A scalable and tunable haptic array based on dielectric elastomer actuators in a patch-like form factor

Abstract

A DEA-based haptic interface was developed using a novel mechanism to create out-of- plane deformation from an otherwise planar actuator. The mechanism relies on an electric field gradient that creates a disparity in induced strain between the topmost and bottommost layers. This buckles that actuator outward in a controlled manner. The actuators achieved displacements of over 0.5 mm and force outputs over 50 mN which is over the perception threshold for the fingertip and forearm. The applied stress that these actuators can generate are significantly higher than other DEA-based haptic interfaces reported in literature. By combining the ultra-low profile actuators with a BAP adhesive, the actuators can integrated into a patch-like form factor.

Description

[0001]A SCALABLE AND TUNABLE HAPTIC ARRAY BASED ON DIELECTRIC ELASTOMER ACTUATORS IN A PATCH-LIKE FORM FACTOR CROSS REFERENCE TO RELATED APPLICATIONS This application claims the benefit under 35 U.S.C. Section 119(e) of co- pending and commonly-assigned U.S. provisional patent application Serial No. 63 / 517,439, filed on August 3, 2023, by Qibing Pei, Roshan Plamthottam, and Yuxuan Guo, entitled “A SCALABLE AND TUNABLE HAPTIC ARRAY BASED ON DIELECTRIC ELASTOMER ACTUATORSIN A PATCH-LIKE FORM FACTOR,” Attorney Docket 30794.475USP1 (UC Ref.2023-203), which application is incorporated by reference herein. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT This invention was made with government support under EY030246 awarded by the National Institutes of Health. The government has certain rights in the invention. BACKGROUND OF THE INVENTION 1. Field of the Invention. The present invention relates to dielectric elastomer actuators and methods of making and using the same. 2. Description of Related Art With the advancement and accessibility of virtual reality (VR) technology increasing at a rapid rate, the need for a VR auxiliary equipment that further integrate the user into a virtual world is becoming increasingly important69,70. Of these equipment, haptic interfaces, often in the form of gloves, handheld controllers, and other physical props, are the most conducive to simulating real world phenomena in a virtual world70. Haptic interfaces are responsible for providing physical feedback to the user in response to their movement and interaction in a virtual world. Haptic interfaces are critical for the implementation of VR systems in various sectors such as healthcare, defense, entertainment, and waste management71–74. VR systems with haptic interfaces may allow for the use of highly immersive, simulated environments where users can be entertained or undergo training for complex medical procedures, dangerous security assignments, or highly sensitive waste management procedures. Broadly speaking, haptic feedback stimulates a user’s sense of touch to provide additional information about their virtual environment. It complements the auditory and visual stimuli that is presented via virtual reality headsets to create a immersive environment. Haptic feedback, can be divided into two categories: kinaesthetic feedback and tactile feedback75. Kinaesthetic feedback provides the user with information about the surroundings and how those surroundings react to the application of force. Tactile feedback, on the hand, provides users with information about their surroundings via changes on the surface of their skin especially on their fingertips and palms76. Generally speaking, kinaesthetic feedback assists users in detecting the presence and macroscopic details of objects, and resists the forces imparted by the musculoskeletal system of the user77. Tactile feedback provides texture and finer detailsabout objects. For example, if drinking a glass of ice water in a virtual environment, kinaesthetic feedback may replicate the weight of the water glass and the sloshing of the water while tactile feedback may simulate the smooth, cold surface of the glass. Kinaesthetic feedback and tactile feedback should operate in tandem to simulate real- world simulations and object interactions, and as mentioned previously, both should work in tandem with auditory and visual stimuli to simulate an immersive virtual world. The applied kinaesthetic and tactile feedback can be divided into categories of stimulation as well. Tactile feedback can be in the form of mechanical stimulation, thermal stimulation, electrical stimulation, or chemical stimulation while kinaesthetic feedback may manipulate body orientation, limb alignment, joint position, and physical forces on the user78. Mechanical stimulation, one of the more common mechanisms for tactile haptic feedback and the focus of the following study, can be implemented using vibrotactile generating elements such an eccentric rotating mass motors (ERM)79, piezoelectric actuators80, electromagnetic actuators81, electrostatic actuators82, and electrodynamic actuators83. While many of these technologies have shown promising results as a haptic stimulation technology, the devices themselves are often designed around the haptic technology resulting in suboptimal form factors that do not lend itself to immersive experiences in VR systems. Haptic interfaces can be incorporated into various form factors. Handheld props are currently available at the consumer level and have integrated haptic interfaces in the form vibro- tactile stimulation, such as the Meta Quest Touch Pro Controller, but their integration into VR systems is not ideal. Firstly, controllers must be continuously held thus preventing the user from freely using their hands to interact with virtual environments. Physical controllers also prevent an immersive experience for the user as they are often limited in haptic feedback capabilities aside from vibrotactile stimulation. Haptic gloves, on the other hand, not only allow users to control the VR system, but they can enable an immersive experience via force feedback and tactile feedback mechanisms77. Haptic gloves also have the added benefit of enabling hand tracking in virtual environments thus allowing for a user’s hand-eye coordination to be implemented in virtual environments77. However, they are often very bulk, heavy, and are somewhat clumsy to use. The bulky nature of these gloves are particularly concerning as it is difficult for users to be desensitized to its size and weight while in virtual environments resulting in discomfort during long term use84. Conformal haptic patches may mitigate these issues as the skin-like form factor ensures comfort for the user while reducing bulk, weight, and intrusiveness. Furthermore, patches allow the free use of a user’s limbs and fingers to interact with a virtual environment more naturally, and can also be incorporated onto other areas on the body such as the legs, chest, or back. The intrinsic flexibility and stretchability of dielectric elastomer actuators have enabled novel DEA-based haptic patches. Koo, et al developed a wearable fingertip tactile display comprised of an array of diaphragm DEAs85. Interestingly, an embossed PET layer was used to bias the actuation of each diaphragm into the user’s skin which provides a convenient means to ensure force output normal to the actuator surface. Each individual taxel was capable of producing 460 µm of vertical displacement and about 13.5 mN of force85. While these metrics may be perceptible for most individuals, it will not be felt by many with less sensitive fingertips and will not be felt if applied to other body parts. Furthermore, the PET layer not only increases the weight of the actuator system, it limits the strain and force output thus decreasing the systems efficiency. Ji, et al developed an ultrathin haptic feedback device using an 18 µm thick silicone actuator23. The incredibly low thickness of the three-layer actuator enabled the driving voltages to remain very low thus making safe for user’s to wear and operate directly on skin. Furthermore, the entire system was untethered allowing for free use of the user’s fingers and hands. While the system was very impressive in terms of form factor, a force output of 9 mN and a displacement of 6 µm leaves much to be desired23. Lee, at al developed a wearable haptic display for use on the forearm, which is less sensitive than the fingertip, using a clever and efficient indenting mechanism86. A multilayered DEA compresses a plastic indenter into the skin when in the off state, but when actuated, the indenter releases the pressure imparted onto the skin. Consequently, it can achieve approximately 2 mm of displacement and 180 mN of force output86. While the form factor is promising, the need for an indenter reduces the