial (EB) and biaxial (BX) loading from this work. The present results are also compared with the fracture toughness obtained under pure shear loading for VHB by Pharr et al. [37]. The fracture toughness values for a diagonal notched EB specimen is coming around 4.4 kJ/m2 for VHB. For biaxial (BX) with DR = 1, 2 and 3, the values of fracture toughness decrease as 6 kJ/m2, 3.6 kJ/m2 and 2 kJ/m2, respectively. Similarly, the fracture toughness values for a diagonal notched EB specimen is coming around 3.9 kJ/m2 for Ecoflex. For biaxial (BX) with DR = 1, 2 and 3, the values of fracture toughness decrease as 5 kJ/m2, 0.6 kJ/m2, and 0.4 kJ/m2, respectively. When a crack advances, the number of elastomer chains available in the material to break keeps on decreasing [57]. Therefore, fracture toughness decreases with increasing DR as drawing the elastomers reduces the number of chains to break. Hence, for BX the failure stretches and fracture toughness both decreases as shown in Figs. 17 and 18, respectively. We have also experimentally obtained fracture toughness for other commonly applied loading method called ‘pure shear’. The fracture toughness obtained under pure shear at a strain rate of 0.3/s is coming around 4.37 kJ/m2 and 3.58 kJ/m2 for VHB and Ecoflex, respectively. The reported value of fracture toughness from Pharr et al. [37] work was around 4.2 which is in close agreement with that obtained in this work under equibiaxial loading as well as pure shear loading. In all the loading conditions, it is observed that fracture toughness is more for VHB than that for Ecoflex.

Fig. 17. Comparison of failure stretch under different loading conditions at a strain rate of 0.3/s.

4. Conclusions DE transducers are gaining its importance due to its wide range of applications in recent times. Uniaxial and pure shear testing methods are commonly used to test the properties of DEs. The contribution of this work is that we have experimentally studied three important properties, hysteresis, fracture toughness and stretchability of two potential DEs (VHB and Ecoflex) under the most common deformation mode called biaxial for the first time. These results are then compared with that obtained from, uniaxial and pure shear. The main findings of the current work are summarized below:

Fig. 18. Comparison of fracture toughness at a strain rate of 0.3/s under different loading conditions and comparison with earlier literature.

pristine VHB specimen under EB, PS and UX are 4.9, 11, and 13.1, respectively. From Fig. 16b, it can be observed that the failure stretches for pristine Ecoflex specimen under EB, PS and UX modes are 4.7, 7, and 8.3, respectively. For biaxial loading (BX) (DR = 1) the values of failure stretches are around 4.5 for VHB and DR = 2, DR = 3, the failure stretches will be 3.45 and 2.34, respectively. For equibiaxial loading with a diagonal notch failure stretch for VHB will be around 3.25. On the other hand, for biaxial loading (BX) (DR = 1) the values of failure stretches are

(a) Developed a biaxial planar tensile testing device to conduct all the experiments under biaxial loading. (b) Hysteresis loss for VHB and Ecoflex are almost equal in all three deformation modes: uniaxial, pure shear, and biaxial. It is 9

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(c)

(d)

(e) (f)

investigated that VHB has almost three times more hysteresis than Ecoflex. Fracture toughness under biaxial loading is more than that obtained under equibiaxial loading. VHB has more fracture toughness than Ecoflex under all deformation modes in a similar environment. Also, with increasing DR fracture toughness and failure stress decreases under biaxial (BX) condition. Stretchability is highest for uniaxial then comes pure shear then equibiaxial and least for biaxial. Also, with increasing DR, stretchability decreases under BX condition. Fracture toughness, stretchability, and failure stress are always more for VHB than Ecoflex under all deformation modes. These achievements can be exploited for the design and development of DEs transducers, which are subjected to biaxial deformation while functioning.

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Acknowledgement [28]

This work has been supported by Department of Science and Technology, India, Government of India through project no. INT/SIN/ P-03.

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Appendix A. Supplementary data

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Supplementary data to this article can be found online at https:// doi.org/10.1016/j.polymertesting.2019.106038.

