IROS2019国际学术会议论文集 1849

Buckling induced Shape Morphing using Dielectric Elastomer Actuators Patterned with Spatially varying Electrodes Feifei Chen Member IEEE Kun Liu and Xiangyang Zhu Member IEEE Abstract Shape morphing is at the core of future re search which shows promise for wide applications ranging from reconfi gurable electronics to soft material robots In this paper we present a novel buckling induced mechanism for shape morphing using dielectric elastomer actuators DEAs by bonding the planar precursor structure s feet with the DEA With spatially varying electric fi elds applied the in plane deformation of the DEA generates compressive loads to trigger buckling of planar precursors into desired three dimensional confi gurations To enlarge the achievable motion range at the feet we develop a design optimization approach to the electrode arrangement which is concisely described by cosine functions By numerically optimizing the cosine function coeffi cients we obtain the optimal spatially varying electrodes for various precursors with different patterns of bonding sites The experimental results demonstrate the remarkable shape morphing from two dimensions to three dimensional confi gurations Our work paves the way to novel actuation mechanisms for shape morphing structures with advantages of rapid response and reversible controllability I INTRODUCTION Shape morphing structures at the core of future appli cations ranging from bio inspired functional materials 1 and origami 2 3 to reconfi gurable electronic devices 4 and soft material robots 5 6 have recently received broad and increasing interest A wide variety of engineering technologies have been developed to enable structures to morph in shape For instance programmable architectures can be achieved by shape changes of printable stimuli responsive polymers e g on immersion in water yielding complex three dimensional morphologies also referred to as four dimensional printing 7 Alternatively buckling has become a favorite avenue to shape morphing 8 typically from two dimensions 2D to three dimensions 3D partly because 2D fabrication technologies are more accessible and affordable From perspective of mechanics the key to inducing buckling is applying compressive loads to the structure of interest and existing actuating mechanisms are mainly based on mechanical compression 8 or shape memory polymers 9 The underlying mechanism is that a planar thin walled structure i e the precursor is bonded onto a prestretched substrate typically made of soft elastomeric fi lms and the structure will buckle into 3D confi gurations upon release of the substrate However mechanical compression usually This work was sponsored by Shanghai Sailing Program 19YF1422900 The authors are with State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong University and Robotics Institute School of Mechanical Engineering Shanghai Jiao Tong University Shanghai 200240 China email ffchen kianliu mexyzhu Corresponding author Feifei Chen Fig 1 A buckled thin walled structure driven by a dielectric elastomer actuator requires quite complex mechanisms like motors linkages etc resulting in bulky systems while shape memory poly mers are typically slow responsive These disadvantages have restricted the use of shape morphing structures in many applications especially those in which rapid response rate and convenient controllability are required Therefore a quick responsive and controllable actuation mechanism is in high demand The emerging soft material actuators in the past decade offer a new solution to enabling reconfi gurable structures Dielectric elastomers a classical type of soft electroactive polymers in response to electric fi elds have shown great promise in such applications due to their advantageous attributes such as large voltage induced deformation quick response and high energy density 10 12 The past decade has witnessed the embodiment of dielectric elastomer actua tors DEAs in many intelligent systems such as soft material machines and robots 13 16 In this paper we propose a novel buckling induced mech anism for shape morphing structures using DEAs as shown in Fig 1 The working principle is that the planar voltage induced deformation of dielectric elastomers provides com pressive loads to trigger buckling of attached precursors from 2D to 3D confi gurations To generate compressive loading at the predefi ned bonding sites requires the dielectric elastomer to undergo inward deformation at these feet Herein the spatial electrode arrangement plays a key role in determining the voltage induced deformation fi eld of the dielectric elastomer 17 18 We propose a design optimization approach to the elec trode arrangement in order to generate maximal compressive loads at the bonding sites The electrode pattern is geomet 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE8300 rically described by cosine functions whose coeffi cients are subject to numerical optimization To verify the effectiveness of the design approach we compare the optimized design with the intuitive design counterpart and it is found that regardless of the number of bonding sites the optimized designs always outperform With the optimized electrode arrangements the dielectric elastomer attains remarkably im proved actuation capabilities and we experimentally realized various buckling induced shape morphing structures Overall the proposed novel DEA based actuating mech anism performs well in driving shape morphing structures by compressive buckling and gains several advantages over existing actuation technologies such as rapid response rate up to 1 Hz and reversible controllability This actuation mechanism paves the way to novel reconfi gurable electronic devices and soft material robots II SYSTEM A Overview The system overview is shown in Fig 2 Initially a planar fl exible precursor structure made of plastics is bonded onto a piece of dielectric elastomer coated with