comfort of the devices, complicates device fabrication, and limits it’s a versatility in terms of the types of sensations it can produce. These patches are a very promising step toward DEA-based haptic interfaces, but many lack the force output and displacement requirements for universal application on a user’s body. Furthermore, they do not offer a convenient and comfortable application mechanism as many are strapped onto the users limbs, thus preventing conformal contact with the skin for efficient coupling. Lastly, the overall mass of the DEA system described previously are relatively high resulting in low specific force outputs and relative displacements. For haptic applications, specific force output and relative displacements are critical metrics as the overall mass of the interface will dictate the comfort, effectiveness, and versatility of the system. The design principles that must be considered when developing a DEA-based haptic patch are highly complex. Most critically, the force generated by the DEA must be able to be transferred into the user. Conventional actuator configurations such as planar DEAs or diaphragm DEAs make this especially challenging as there is a limited vertical component to the outputted force without an external bias. Other more complex actuator configurations, such as rolled actuators, do have large vertical force components, but often require significant volume53. This invariably causes problem for patch-like form factors. Second, the DEAs must be able to transfer a sufficient and perceptible force so that the user experiences touch feedback from visual and auditory stimuli in VR headsets. Force and displacement thresholds, the minimum amount required to be perceived, vary greatly among individuals and locations on the body87. Fingers generally have the lowest force and displacement thresholds due to the high density of mechanoreceptors. This results in a force threshold of approximately 0.8 mN and deformation threshold of 10 µm78. The palm is slightly less sensitive with a force threshold of 1.5 mN78. The forearm, which is even less sensitive, has a force threshold between 5 mN and 12 mN depending on the individual88. While DEAs in general are more than capable of generating sufficient force to exceed these thresholds, the volume, mass, and device complexity restrictions for practical implementations make a DEA-based haptic interface quite challenging. DEAs must output the required force / displacement over an area that is approximately the size of the 2-point-discrimination (2PD) threshold or less. The 2PD threshold is the minimum distance between two points that a person can distinguish between. The highly sensitive areas, such as the fingertips and palms, have a 2PD threshold of approximately 2-4 mm while the back, a less sensitive area, has a 2PD threshold of over 2 cm87. Actuators that are larger than the 2PD threshold will not have the spatial resolution to generate smooth haptic feedback. Textures may feel disjointed and unrealistic. Actuators must be less than or equal to the 2PD threshold in size to fully utilize the spatial resolution of human skin and ensure that perceptible, smooth feedback. What is needed, then, are improved DEA suitable for use as haptic devices. The present invention satisfies this need. SUMMARY OF THE INVENTION Embodiments of the inventive subject matter disclosed herein include, but are not limited to, the following examples. 1. An out-of-plane dielectric elastomer actuator (DEA), comprising: a plurality of elastomeric films comprising a plurality of defined thicknesses; wherein each of the elastomeric films include a first side and a second side; an electrode material layers deposited on the first side and / or the second side of each of the elastomeric films so as to form a plurality of the electrode material layers; and wherein the plurality of elastomeric films and the plurality of electrode material layers are assembled into a multilayer structure; and wherein the multilayer structure has a bottom side and a top side so that the thicknesses of the elastomeric films, and / or different binder layers attached to each of the films, generally increase and / or decrease going from the bottom side to the top side so as to form a thickness gradient, and such that when subjected to an applied electric field applied across the electrode material layers, the multilayer structure exhibits non-planar deformation. Embodiments of the present invention further include a haptic array with high force and displacement output in a patch-like form factor. The device uses an array of multilayer dielectric elastomer actuators (DEA) that deform out-of-plane in a hemisphere-like shape into the user. Each multilayer actuator has layers of varying thickness. The bottom most layer (bottom of hemisphere) is the thickest layer in the structure. The thickness of the layers gradually decreases so that the topmost layer (top of hemisphere) is the thinnest. This thickness gradient through the thickness of the actuator effectively creates an electric field gradient resulting in a lower strain at the bottommost layer and a higher strain at the topmost layer. This strain differential results in the actuator consistently deforming out-of-plane to accommodate this strain differential. More information about this mechanism can be found in the following sections. BRIEF DESCRIPTION OF THE DRAWINGS The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. Referring now to the drawings in which like reference numbers represent corresponding parts throughout: Fig.1. The internal architecture of the out-of-plane DEAs are shown in the diagram. The film thickness decreases towards the top surface of the actuator. Fig.2. The electric field along the Y-direction is shown. Throughout the thickness of the actuator, there is an electric field disparity at a given voltage resulting in differences in the actuation strain per layer. This results in out-of-plane deformation. Fig.3. A) A 4 mm diameter actuator with a thickness gradient is shown on left. The actuated state is on the right. Note the out-of-plane deformation that occurs. B) A 4 mm diameter actuator without a thickness is shown on the left. The actuated state is on the right indicating no out-of-plane deformation. Fig.4. Several electric field gradient profiles that can be applied to a 10-Layer actuator are shown. A bias layer is defined as a layer greater or equal to 45 µm in thickness while drive layers are defined as layers less than 45 µm. Fig.5. The resulting linear displacements from applying the electric field profiles in Fig.4 to 10-Layer actuators of varying diameters. The diameters simulated range between 1 mm and 3 mm. Note that increasing the number of drive layers increases displacement. Fig. 6. The fabrication process used to create a thickness gradient across a multilayer actuator is shown. Note that the order of lamination determines the resulting gradient. Fig.7. A fabricated batch of actuators is shown . Note that the versatility in the fabrication process enables actuators of various sizes and geometries. Over 100 actuators can be made in a single batch. Fig.8. An optical microscopy cross-section of the actuators is shown. The thickest layer is shown as the topmost layer. Note the thicker binder layer between the first two layers. Fig.9. A) Each individual actuator is assembled using two PET frames. Silver glue is used to interconnect the electrodes and adhere the leads. B) The assembled actuator is placed under a laser displacement sensor to measure the linear displacement of the actuator. Fig.10. Still images of the actuation of a 2 mm diameter actuator are shown at 2 kV, 2.5 kV, 3 kV, and 3.5 kV. Note the wrinkling that occurs at 3.5 kV Fig.11. A) The displacement normalized by the actuator radius is shown. The dimensions in the legend correspond to the actuator’s diameter. B) The linear displacement of actuators with varying radius as a function of driving voltage. Fig.12. The simulation linear displacement results as compared to experimental data. Note that the disparity between the simulation increases with increasing diameter. This is most likely due to effects of the CNT network losing conductive at higher displacements for larger diameters. This is not considered in the simulation. Fig.13. A sample data set from a frequency sweep is shown. The stroke is defined as the difference between the maximum and minimum displacements Fig. 14. The stroke normalized by the highest achieved actuation displacement at 3.5 kV 0.5 Hz is shown. Fig.15. The minimum displacement is also normalized by the maximum achieved displacement at 3.5 kV at 0.5 Hz. Fig.16. To characterize the force output of each actuator, the setup was used. Note that the