[32]

References

[33]

[1] M. Mehnert, P. Steinmann, On the influence of the compliant electrodes on the mechanical behavior of VHB 4905, Comput. Mater. Sci. (160) (2019) 287–294. [2] M. Mehnert, M. Hossain, P. Steinmann, Towards a thermo-magneto-mechanical coupling framework for magneto-rheological elastomers, Int. J. Solids Struct. (128) (2017) 1689–1699. [3] F. Carpi, D.D. Rossi, R. Kornbluh, R. Pelrine, P.S. Larsen, Dielectric elastomers as electromechanical transducers, J. Chem. Inf. Model. (53) (2013) 1689–1699. [4] A.T. Mathew, S.J.A. Koh, Operational limits of a non-homogeneous dielectric elastomer transducer, Int. J. Soc. Netw. Min. 8 (4) (2017) 214–231. [5] F. Carpi, I. Anderson, S. Bauer, G. Frediani, G. Gallone, M. Gei, et al., Standards for dielectric elastomer transducers, Smart Mater. Struct. 24 (10) (2015) 105025. [6] S.J.A. Koh, T. Li, J. Zhou, X. Zhao, W. Hong, J. Zhu, et al., Mechanisms of large actuation strain in dielectric elastomers, J. Polym. Sci. B Polym. Phys. 49 (7) (2011) 504–515. [7] S. Rosset, O.A. Araromi, H.R. Shea, Maximizing the displacement of compact planar dielectric elastomer actuators, Extrem. Mech. Lett. (3) (2015) 72–81. [8] M. Moscardo, X. Zhao, Z. Suo, Y. Lapusta, On designing dielectric elastomer actuators, J. Appl. Phys. 104 (9) (2008) 1–7. [9] S. Akbari, S. Rosset, H.R. Shea, More than 10-fold increase in the actuation strain of silicone dielectric elastomer actuators by applying prestrain, Proc. SPIE 8687 (2013) 86871P. [10] G. Kofod, The static actuation of dielectric elastomer actuators: how does prestretch improve actuation? J. Phys. D Appl. Phys. 41 (21) (2008 Nov 7) 215405. [11] B. Li, H. Chen, J. Qiang, S. Hu, Z. Zhu, Y. Wang, Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation, J. Phys. D Appl. Phys. 44 (15) (2011) 155301. [12] L. Jiang, A. Betts, D. Kennedy, S. Jerrams, Eliminating electromechanical instability in dielectric elastomers by employing pre-stretch, J. Phys. D Appl. Phys. 49 (26) (2016) 265401. [13] Y. Wang, B. Chen, Y. Bai, H. Wang, J. Zhou, Actuating dielectric elastomers in pure shear deformation by elastomeric conductors, Appl. Phys. Lett. 104 (6) (2014) 064101. [14] R.K. Sahu, K. Patra, Rate-dependent mechanical behavior of VHB 4910 elastomer, Mech. Adv. Mater. Struct. 23 (2) (2016) 170–179. [15] K. Patra, R.K. Sahu, A visco-hyperelastic approach to modelling rate-dependent large deformation of a dielectric acrylic elastomer, Int. J. Mech. Mater. Des. 11 (1) (2015) 79–90. [16] F. Carpi, D. De Rossi, Electroactive polymer-based devices for e-textiles in biomedicine, IEEE Trans. Inf. Technol. Biomed. 9 (3) (2005) 295–318. [17] R. Pelrine, P. Sommer-larsen, R.D. Kornbluh, R. Heydt, G. Kofod, P. Gravesen, Applications of dielectric elastomer actuators, Proc. SPIE (4329) (2001) 335–349. [18] D. Ahmad, K. Patra, Experimental and theoretical analysis of laterally pre-stretched pure shear deformation of dielectric elastomer, Polym. Test. (75) (2019) 291–297. [19] A. Kumar, D. Ahmad, K. Patra, Dependence of actuation strain of dielectric elastomer on equibiaxial, pure shear and uniaxial modes of pre-stretching, IOP Conf. Ser. Mater. Sci. Eng. 310 (2018) 012104. [20] S.J.A. Koh, C. Keplinger, R. Kaltseis, C.-C. Foo, R. Baumgartner, S. Bauer, et al., High-performance electromechanical transduction using laterally-constrained

