A dielectric elastomer actuator coupled with water: snap-through instability and giant deformation Hareesh Godaba1, Choon Chiang Foo2, Zhi Qian Zhang2, Boo Cheong Khoo1, Jian Zhu1,a) 1 Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576 2 Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632 ABSTRACT A dielectric elastomer actuator is one class of soft actuators which can deform in response to voltage. Dielectric elastomer actuators coupled with liquid have recently been developed as soft pumps, soft lenses, Braille displays, etc. In this paper, we conduct experiments to investigate the performance of a dielectric elastomer actuator which is coupled with water. The membrane is subject to a constant water pressure, which is found to significantly affect the electromechanical behaviour of the membrane. When the pressure is small, the membrane suffers electrical breakdown before snap-through instability, and achieves a small voltage-induced deformation. When the pressure is higher to make the membrane near the verge of the instability, the membrane can achieve a giant voltage-induced deformation, with an area strain of 1165%. When the pressure is large, the membrane suffers pressure-induced snap-through instability and may collapse due to a large amount of liquid enclosed by the membrane. Theoretical analyses are conducted to interpret these experimental observations. Keywords: Dielectric elastomer, large deformation, electromechanical instability, soft pump a)
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1. INTRODUCTION Soft active materials have gained a lot of interest in the recent years following the demonstration of their importance in developing soft robots and devices. One particular class of soft active materials, dielectric elastomers, also known as ‘artificial muscles’, have been shown to take roles as actuators, generators and sensors. A dielectric elastomer actuator is a thin layer of an elastomer sandwiched between two compliant conductive layers. Electric voltage applied across the elastomer results in expansion of the membrane. Different from smart actuators such as piezoceramics, dielectric elastomers can exhibit linear strains greater than 100%1. Due to the high actuation strains in dielectric elastomer actuators, they have been applied to a myriad of applications such as legged robots, planar motors, bistable systems, ionic conductors, adaptive lenses, Braille displays, flexible controllers, soft pumps, etc2. The basic operation mechanism of dielectric elastomer actuator is as follows. When an electric field is applied across the elastomer layer, stresses are generated in the plane orthogonal to the thickness direction. These stresses are known as Maxwell stresses and cause the membrane to expand in response to voltage. Consequently the membrane undergoes a reduction in its thickness because of its incompressibility. For a given voltage, the stresses induced due to electric field are in equilibrium with the elastic restoring forces in the membrane. When the electric field increases over a certain threshold, the elastic restoring forces in the membrane are no longer able to balance the increase in Maxwell’s stresses induced by the positive feedback due to reduction in thickness of the membrane3. This phenomenon is known as electromechanical instability. Electromechanical instability may induce dielectric breakdown during the snap of the membrane. Electromechanical instability can be averted by prestretching the elastomer1, spraying charges4, employing an elastomer made of interpenetrating networks5, etc. But harnessing instabilities in dielectric elastomer has become a recent topic of interest as it enables us to achieve novel functions that are not otherwise possible 6. Keplinger et al. demonstrated large voltage-induced deformation of a dielectric elastomer membrane mounted on an air chamber by harnessing snap-through instability7,8. In their work, the membrane is placed at the verge of instability by setting the initial pressure and the loading path is designed by changing the volume of air chamber on which the membrane is
mounted. At certain volum me of the air chamber, the system exhibbits a pressurre volume currve that can ssafely undergoo ggered by a vooltage. snap-through evading dieleectric breakdoown, when trig C et al. deeveloped a peeristaltic pumpp Dielectric elaastomer actuattors have alsoo been used inn conjunction with fluids. Carpi using several modules of tu ubular dielectrric elastomer actuators9. Taavakol et al. used buckling of o thin elastom meric plates too i a microfluidic channel10. Several grou ups have developed lenses in i which dieleectric elastom mer membraness pump fluids in coupled with a transparentt fluid have been used to tu une the focal length11,12. Th he applicationn of dielectric elastomers too refreshable B Braille display ys, soft robots and soft pum mps warrant thhe need for a systematic sttudy of dielecctric elastomerr actuators couupled with fluuids13. In manny of the applications menttioned above, the performaance of dielecctric elastomerr actuator is limited by dielectric breakddown and larg ger actuation strains may greatly enhannce their perfformance. Wee investigated the t performan nce of a dieleectric elastom mer membranee bulged undeer constant prressure due too a fluid. Thee experiments and a theoreticaal analyses shhow that theree is an optimuum pressure att which the membrane m can undergo veryy large deformaation. Maximuum area strainn of 1165% haas been achievved under connstant pressuree after which the t membranee falls due to its own weight14.
2. EXPERIMENTA AL SETUP AND PROC CEDURE ut prestretchess on a tubularr A dielectric elastomer meembrane (3M VHB 4910) of thickness,, 1mm is mounted withou chamber of ccircular cross--section with diameter, d 3.955 cm. The meembrane is sm meared with carbon c grease which acts ass the electrodee. A pipe of internal diam meter, 2mm connects to a water reserrvoir of rectaangular crosss section withh dimensions 220.5 cm × 19 cm. c Water floows into the chhamber from the reservoir and the memb mbrane bulges in response too the pressure head of waterr in the reservvoir. Let the height of the bulged mem mbrane be h1 and a the heighht of the waterr i inhomogeneeous due to cuurvature of thee column in thee reservoir be h2. Generallyy, the pressuree on the bulgedd membrane is bulged membbrane. When h1