gap, highlighted in red, was controlled using a precision z-stage. Fig.17. The force output of 5-Layer PHDE actuators with thickness gradients. Fig.18. A) The specific force output as a function of actuator diameter. Generally, smaller actuators tend be more efficient with regards to force output. B) A literature comparison is shown above comparing the applied stress and specific force output of various DEA-based haptic interfaces. Each DEA-based haptic interface included in this comparison utilizes a unique configuration and actuator geometry23,85,86. Fig.19. A) An assembled array is shown above with silver glue contacts. B) To interconnect the multilayers, a via was created and filled with silver glue as shown above. These vias were located between cutouts for the active areas. C) An exploded CAD view of the array structure. Note the geometry of the silver glue leads are designed to avoid overlap with the active areas. Fig.20. A PHDE haptic interface adhered to a hand with a BAP film. The circuitry needed for operation is not included for demonstration purposes. Fig.21 is a table illustrating example elastomer materials that can be used (taken from [5]). Fig.22. Working principle of the TVMDE. (A) Schematic illustration of how TVMDE, a skin-integrated soft actuator with out-of-plane actuation, enables effective tactile perception. When turned on, TVMDE deforms and indents the skin, stimulating multiple mechanosensory organs within the dermis, such as Meissner corpuscles, Merkel cells, and Pacinian corpuscles. These organs then send the haptic stimuli to the brain to complete the tactile perception process. (B) Schematic of a TVMDE design consisting of 3 layers of DE with gradually decreasing thicknesses. At a given voltage, thinner layers experience higher electric fields, resulting in a gradient actuation strain that ultimately leads to out-of-plane actuation. (C) Side-view images of a 10-layer TVMDE at rest (left) and during actuation at 3 kV (right). The scales bars are 5 mm. Fig. 23. Performance of the 10-layer TVMDE. Results with error bars indicate the average results ± standard deviation for 3 samples. (A) Displacement vs. voltage curve of samples with specified actuator diameter. (B) Force output vs. voltage curve. (C) Maximum displacement and force output vs. actuator diameter at 3.5 kV. Solid and dash lines represent experimental and simulated results, respectively. (D) Bar graph of the displacement to diameter ratio (DDR) and specific force output of the actuators vs. diameter. (E) Measured stroke length (difference between maximum and minimum displacement in each cycle) of a 4-mm TVMDE actuator operated for over 200,000 cycles under a 20-Hz, 3.5-kV square wave voltage. (F) Frequency response data of the 10-layer, 4-mm TVMDE actuators at 3.5 kV. Fig.24. Integration of HAMS. (A) Schematic illustration of the exploded view of a 3- by-3 HAMS. (B) Detailed schematic of an actuator element showing the VIA connection. (C) HAMS underwent severe deformation when attached to skin, showing robust adhesion and high stretchability. (D) Photographs of a HAMS programed to show patterns of “U”, “C”, “L”, and “A”. Fig. 25. Perception validation of HAMS. (A) Confusion matrix for the intensity test. Subjects were asked to identify the intensity of the actuation they received. (B) Confusion matrix for the frequency test. Subjects were asked to identify the frequency of the actuation they received. (C) Confusion matrix for the pattern test. Subjects were given actuation stimuli with 9 sets of patterns. Pattern 1 to 9 correspond to right, left, down, up, diagonal down, diagonal up, radial ripple, counter-clockwise rotation, and clockwise rotation, respectively. Fig.26. XR demonstrations enabled by HAMS. (A) Photo of the user wearing HAMS and HMD for immersive XR experience. The HMD is connected to the PC via USB, and the HAMS is wired to the HVPS. (B) Experiencing Rain. The top two images show screenshots of the rain scene during “light rain,” and “heavy rain” conditions. Actuators received lower voltage inputs at lower frequencies to simulate light rain and higher voltage signals at higher frequencies to simulate heavy rain. (C) Real-time voltage across the 9 actuators within HAMS when the weather went from light rain to heavy rain. (D) Demonstration of virtual object manipulation. The figure set depicts the incident when the user rolled a golf ball from (i) the top-left corner to (ii) bottom left corner, then to (iii) the bottom right corner in the palm. The left three figures show the virtual scene seen by the user, while the right figures display the heat maps of the actuators’ force output. Color bar is shown at the bottom. Fig.27. Fabrication of the TVMDE. (A) Schematic of the fabrication process. (B) Cross section view of the first stacking step showing how the added thickness was formed. (C) Schematic of the cross-section of a 10-layer TVMDE showing the parallel connection between layers. Fig.28. Swelling test in THF solution to verify interlayer adhesion. The photo set on the left is a stack of 1040-µm PHDE films without binder, and the photo set on the right is the 10-layer TVMDE. The PHDE stack without binder quickly delaminated in the solution, while the 10-layer TVMDE with binders maintained strong interlayer adhesion and behaved like a single film after 24 hours of soaking. Fig.29. The scalable stacking process enables the fabrication of TVMDE with different array size and dimension across a large area. The scale bar in the right figure is 2 cm. Fig.30. SEM image of the cross section of a 10-layer TVDES showing seamless integration between the precursor and the pre-formed DE layers. The scale bar is 100 µm. Fig.31. FEA of the TVMDE. (A) Material stress-stretch curve fitting for simulating TVMDE. (B) Setup to simulate (i) deformation and (ii) force output. (C) Simulated displacement output of a 4-mm, 10-layer TVMDE under 0 V at the top and 3 kV at the bottom. Fig.32. Experimental setup to measure the output of TVMDEs. (A) Displacement measurement setup. (B) Force output measurement setup. The inset shows the side-view near the probe and the sample. Fig.33. Comparison of experimental and simulated performance for 10-layer TVMDEs with diameter of 3-, 4-, 5-, 6-, and 7-mm. Solid and dash lines represent experimental and simulated results, respectively. The top 5 plots are displacement data, and the bottom 5 plots are force data. Each experimental result is the average of 3 TVMDE samples. Fig.34. Comparison of performance between TVMDE and other buckling actuators in literature. Force per unit area was calculated by dividing the actuators’ force output by their active (electrode) areas. DDR was calculated by dividing their vertical displacement by their active diameters. Fig.35. Lifetime data of the 4-mm TVMDE. A. Cyclic lifetime data. Displacement output profile of a 4-mm TVMDE during the cyclic test between 50,000thand 150,000thcycle. B. Storage lifetime data under an ambient environment. Displacement output at 3.5 kV for 4- mm TVMDEs that were stored for different amount of time. Results were the average of 3 samples with error bars being ± standard deviation. Samples with different storage time were made from different batches. C. Storage lifetime data under a humid environment. Displacement output at 3.5 kV for 4-mm TVMDEs that were immersed in water for different amount of time. Results were the average of 3 samples with error bars being ± standard deviation. Fig.36. Dynamic performance of a 4-mm TVMDE. As measured displacement (A) and force (B) profile under a 3-kV square wave voltage at 2 Hz. (C) Additional displacement output vs frequency at 3.5 kV. Fig.37. Diagram of the assembly process of HAMS with a 3x3 array. Fig.38. Array dimension and electrical path design for the 3-by-3 HAMS. Fig.39. Connecting HAMS to external circuit using a custom-made FFC. (A) Photograph showing the connection from HAMS to circuit. (B) Schematic illustration of the connection between FFC and the pin headers. (C) Cross-sectional view of the connection between the FFC and HAMS. Fig.40. Mechanical properties of the skin adhesive polymer film. (A) Storage modulus vs. temperature curve. (B) Stress strain curve at 35°C. The film is not tested until mechanical failure. Fig.41. Photographs of HAMS under different mechanical manipulations. (A) HAMS was wrapped around a rod. (B) HAMS was under uniaxial stretching. Fig.42. Other design of HAMS. (A) A HAMS with 2x2, 5-layer TVMDEs of 2.5 mm active diameter can fit on a fingertip. (B) Thickness arrangement of the 5-layer TVMDE in the fingertip HAMS. The black layers are SWNT electrodes. (C) Displacement vs. voltage curve of the 5-layer TVMDEs with specified actuator diameter. (D) Force vs. voltage curve of the 5-layer