spatially varying compliant electrodes The bonding sites serve as feet of the precursor and upon electric activation the dielectric elastomer will apply compressive loads to the precursor at its feet With the increase of the applied voltage the compressive load will cause the structure to buckle into 3D confi gurations In the following we will introduce in detail the components of the system B Dielectric Elastomers Dielectric elastomers are typically silicon or acrylic based polymers e g polydimethylsiloxane or the widely used Very High Bond VHB acrylic adhesive by 3M company 19 and they work as follows when an external electric fi eld is applied to a DEA due to coulombic attraction effects accumulation of opposite charges on the two sides of the membrane leads the elastomer to shrink in thickness and to expand in area 10 20 In their most basic form dielectric elastomers are planar membranes Prestretch of a dielectric elastomer is widely employed to elevate the breakdown strength 21 22 and to suppress their snap through instability 23 24 A dielectric elastomer is typically bi axially stretched prior to electric activation Based on our experimental experience in this work the prestretch is set to be 3 3 In a current state a high voltage is applied to activate the areas patterned with electrodes The principal stretches of any material point in the dielec tric elastomer are denoted by 1 2and 3 respectively in the Cartesian coordinates Using an ideal dielectric elastomer model as developed by Suo 20 the in plane stress stretch follows the relations 1 E2 1 Wstretch 1 2 3 1 1 2 E2 2 Wstretch 1 2 3 2 2 Fig 2 System overview where 1and 2denote the principal stresses respectively is the permittivity 4 10 11F m E denotes the electric fi eld and Wstretchis the free energy density of the elastomer as a function of the stretches in the absence of the electric fi eld In this work we employ the generalized Neo Hookean model 25 to characterize the hyperelasticity and incompressibility of DEAs Wstretch 2 I1 3 2 I3 1 2 3 where and denote the initial shear modulus and bulk modulus at small stretches respectively I1and I3denote the fi rst and third regulated strain invariants of the right Cauchy Green deformation tensor respectively taking the following form as follows I1 2 1 22 23 I2 3 3 I3 1 2 3 4 The material parameters in the hyperelastic Neo Hookean model are fi tted to be 45kPa and 2 35MPa based on mechanical tests C Precursor Structures To obtain a desired 3D confi guration it requires delicate design of the corresponding 2D precursor Xu et al proposed a systematic design algorithm for implementing the inverse design problem in which an initial guess of the precursor is provided and it is iteratively updated 8 In this paper we will focus on the actuation mechanism only and for proof of concept we will use symmetric 2D precursors to substantiate the buckling process 8301 III ELECTRODE DESIGN OPTIMIZATION In this section we will introduce the design optimiza tion of electrode arrangements in order to deliver the best actuation performance i e maximization of the inward de formation for generating compressive loads The electrode arrangements embody the profi le of the input spatial electric fi elds and critically determine the output displacement fi eld of the DEA in a highly nonlinear manner due to the geo metric and material nonlinearities and the electromechanical coupling effect A number of intuitive designs of SEFs have been reported for specifi c applications e g active shape control of infl ated DEAs 26 and a DEA based walking robot with multiple degrees of freedom DOFs 27 28 However the role of the spatially varying electrode pattern in shaping the deformed confi guration of DEAs has not been well understood or exploited A Geometric Model Suppose that the precursor is rotationally symmetric and it has a number of N bonding sites distributed along a circle of radius R as shown in Fig 3 The radius is set to be R 15 mm in this paper We devise a circular DEA of radius 2R after prestretch concentric to the precursor Analogous to the bonding sites the electrode patterns should also be rotationally symmetric As shown in Fig 3 the electrode arrangement is geometrically described by intersection of N cosine functions with the dielectric elastomer expressed by y h cos 2 T x 1 i 5 where x and y denote the Cartesian coordinates in Fig 3 is the amplitude of the cosine function and T is the period of the cosine function determined by the number of feet as follows T 8Rsin 2 6 with 2 N It is noted that the amplitude and period T fully deter mine the cosine function The cosine function as expressed in 5 always passes through the origin i e y 0 when x 0 The physical signifi cance is that the bonding site is the apex of the electrode area in order to induce the largest inward displacement therein upon electric activation The period T will be determined by the number of bonding sites i e T 8Rsin N while the amplitude is unknown and is subject to parametric optimization to improve the actuation performance We would like to emphasize that by modulating the amplitude in the cosine function which can be positive negative or zero a large range of electrode profi les can be obtained That is the geometric fl exibility of spatial electrodes is concisely embodied into one parameter of a cosine function which will greatly save the computational cost when carrying out the design optimization Fig 3 Schematic spatially varying electrode arrangements described by cosine functions Fig 4 History of electrode design optimization for N 2 at 6 kV B Optimization Algorithm The design optimization process is as follows 1 we vary the amplitude of the cosine function from 20 to 20 unit mm 2 for each cosine function the electrode arrange ment is generated and imported into Abaqus to create a corresponding spatially varying electric fi eld 3 using a user subroutine UMAT 29 we carry out nonlinear fi nite element