[34] [35] [36]

[37] [38]

[39] [40]

[41] [42]

[43]

[44] [45] [46] [47] [48]

[49] [50] [51] [52]

[53] [54]

10

dielectric elastomers part I: actuation processes, J. Mech. Phys. Solids (105) (2017) 81–94. Y.F. Goh, S. Akbari, T.V. Khanh Vo, S.J.A. Koh, Electrically-induced actuation of acrylic based dielectric elastomers in excess of 500% strain, Soft Robot. (0) (2018) 1–10. L.J. Romasanta, M.A. Lopez-Manchado, R. Verdejo, Increasing the performance of dielectric elastomer actuators: a review from the materials perspective, Prog. Polym. Sci. (51) (2015) 188–211. P. Brochu, Q. Pei, Advances in dielectric elastomers for actuators and artificial muscles, Macromol. Rapid Commun. 31 (1) (2010) 10–36. B. Chen, Y. Bai, F. Xiang, J. Sun, Y.M. Chen, H. Wang, et al., Stretchable and Transparent Hydrogels as Soft Conductors for Dielectric Elastomer Actuators, (2014) 1055–60. L. Jiang, T. Betts, D. Kennedy, S. Jerrams, The fabrication of dielectric elastomers from silicone rubber and barium titanate : employing equibiaxial pre-Stretch to achieve large deformations, J. Mater. Sci. (2015) 0–14. A. Saini, D. Ahmad, K. Patra, Electromechanical Performance Analysis of inflated dielectric elastomer membrane for micro pump applications, Proc. SPIE 9798 (2016) 979813. F.A. Mohd Ghazali, C.K. Mah, A. AbuZaiter, P.S. Chee, M.S. Mohamed Ali, Soft dielectric elastomer actuator micropump, Sens. Actuators A Phys. 263 (2017) 276–284. R. Pelrine, R. Kornbluh, Q. Pei, J. Joseph, High-Speed electrically actuated elastomers with strain greater than 100%, Science 287 (5454) (2000) 836–839. M. Kollosche, J. Zhu, Z. Suo, G. Kofod, Complex interplay of nonlinear processes in dielectric elastomers, Phys. Rev. E - Stat. Nonlinear Soft Matter Phys. 85 (5) (2012) 2–5. A. Phys, Giant , voltage-actuated deformation of a dielectric elastomer under dead load, Appl. Phys. Lett. (2012) 041911. C. Keplinger, T. Li, R. Baumgartner, Z. Suo, S. Bauer, Harnessing snap-through instability in soft dielectrics to achieve giant voltage-triggered deformation, Soft Matter 8 (2) (2012) 285–288. G. Palmieri, M. Sasso, G. Chiappini, D. Amodio, Mullins effect characterization of elastomers by multi-axial cyclic tests and optical experimental methods, Mech. Mater. 41 (9) (2009) 1059–1067. T. Rey, G. Chagnon, J.B. Le Cam, D. Favier, Influence of the temperature on the mechanical behaviour of filled and unfilled silicone rubbers, Polym. Test. 32 (3) (2013) 492–501. Z. Wang, C. Xiang, X. Yao, P. Le, J. Mendez, Z. Suo, Stretchable materials of high toughness and low hysteresis, Proc. Natl. Acad. Sci. 1–6 (2019). C. Chen, Z. Wang, Z. Suo, Flaw sensitivity of highly stretchable materials, Extrem. Mech. Lett. 10 (2017) 50–57. R.K. Sahu, A. Saini, D. Ahmad, K. Patra, J. Szpunar, Estimation and validation of maxwell stress of planar dielectric elastomer actuators, J. Mech. Sci. Technol. 