TVMDE. Fig.43. Block diagram of the 9-channel HVPS for individual addressing of actuators within HAMS. Fig.44. Electrical characterization of a 10-layer, 4-mm TVMDE. (A) Equivalent circuit diagram of the shunt resistor method to measure current in the TVMDE actuator. (B) The blue curve represents the maximum current occurred during actuation of the TVMDE at different actuation voltage. The red shows the average power consumption during actuation at different actuation voltage. Fig.45. Additional current data of a 10-layer, 4-mm TVMDE. Red curves represent the current level in the TVMDE during a 1-Hz actuation cycle. Each blue curve shows the voltage across to the TVMDE during a 1-Hz actuation cycle. Fig.46. Power consumption to charge and maintain actuation for a 10-layer, 4-mm TVMDE. Each plot shows the instantaneous power consumption to actuate the TVMDE under different DC voltages. The power consumption during discharging state is not plotted. Fig.47. Voltage output data for the control circuit. (A) Voltage output at 0.5 Hz with different duty cycles. Each channel’s output voltage can be tuned by adjusting the duty cycle of the PWM signals. The red number labels correspond to the duty cycle in percentage. (B) Voltage output at different frequencies at 80% duty cycle. By switching the on and off time of the optocouplers, each channel’s output frequency can be varied. Fig.48.9 different patterns used in the perception test. All patterns have the same frequency and number of steps to avoid “guessing” by the subjects due to variation in the actuation rhythm. Fig.49. Overall correct identification rate for three perception tests. Fig.50. Table S1. DETAILED DESCRIPTION OF THE INVENTION In the following description of the preferred embodiment, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration a specific embodiment in which the invention may be practiced. It is to be understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. Technical Description Virtual reality and augmented reality (VR / AR) technologies have advanced at a rapid pace of the past several years. They can sufficiently provide realistic visual stimuli so that users can experience a visually immersive environment. However, to create a truly immersive environment, other forms of stimulation must be incorporated into VR systems. Haptic devices can be used to provide tactile feedback to replicate the presence, texture, and / or impact of an object, but advances in haptics have not kept up with the steep pace of VR / AR development. Conventional haptic devices often use vibrotactile actuators, microfluidic / pneaumatic actuators, and other actuator technologies that are limited in force and displacement output or require extensive auxiliary equipment (pumps, compressors, tubing, reservoirs, etc) leading to bulky form factors. This is particularly a concern because haptic devices are generally wearable, and must be comfortable / compact to ensure long durations of use without disrupting the immersive nature of the virtual environment. Dielectric elastomer actuator (DEAs) provide a potential solution to many of the issues current haptic devices face. DEAs are essentially a deformable capacitor with a highly stretchable and high dielectric constant elastomer sandwiched between two compliant electrodes. When an electric field is applied to the electrodes, the electrostatic interaction between them compresses the film in thickness and expands it in area. DEAs are a promising actuator technology for haptic devices due to their high energy density, inherent flexibility, high force output, large stroke lengths, light weight, and silent operation. A DEA-based haptic interface in a patch-like form factor To fabricate this device, a processable, high performance dielectric elastomer (PHDE) and a novel multilayering process was used. More information about this material and multilayering process can be found in reference 1 [1]. The multilayering process was slightly modified to create the multilayer structure with a thickness gradient. The thickness of each layer was controlled via the application of the binder layer [1]. That is, a higher concentration or larger volume of deposited binder layer increases the thickness the layer of the laminated layer. The haptic devices have been demonstrated with actuator sizes between 1 mm and 7 mm, although actuators of other sizes can also be developed. The overall thickness of the active films range between 200 microns to 450 microns with the entire haptic patch have a thickness of less than < 1 mm. The actuators can output a range of forces between 5 mN and over 400 mN by tuning the driving voltage, frequency, and geometry of the actuator. Displacement can also be controlled using the same parameters and range between <100 microns to over 1.5 mm. The actuators also respond well at high frequencies exceeding 25 Hz with limited displacement degradation. The actuator can also be patterned into actuator arrays to ensure wide coverage tactile stimulation. To ensure conformal contact with skin and secure placement, a bistable adhesive polymer BAP [2] was adhered to the actuator array with the same binder solution[1]. The BAP film enables conformal contact with skin, provides insulation from the voltage used to drive the actuator, and secures placement of the patch. The BAP film also enables adheres when body temperature is applied and can be debonded once cooled to room temperature (can be achieved using water / ice pack). More details including images and diagrams can be found in the following sections. First Example Preparation of PHDE Multilayer Actuators The PHDE prepolymer solution was blade coated using a 0.003” gap onto 4” by 5” glass substrates at a speed of 1 in / s. The films were then cured in an inert environment with a 2.5 W / cm2Fusion 300s curing system. The same casting and curing method was carried out for PHDE films on PET substrates. After the films were cured, a contact mask was adhered to the film and CNTs were deposited onto the PHDE / Glass films. The masks were then removed, and 10 mL of a 1 wt% PHDE in acetone was spray deposited onto films designed to have a 41 µm thickness. For films requiring a 45 µm and 50 µm thickness, 5 mL and 10 mL of a 10 wt% PHDE in acetone solution was deposited, respectively. The PHDE / glass films were then sequentially laminated onto the PHDE / PET film, cured, and peeled off. After each peeling step, a new layer was added to the PHDE / PET film. To create the desired thickness gradient in the sample, the PHDE / Glass films was laminated so that the thicker binding layers are laminated first. After all PHDE / Glass films were laminated, the PHDE stack was peeled off the PET substrate. Contact masks were applied to the top and bottom surface of the stack, and CNT electrodes were spray deposited. First Example Assembly of PHDE DEAs Individual actuators were cut from the stack using a razor blade and placed onto a PET frame backed with adhesive. The center of the bottom frame had holes that were 0.15 mm larger than the active area of the actuator. The center of the top frame had holes that were 0.25 mm large than the diameter. The ends of the actuator leads were cut off to expose the inner CNT layers. Silver glue was then smeared onto the edges of the actuator to ensure all CNT layers are connected appropriately. Tinned Cu wire was then used to make electrical contact with the actuators. Second Example: Characterization of the devices fabricated according to the first example 1. Actuation Displacement Measurement To measure the linear displacement of individual actuators, the assembled actuators were placed under a laser displacement sensor (Micro-Epsilon ILD1420). The thick side of the actuator was placed downward away from the sensor to ensure the actuation moves toward the sensor. A small dot of carbon grease was placed in the center of the active area to ensure the laser displacement sensor tracks the appropriate surface. Actuators were then driven at high voltage starting at 0.5 kV and 0.5 Hz for three cycles before increasing the driving voltage in 0.25 kV increments up to 3.5 kV. At 2 kV, 2.5 kV, 3 kV, and 3.5 kV frequency sweeps were conducted at 1 HZ, 5 Hz, 10 Hz, 15 Hz, 20 Hz, and 25 Hz. 2. Force Output Measurement To measure the force output of the actuator, the actuator’s were placed with their thick layers downward on to a precision z-axis stage below a Mark-10 force gauge. The z-axis stage enables the gap between the actuator and the force gauge to be precisely controlled. The actuator was then driven at 0.25 Hz from 2 kV to 3.5 kV, and the force registered by the force gauge was recorded. Third Example: Lamination of BAP to PHDE Multilayer Actuators The BAP films were fabricated by injecting