analysis in Abaqus with hexagon dominated meshes to ob tain the current induced displacement fi eld Both geometric nonlinearity and material hyperelasticity are incorporated in the analysis and to ensure numerical stability we predefi ne the applied voltage to be 6 kV The steps above are repeated with a python script and fi nally we select the optimal cosine function that gives rise to the largest desired displacement at the bonding sites C Optimization Results Fig 4 shows the optimization history for N 2 It is observed that with the increase of the amplitude the induced displacement at the bonding sites denoted by ud increases gradually until reaching the peak at 12 mm 8302 Fig 5 Optimal electrode arrangements for N 2 3 4 8 and the corresponding voltage induced displacement magnitudes at 6 kV and then decreases when increases further Therefore the optimal solution 12 mm is selected for the fi nal design of the electrode arrangement for N 2 as depicted in the inset of Fig 4 We further obtain the optimal electrode patterns for N 3 4 8 as shown in Fig 5 Also plotted in Fig 5 are the deformed confi guration of dielectric elastomers subject to the optimized electrode pattern By comparing the optimization results for different numbers of bonding sites it is observed that the electrode module for a single bonding site or foot becomes more narrow with the increase of N For N 2 3 4 5 the electrodes are symmetrically distributed in accord with the bonding sites each part isolated When N 6 the neighbouring electrodes start to merge with each other and the electrodes at all the bonding sites form an integral part We may imagine that when the number of feet is ex tremely large i e N the optimal electrode arrangement should be an annulus as shown by the last column Fig 5 Very interestingly this optimal design for N agrees very well with our human intuition that it is able to generate inward deformation of the DEA at the circle where bonding sites reside regardless of the value of N The fact is that this intuitive design is optimal for N only but is non optimal for N of any other values As shown in Fig 6 for any N 2 8 the maximal induced inward displacements at the bonding sites each denoted by u are larger than the intuitive design counterpart As a matter of fact with the increase of N the optimal design will gradually converge to the intuitive design The dashed line in Fig 6 is an asymptotic line that bounds the minimum of the maximal induced displacement for any N Remark 1 At the whole design stage to ensure numerical stability during the optimization process the applied voltage is prescribed to be 6 kV In practice the DEA may sustain a large range of applied voltage and will undergo much larger deformation than what has been reported in this section as will be shown by the experiments in the following section Fig 6 Comparison of maximal displacements for different number of feet N 2 3 8 at 6 kV with the intuitive design counterpart plotted by the blue dashed line IV EXPERIMENT In this section we will employ the optimized spatially varying electrode arrangements to fabricate DEAs and exper imentally drive shape morphing of precursor structures from 2D to 3D confi gurations A Fabrication of DEAs We use VHB 4910 3M company for prototype of DEAs and the fabrication process is as follows i biaxially stretch a piece of VHB 4910 sheet by 3 3 with a custom built stretcher ii a stiff acrylic frame thickness 2mm fabricated by a laser cutting machine VLS3 50 SYS is utilized to take the prestretched dielectric elastomer membrane from the stretcher and maintain prestretch of the membrane iii according to the optimized electrode arrangements a release paper based mask is fabricated by the laser cutting machine and then attached onto both sides of the VHB iv coat the electrodes carbon grease with a paintbrush on both sides of the electrode area v remove the mask and connect the electrodes to the amplifi er with copper tapes 8303 Fig 7 An overview of the system setup B Setup The experimental setup is shown in Fig 7 The fabricated DEA is connected to the high voltage amplifi er 10 10B HS Trek Inc and is controlled by a dSPACE DS1103 control board equipped with digital to analog converters DACs The DACs are used to output analog ramping voltages that is amplifi ed by the high voltage amplifi er with a fi xed gain of 1000 The MATLAB Simulink software is used to implement the algorithms which are directly downloaded to the dSPACE DS1103 control board via the ControlDesk interface The 2D precursors are made of polypropylene The feet of the precursors are attached to the DEA while their bodies are smeared with silicone oil and thus are able to detach themselves from the DEA C Results As shown in Fig 8 four 2D precursors N 2 3 4 5 buckled into 3D confi gurations driven by DEAs patterned with optimized spatially varying electrodes We increase the applied voltage from 0 kV to 7 0 kV without encountering any material failures It is observed that as expected each precursor would start to buckle at a certain voltage which is defi ned as the critical buckling voltage Specifi cally the critical buckling voltages for the four structures are estimated to be 1 2 kV 3 1 kV 3 6 kV and 3 9 kV based on the supplemental video Upon switch off of the applied voltage the buckled structures quickly return to their original planar confi gurations The reader may refer to the supplemental video for the shape morphing processes The experimental observations also demonstrate the robustness of the opti mized designs over a large range of applied voltage The shape morphing process from 2D to 3D can be very quick In the experiments the applied voltage linearly ramps from 0 kV to 7 0 kV within 1 second and the DEA reacts very quickly to trigger buckling of the precursors though at some expense of the voltage induced deformation due to the viscoelasticity of DEAs 30 31 This fi nding validates the advantage of DEA based driving