30 (1) (2016) 429–436. M. Pharr, J.Y. Sun, Z. Suo, Rupture of a highly stretchable acrylic dielectric elastomer, J. Appl. Phys. 111 (10) (2012) 104114. R. Kaltseis, C. Keplinger, S.J. Adrian Koh, R. Baumgartner, Y.F. Goh, W.H. Ng, et al., Natural rubber for sustainable high-power electrical energy generation, RSC Adv. 4 (53) (2014) 27905–27913. D. Ahmad, K. Patra, Fracture Behavior of Dielectric elastomer under pure shear loading, IOP Conf. Ser. Mater. Sci. Eng. 229 (1) (2017). L. Bernardi, E. Mazza, A.E. Ehret, The effect of clamping conditions on tearing energy estimation for highly stretchable materials, Eng. Fract. Mech. 188 (2018) 300–308. A. Schmidt, P. Rothemund, E. Mazza, Multiaxial deformation and failure of acrylic elastomer membranes, Sens. Actuators A Phys. 174 (1) (2012) 133–138. F. Caimmi, R. Calabrò, F. Briatico-Vangosa, C. Marano, M. Rink, Toughness of natural rubber compounds under biaxial loading, Eng. Fract. Mech. 149 (2015) 250–261. M. Claudia, R.R.M. Calabro, Effect of molecular orientation on the fracture behavior of carbon black-filled natural rubber compounds, J. Polym. Sci. B Polym. Phys. 48 (2007) 1509–1515. A. Helal, M. Doumit, R. Shaheen, Biaxial experimental and analytical characterization of a dielectric elastomer, Appl. Phys. A 124 (1) (2018) 2. dated on 17-7-2019 at 11:20am https://www.smooth-on.com. M. Wissler, E. Mazza, Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators, Sens. Actuators 134 (2007) 494–504. M. Hossain, D.K. Vu, P. Steinmann, Experimental study and numerical modelling of VHB 4910 polymer, Comput. Mater. Sci. 59 (2012) 65–74. Z. Liao, X. Yao, L. Zhang, M. Hossain, J. Wang, S. Zang, Temperature and strain rate dependent large tensile deformation and tensile failure behavior of transparent polyurethane at intermediate strain rates, Int. J. Impact Eng. (129) (2019) 152–167. Sahu SK, Javed A, Ahmad D, Patra K. Biaxial Planar Tensile Testing Device.India Patent: 201831040019 Published on 16-11-2018. L.R.G. Treloar, Trans. Faraday Soc. 40 (1944) 59–70. C. Galliot, R.H. Luchsinger, Uniaxial and biaxial mechanical properties of ETFE foils, Polym. Test. (30) (2011) 356–365. M. Hosain, P. Steinmann, More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study, J. Mech. Behav. Mater. 22 (1–2) (2013) 27–50. G. Kofod, The static actuation of dielectric elastomer actuators: how does prestretch improve actuation? J. Phys. D Appl. Phys. 41 (2008) 215405: 1-11. S. Rosset, L. Maffli, S. Houis, H.R. Shea, An instrument to obtain the correct biaxial hyperelastic parameters of silicones for accurate DEA modeling, Proc. SPIE 9056 (2014) 90560M.

Polymer Testing 79 (2019) 106038

D. Ahmad, et al.

[57] S. Lee, M. Pharr, Sideways and stable crack propagation in a silicone elastomer, Proc. Natl. Acad. Sci. 116 (19) (2019) 9251–9256. [58] T.L. Anderson, Fracture Mechanics-Fundamentals and Applications, Taylor & Francis, 2005. [59] B.H. Kim, C.R. Joe, Single specimen test method for determining fracture energy (Jc) of highly deformable materials, Eng. Fract. Mech. 32 (1) (1989) 155–161.

[55] C. Federico, D.D. Rossi, K. Roy, Ronald, P.S. Larsen, Dielectric elastomers as electromechanical transducers, J. Chem. Inf. Model. 53 (9) (2013) 1689–1699. [56] S.J.A. Koh, C. Keplinger, R. Kaltseis, C.C. Foo, R. Baumgartner, S. Bauer, Z. Suo, High-performance electromechanical transduction using laterally-constrained dielectric elastomers part I: actuation processes, J. Mech. Phys. Solids (105) (2017) 81–94.

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