BAP prepolymer in between two glass slides coated with RainX. Spacers of 150 μm were used to ensure the film was sufficiently thick and uniform. The resulting film was then cured under UV light. The BAP film was then removed from the glass and adhered to the PHDE multilayer stack so that the two materials were seamlessly bonded. The PHDE actuators were sprayed with 1 mL of 1 wt% PHDE in acetone. The BAP was then laminated onto the PHDE using the same conditions as that during the stacked actuator fabrication. Fourth Example: DEA Haptic Patch Design and Modeling A DEA-based haptic interface should be capable of generating and transferring a perceptible force and displacement onto the user in a light-weight, compact, practical form factor. The device described below is designed to do accomplish these requirements and the resulting study describes its overall efficacy. To generate large forces and displacement, exemplary embodiments of the out-of-plane haptic actuators may rely on the high actuation performance of PHDE. This not only allows the actuator to generate the necessary forces, it limits the complexity of the overall device as a rigid frame is not needed to maintain a pre- stretch. Using a multilayering process, the haptic actuators can be comprised of several layers depending on the location the device will be used. For example, a five- layer actuator can be used for highly sensitive areas, such as on fingers, while a 10- layer actuator may be used on less sensitive areas such as the back. The actuator geometry and diameter will be tailored to the 2PD threshold of the region of interest and will be arranged in array-like structure to ensure adequate coverage across the skin. To transfer a perceptible force and displacement into the user, diaphragm actuators may be used. However, instead of a traditional external biasing method, such as pneumatic pressure or passive stiff layer, a device according to embodiments described herein utilizes an innovative and efficient method to bias the actuation strain. The structure in Figure 1 depicts the internal architecture of the DEA. The architecture of the multilayer actuator will include layer of varying thicknesses oriented in a gradient-like arrangement. When actuated, this creates an electric field gradient along the thickness direction of the actuator as shown in Figure 2. At a given voltage, the thin layers will experience a higher electric field than the thick layers and will result in different actuation strains, resulting in the actuator buckling out of plane and transferring force vertically without inactive material or inefficient pneumatic mechanism. The electric field gradient that is created also limits any intense stress concentrations that may occur with other biasing means, such as passive layers, as the incremental change in strain between each layer is relatively small. By simply varying the thickness of each layer, not only do we create a vertical force component, but we eliminate the need for indenters and other perception aids that increase the overall device volume and fabrication complexity. This enables the use of a patch form factor that is more convenient, comfortable, and versatile than the other previously discussed alternatives. The electric field gradient in a multilayer can be modeled COMSOL to show the vertical displacement that it enables. In Figure 3, two initial geometries are shown. Figure 3a depicts the cross-section of a 4 mm diameter, 5 layer PHDE actuator with film thicknesses of 50 µm, 45 µm, 41 µm, 41 µm, and 40 µm from bottom to top. The 45 µm layer decreases the shear deformation experienced at the boundaries of each layer and is used as a buffer between the thick (50 µm) layers and thin (41 / 40 µm) layers. When actuated at 3000V, the film area expands upward (thickest layer on bottom) in a diaphragm-like shape. This occurs because the electric field on the bottommost layer is slightly lower than the subsequent layer (Figure 2), resulting in a small strain and a buckling motion that generates out of plane deformation. The center of the displacement in Figure 3 shows the actuator achieves a displacement of approximately 1.14 mm vertically. Figure 3b shows a similar 5-layer actuator with 40 µm layers. When actuated at 3000 V, the highest field in the previous example, the actuator behaves similar to a highly-constrained planar actuator and deforms strictly in-plane with no observable out-of-plane deformation. While the model accurately depicts the buckling phenomenon, the 5-layer actuator with equal layer thicknesses will most likely wrinkle in practice due to defects and localized stress concentrations. Overall, the thickness gradient clearly allows for substantial out-of-plane deformations from an actuator configuration that traditionally operates strictly in plane. Haptic applications require perceptible displacements to be applied to the user, and by tuning the electric field gradient, it is possible to optimize the vertical displacement component of the actuator. Figure 4 shows various electric gradients that can be applied to a ten layer actuator with the previously described strategy. A 10- layer actuator was chosen, as opposed to a 5-layer actuator, to effectively give the model a higher resolution when studying the changes in the gradient. When these gradients are applied to actuators of varying diameter (Figure 4-5), it is clear that the vertical displacement is dictated by a number of variables. First, the ratio of bias layers (B) to drive layer (D) dictates the maximum displacement an actuator of a given size can produce. More bias layers result in a lower average field across the actuator thus resulting in lower displacement. More drive layers will result in the opposite as the average field will be slightly higher. However it is important to note that this does not necessarily mean more drive layers result in higher force output. Force output is dictated by a number of factors and will be described later in this chapter. Second, actuator diameter strongly dictates the displacement magnitude. A large diameter will result in a larger displacement at maximum field. This is expected, but more interestingly, the field required to achieve observable deformation changes. That is, at smaller diameter, or lower aspects ratios, the field required to achieve observable displacements is higher. This is most likely due to increase in energy required to buckle the actuator out-of-plane. While this may consume more energy, it is possible that this may result in a more robust diaphragm actuator that resists collapse. Lower aspect ratio actuator may buckle out-of-plane with greater force and consequently be capable of resisting high applied forces such as when actuating against skin. To create a DEA-based haptic interface patch, the array of PHDE actuators will be laminated onto a bistable adhesive polymer (BAP) that has proven to be a highly versatile adhesive for wearable electronics89. With a melting temperature of around body temperature, BAP exhibits a steep modulus change around ~32°C from over 30 MPa to 0.03 MPa. This enables BAP to conformal bond to skin at body temperature but can be removed seamlessly from skin with the application of cool water. In addition, the BAP will act as an insulation layer to protect the user from high voltage. The low modulus of the BAP film in the heated state will prevent excessive losses of actuation force and strain to the deformation of the BAP film. Limited energy will be wasted deforming BAP on the actuator surface due to its low modulus. Furthermore, the use of an biocompatible adhesive, as opposed to straps, enables the haptic interface to applied to a wide range of areas on a user’s body. The same patch can be applied to a palm or back with altering the patch in any way. Straps or other means for securing a haptic device will have to tailored to the location on the user’s body. Fifth Example : Scalable Fabrication Process Scalability is an important aspect of any device manufacturing process as it dictates whether technology can be practically implemented in real-life applications. The fabrication process for the PHDE haptic interface is shown in Figure 6. Four 40 μm PHDE films were cast onto glass substrates (PHDE / Glass) and one PHDE film was cast onto PET (PHDE / PET). The PHDE / Glass films underwent two spray- deposition processes: a patterned CNT deposition process through a contact mask and a binder layer deposition process without a contact mask. To obtain the desired thickness gradient shown in Figure 2, PHDE / Glass was coated with either a 1 μm, 5 μm, or a 10 μm binder layer to create a 41 μm, 45 μm, or 50 μm films, respectively. These PHDE / Glass films with binder were then stacked according to Figure 6 resulting in a 5-layer actuator. Outer electrodes were deposited after the stacking process. To create a tunable electric field gradient within the actuator, controlled amounts of binder material is deposited onto PHDE / Glass films to vary the thickness layer by layer. In one example, the green layer is the binder layer 601a having a 10 micron thickness and after curing, the binder layer 601b is cured into so the total thickness 40+10 microns. The resulting multilayering process is highly scalable with actuators yields exceeding 90%. As further evidence of its scalability, Figure 7 shows a fabricated 5- layer sample with over 100 fabricated actuators. The geometry can also be tailored to the application as arrays can be fabricated simultaneously with individual actuators. The inset figure in Figure 7 shows the precision alignment that was achieved with 1 mm actuators. Figure 4-8 shows an optical microscopy cross-section of the fabricated actuators. The binding layer was clearly distinct from the blade-coated PHDE films and remained uniform despite the additional thickness. Furthermore, the thickness gradient is clearly observed as the thinner binding layers (1 µm) were more difficult to distinguish than the 5 µm and 10 µm binding layers. Furthermore, the layers were well laminated and cured to form a single membrane. No bubbles, delamination, or non- uniformities in the binding layers were observed, but foreign particles (dust, debris, etc.) is visible in some parts of the sample. This is most likely the result of carrying out processing steps outside a cleanroom environment. Sixth Example: Linear Displacement Characterization The actuation performance of individual actuators of 1.5 mm, 2 mm , 2.5 mm, 3 mm, and 3.5 mm diameters were characterized. Actuators were assembled as shown in Figure 9a, and tested using the setup shown in Figure 9b. To assess their actuation strain, actuators were driven at voltages between 0.5 kV and 3.5 kV at 0.5 Hz. Figure 10 shows still images of a 2 mm actuator under a variety of driving voltages. Observable out-of-plane strain can be generated at voltages as low as 1.5 kV, and with increasing driving voltage, the linear displacement increases dramatically. Figure 11a shows the performance of the haptic actuators under a voltage sweep from 1.5 kV to 3.5 kV. A larger diameter results in a higher linear displacement. However, it is important to note that as the actuator diameter increases, the aspect ratio (the ratio of the thickness relative to the diameter) also increases. The higher aspect ratio actuators did not achieve an relatively higher displacement at voltages greater than 2.5 kV (Figure 37b). At 3.5 kV, the 1.5 mm diameter actuators achieved 0.4 mm displacement while the 3.5 mm actuators had achieved 0.74 mm displacement. However, relative to their radius, the 1.5 mm actuators had a relative displacement of 0.54 compared to only 0.42 for the 3.5 mm actuators. The 2 mm actuators, interestingly, had the highest relative displacement at 0.57 despite achieving only the fourth highest displacement at 0.57 mm. The 2.5 mm and 3 mm actuators achieved displacements of 0.63 mm and 0.72 mm, and relative displacements of 0.51 and 0.48, respectively. While larger diameter actuators are capable of higher linear displacements, they are not necessarily geometrically efficient. Furthermore, large actuators reduce the resolution of haptic interfaces, are more prone to defects, and require significantly more material to produce. Based on these results and considerations, actuators between 2 mm and 2.5 mm are more suitable for haptic interfaces. The results of the displacement characterization are also compared to the results of the simulation in Figure 12. The larger diameter actuators clearly diverge from the simulation results. This is most likely due to the face that the larger diameter actuators cannot maintain sufficient conductivity to ensure efficient actuation. This is not an issue for the smaller actuators as the resistance across the active area is relatively low compared to the larger actuators. The simulation also does not consider this effect and does not incorporate the stiffness of CNTs. While displacement is important to induce perception, it is not the only metric of interest. Frequency-response and force output are also critical for a functioning haptic interface. Seventh Example: Frequency Response Actuators of various sizes were driven with a square wave at 1 Hz to 25 Hz in 5 Hz increments, and their static and dynamic displacement was characterized. The minimum displacement is defined as the minimum displacement sustained throughout the test (Figure 13) while the stroke displacement is defined as the difference between the minimum and maximum displacements. The minimum displacement at 2 kV, 2.5 kV, 3.0 kV, and 3.5 kV is shown in Figure 15. The static displacement increases with increasing driving voltage and increasing diameter. However, it is important note the limited disparity between the 3.0 mm and 3.5 mm actuators as their displacements are very similar despite their different sizes. This results can be attributed to their high aspect ratio. The dynamic strain, shown in Figure 4-14, shows a similar trend. The larger actuator are able to achieve larger strokes, but the 3 mm and 3.5 mm actuators have strikingly similar strokes despite their dissimilar sizes. The results in Figure 14 and Figure 15 are both normalized by the highest achieved strain at 3.5 kV 0.5 Hz. Overall, the excellent frequency response of the actuators may enable more versatility in haptic applications. Eighth Example: Force Output Characterization Displacement characterization alone is insufficient when determining the capability of tactile actuators as force output is just as, if not more, critical for haptic interfaces. To test the force output of the actuators, a single actuator was placed under a force gauge as shown in Figure 16. A small gap, controlled by a precision z-stage, was introduced to allow the actuator to buckle out-of-plane. The force output of various sized actuators are shown in Figure 17. The 1.5 mm, 2 mm, 2.5 mm, 3 mm, and 3.5 mm diameter actuators achieved a force output of 32.6 mN, 51 mN, 81.6 mN, 77.4 mN, and 61.9 mN, respectively at 3.5 kV. It is important that all actuator sizes far exceed the perceptible force threshold of the finertip, palm, and forearm78,88. Furthermore, the specific force output (Figure 18) of the 1.5 mm and 2.5 mm actuators (71 N / g and 64 N / g, respectively) meet or exceed the specific force output of other PHDE actuators27. The maximum force output and maximum displacement of each actuator size at 3.5 kV is compared in Figure 18a. It is clear that actuator geometry influences these performance metrics most likely due to the varying aspect ratios. The 2.5 mm actuator seems to have the most optimal balance between force and displacement especially when considering their stability. The larger actuator sizes are more prone to defects during manufacturing, reducing their yield. Figure 18b compares this actuator to others cited in literature. The applied stress and the specific force output of various DEA-based haptic interfaces found in literature are plotted23,85,86. Our work here has the highest applied stress relative to the cited studies and the second highest specific force output. This demonstrates that this actuator configuration not only ensures a high applied stress for haptic applications, but it does so in an efficient form factor enabling a high specific force output. Ninth Example: Array Fabrication After characterizing individual actuators and determining their performance capabilities, an array was fabricated with the geometry and architecture described in Figure 19. The 3X3 actuator array has individually addressable actuators that can be activated as needed. A PET frame was used to support the actuators and provide a surface to place electrical contacts for the control circuitry. To make electrical contact with each of the five layer in a compact fashion, vias were created from the bottom top layer of the actuator array through the PET frame. Silver glue was used to fill the vias and make conductive patterning on the top surface of the PET. The high voltage source was then connected to contacts on the PET frame. Prior to assembly of the actuator array, a 150 µm BAP film was cast, cured, and laminated onto the PHDE actuator array. To ensure adequate adhesion between the BAP films and the actuator array, 2 mL of the 1 wt% PHDE binder was sprayed onto the array prior to lamination prior to curing. This ensures that the BAP film and PHDE array conform to each other and the user’s skin when the BAP is in the heated state and helps prevent delamination during actuation. In one or more examples, the BAP film is critical for integrating the PHDE array into patch-like form factor. The completed array with a BAP film is shown on a glove in figure 4-20. The circuitry was not included for demonstration purposes. Process Steps Fig.6 illustrates a method ofmaking a DEA. Step 1 represents depositing n-1 elastomeric films (e.g., PHDE) on a smooth substrate (e.g., glass) from which the films can be peeled. Step 2 represents depositing (e.g., casting) an elastomeric film (e.g.,PHDE) on any stiff but flexible material (e.g., PET) Step 3 represents depositing an electrode layer (e.g., CNT) on the elastomeric films on the substrate. Step 4 represents depositing a binder on the electrode layer. Step 5 represents attaching the elastomeric film (on the stiff but flexible material) to the binder. Step 6 represents curing the structure. Step 7 represents peeling the structure from the substrate. Step 8 represents repeating steps 3-7 with decreasing thickness of binder. The last structure 600 represents an example end result, an example DEA. Examples include, but are not limited to, the following (referring also to Figures 1- 50). 1. Fig.1 illustrates an out-of-plane dielectric elastomer actuator (DEA) 100, comprising: a plurality of elastomeric films 102 comprising a plurality of (e.g.,defined) thicknesses T; wherein each of the elastomeric films include a first side 104 and a second side 106; a plurality of electrode material layers 108 deposited on the first side and / or the second side of each of the elastomeric films; and wherein the plurality of elastomeric films and the plurality of electrode material layers are assembled into a multilayer structure 110; and wherein the multilayer structure has a bottom side 112 and a top side 114 so that the thicknesses T of the elastomeric films, and / or different spacer / binder layers 102a, 601a, 601b (see Fig.6) attached to each of the films, generally increase or decrease going from the bottom side to the top side so as to form a thickness gradient, and such that when subjected to an applied electric field applied across the electrode material layers, the multilayer structure exhibits non-planar deformation. 2 The DEA or example 1, wherein the elastomeric films each comprise, consist of, or consist essentially of PHDE or other acrylate or silicone dielectric elastomers such as, but not limited to, 3M VHB 49054910, elastosil by Wacker, sylgard 184, etc. Other non-commercial DEs can also be used (see DOI: 10.1002 / polb.23197) 3. The DEA of example 1, wherein the electrode material layers comprise or are disposed in at least a first pattern 2002, 118 or a second pattern 2004, 120, 700 (e.g., as illustrated in Fig.7 or Fig.20). 4. The DEA of example 3, wherein each of the patterns is essentially a union between a circle 2006, 122 and a partially intersecting rectangle 2008a or 2008b. The circle component is the active region 116 while the rectangular component 2008a, 2008b acts as an electrical lead. The second pattern is the first pattern but rotated 180 degrees (or any other angle between 90 degrees and 180 degrees depending on the pattern design) and placed on the opposite side of the elastomer film. Figure 1-4 and 20 shows this electrode shape and orientation. 5. The DEA of any of the examples 2-4, wherein the conductive electrode materials can be patterned into more intricate planar structures, but the critical feature is that a portion 124 of the first and second electrode patterns 118, 120 overlap to form a capacitive structure 126. The shape of the overlapping portion, while a circle 122 in this embodiment, could be a number of different shapes / patterns. 6. The DEA of any of the examples 2-5, wherein the first pattern 118 is deposited on the first side 104 of the elastomeric film 102, the second pattern 120 is deposited on the second side 106 of the elastomeric film, and a portion 124 of the first pattern and a portion of the second pattern overlap to form a dielectric capacitor structure 126. 7. The DEA of any of the examples 2-6, further comprising a binder material 102a deposited on the first side 104 and / or the second side 106 of each elastomeric films. 8. The DEA of example 7, wherein the binder material comprises or consists of, or consists essentially of a PHDE formulation without acrylic acid and functions as a dielectric elastomer adhesive to adhere the layers together while still contributing to the overall output of the actuator (the binder material participates in the actuation process). Other silicone or acrylate dielectric elastomers (examples mentioned in above comments on example 1) can be used. Additionally, other soft stretchable adhesive can also be used, e.g., such as Fastbond. 9. The DEA of example 7 or 8, wherein the binder material is crosslinked to adhere the elastomeric films 102 together. 10. The DEA of any of the examples 1-9, wherein the plurality of defined thicknesses T range from 5 micrometers to 200 micrometers (5 micrometers ≤ T ≤ 200 micrometers). 11. The DEA of any of the examples 1-10, wherein the plurality of defined thicknesses T range from 10 micrometers to 50 micrometers (10 micrometers ≤ T ≤ 50 micrometers). 12. An out-of-plane dielectric elastomer actuator (DEA) 100 comprising: a plurality of elastomeric films 102 comprising a plurality of (e.g., defined) elastic moduli; wherein each of the elastomeric films 102 include a first side 104 and a second side 106; and a plurality of electrode material layers 108, each of the electrode material layers deposited on the first side 104 and / or the second side 106 of a different one of the elastomeric films 102. 13. The DEA of example 12, wherein the electrode material layers 108 comprise or are disposed in at least one of a first pattern 118 or a second pattern 120. 14. The DEA of example 13, wherein the first pattern 118 and / or the second pattern 120 are deposited on the first side 104 and / or the second side 106 of the elastomeric films 102. 15. The DEA of any of the examples 12-14, wherein: the plurality of elastomeric films 102 and the plurality of electrode material layers 108 are assembled into a multilayer structure 110; and the multilayer structure has a bottom side 112 and a top side 114 so that the Young's modulus of the elastomeric films 102 generally increases or decreases going from the bottom side 112 to the top side 114 so as to form a stiffness gradient leading to out-of-plane (non-planar) deformation of the multilayer structure 110 when the multilayer structure is subjected to an applied electric field applied across (a thickness T2 of) the electrode material layers 102. 16. The DEA of any of the examples 12-15, further comprising a binder material 102a deposited on the first side 104 and / or the second side 106 of each elastomeric films 102. 17. The DEA of example 16, wherein the binder material is crosslinked to adhere the elastomeric films together. 18. The DEA of any of the examples 12-17, wherein the plurality of defined elastic moduli range from 10kPa to 10MPa (10 kPa ≤ elastic moduli ≤ 10 MPa). 19. The DEA of any of the examples 12-18, wherein the plurality ofdefined elastic moduli range from 100kPa to 5MPa ^100 kPa ^ elastic moduli ^5 MPa^..20. A device 100, 2000 for providing haptic stimulation comprising: a plurality of elastomeric films 102 comprising a plurality of (e.g., defined) thicknesses T wherein the elastomeric films 102 include a first side 104 and a second side 106; an electrode material layer 108 deposited on the first side and / or the second side of each of the elastomeric films, so as to form a plurality of the electrode material layers. 21. The device of example 20, wherein the electrode material layers have at least one of a first pattern 118 or a second pattern 120; 22. The device of example 21, wherein the first pattern 118 and / or the second pattern 120 are deposited on the first side 104 and / or the second side 106 of the elastomeric films. 23. The device of any of the examples 20-23, wherein: the plurality of elastomeric films 102 and the plurality of electrode material layers 108 are assembled into a multilayer structure 110; and the multilayer structure has a bottom side 112 and a top side 114 so that the thicknesses T of the elastomeric films generally increase or decrease going from bottom side to the top side, and when subjected to an applied electric field across the thickness T2 between the bottom side and the top side, the multilayer structure exhibits non-planar deformation. 24. The device of any of the examples 20-24, further comprising: an adhesive 2400 (e.g., BAP, or any commercial, soft biocompatible adhesive) comprising a first surface 2402 opposite a second surface 2404, wherein: the first surface 2402 is bonded to the top side 114 of the multilayer structure 110 comprising the haptic device and the second surface 2404 may optionally be bonded to a surface (e.g. skin) on a user; and the haptic device transfers a perceptible force onto the surface on the user. 25. The device of any of the examples 1-24, wherein the applied electric field at frequencies that induce the non-planar deformations at frequency ranges from static ^0 Hz^ up to 10kHz 0 ^ f ^ 10 kHz. 26. The device of any of the examples 1-25 wherein the applied electric Field ranges from 5MV / m to 200MV / m 5MV / m ≤ E ≤ 200 MV / m) . 27. An array of the devices of any of the examples, wherein the array has a size or dimension (length and / or width W) from 0.2 mm to 10 mm. 28. The device of any of the examples, wherein the devices are configured for attaching to one or more surfaces on the user. 29. A device 100, 2000 for providing haptic stimulation comprising: a plurality of elastomeric films 102 comprising a plurality of defined Young's moduli; wherein the elastomeric films include a first side 104 and a second side 106; an electrode material layer 108 deposited on the first side and / or the second side of each of the elastomeric films, so as to form a plurality of the electrode material layers. 30. The device of example 29, wherein the electrode material layers have a first pattern 118 and / or a second pattern 120. 31. The device of example 30, wherein the first pattern and / or the second pattern are deposited on the first side 104 and / or the second side 106 of the elastomeric film. 32. The device of any of the examples 29-31, wherein: the plurality of elastomeric films and the plurality of electrode material layers are assembled into a multilayer structure 110; the multilayer structure has a bottom side 112 and a top side 114 so that the Young's modulus of the elastomeric films generally increases or decreases going from bottom side to the top side, and when subjected to an applied electric field across a thickness T2, the multilayer structure exhibits non-planar deformation. 33. The device of any of the examples 29-32, further comprising an adhesive 2400 comprising a first surface 2402 opposite a second surface 2404, wherein: the first surface 2402 is bonded to the top side 114 of the multilayer structure comprising a haptic device and the second surface 116 can be bonded to a surface (e.g., skin) on a user and the haptic device transfers a perceptible force onto the surface on the user. 34. The device of any of the examples 29-33, wherein the electric field applied across the multilayer structure is applied at frequencies that induce the non- planar deformations at frequency ranges from static ^0 Hz^ up to 10kHz. 35. The device of any of the examples 29-34, wherein the applied electric field applied across the multilayer structure ranges from 5MV / m to 200MV / m. 36. An array 2010 of the devices of any of the examples 29-35, whereinthe array has a size (e.g., area) or dimension (length and / or width W) from 0.2 mm to10 mm.37. The device of any of the examples 29-36, wherein the devices are configured for attaching to one or more surfaces on the user. 38. The device of any of the examples 1-37, wherein the elastomeric films 102 comprise a crosslinked network comprising a poly(propylene oxide) unit on a network chain or a pendant group, wherein the pol(propylene oxide) unit comprises the structure -O-(C3H6O)n- and n is and integer greater than or equal to 1. 39. The device of example 38, wherein the crosslinked network is formed by polymerization of a formulation comprising a difunctional monomer comprising a poly(propylene oxide) unit or a monofunctional monomer comprising a poly(propylene oxide) unit, wherein the poly(propylene oxide) unit constitutes or comprises 50 wt% or more in the formulation. 40. The device of example 38 or 39 wherein the crosslinked network is formed by polymerization of a formulation comprising a difunctional monomer comprising a poly(propylene oxide) unit having a molecular weight at least 2000 g / mol and a difunctional monomer having a molecular weight less than 2000 g / mol. 41. The device of any of the examples 39-40, wherein the formulation comprises at least one photoinitiator. 42. The device of any of the examples 38-41, wherein the crosslinked network is formed by polymerization of a formulation comprising an oligomer comprising a urethane unit, a difunctional monomer comprising a poly(propylene oxide) unit, a monofunctional reactive diluent, and a photoinitiator. 43. The device of any of the examples 38-42, wherein the monofunctional reactive diluent comprises a monomer comprising at least one of a poly(propylene oxide) unit, a butyl group, an isobornyl group, a carboxylic acid group, a 2-ethylhexyl group, or a mixture thereof. 44. The device of example 42 or 43, wherein the oligomer comprising the urethane unit is a difunctional monomer having a molecular weight greater than 2000 g / mol. 45. The device of any of the examples 39-44, wherein the formulation comprises a polymerizable functional group comprising at least one of an acrylate, a methacrylate, or a mixture thereof. 46. The device of any of the examples 39-45, wherein the difunctional monomer comprising the poly(propylene oxide) unit has a molecular weight less than 2000 g / mol. 47 The device of any of the examples 39-46, wherein the difunctional monomer comprising the poly(propylene oxide) unit comprises an oligo(propylene oxide) and two terminal polymerizable groups. 48. The device of any of the examples 39-47, wherein the monofunctional monomer comprising the poly(propylene oxide) unit comprises an oligo(propylene oxide) with a molecular weight less than 500 g / mol. 49. The device of any of the examples 1-48, wherein the electrode material layer 108 comprises a conductive material comprising at least one of single walled carbon nanotubes, multi walled carbon nanotubes, carbon nanopowder, metal nanowires, metal nanoparticles, conductive polymer, liquid metals (e.g., galinstan), conductive pastes / greases (e.g., carbon grease which is carbon powder suspended in a dielectric oil), any conductive nanoparticles / nanowires / powders embedded in polymer matrices, or a mixtures thereof. 50. The device of any of the examples 1-49, wherein the top side 112 and the bottom side 114 of the multilayer structure are covered with a material 1900 or the multilayer structure is supported by the material, or a frame 1910 comprising material, wherein the material comprises or consists of or consists essentially of PET or any stiff but flexible material (e.g., but not limited to kapton, PS, PP, PLA, ABS, PMMA). 51. The device of any of the examples 1-50, comprising a conductive track 1902 passing through a via 1904 in a middle region 1906 of the multilayer structure, wherein the conductive track 1902 electrically contacts an edge of the electrode material layers 108 in the middle region 116 to apply a voltage, with respect to non- biased or differently biased edges 2700, 1906 of the electrode material layers 108, so as to generate the electric field. 52. The device of any of the examples 1-51, comprising conductive tracks 1902 connecting the electrode material layers 108 in the middle region 1906 as well as any electrode materials on the outer surfaces 1912. 53. An array 2010 of the device of example 51 or 52, wherein the conductive track comprises an array 1914 of tracks, each of the tracks electrically contacting a different one of the multilayer structures. 54. The device of any of the examples 1-53, comprising a first electrical contact 2702 (e.g., silver epoxy or metal) electrically contacting the electrode material layers 108 in the first pattern 2704, 118 and a second electrical contact 2706 (e.g. silver epoxy or metal) electrically contacting the electrode material layers in the second pattern 2708, 120, so that a voltage applied between the first electrical contact and the second electrical contact generates the electric field used to deform the multilayer structure. 55. The device of example 54, wherein the first electrical contact to the electrode material layers in the first pattern is at a first end 2710 of the multilayer structure / stack 110 , the second electrical contact in the second pattern is at a second end 2712 of the multilayer stack / structure, the electrode material layers connected to the first end do not extend all the way to the second end, and the electrode material layers connected to the second end do not extend all the way to the first end. 56. The device of any of the examples 1-55, wherein an active region 116 of maximum deformation, used for haptic communication, is in a middle of the multilayer structure or any position of the multilayer actuator structure, e.g., as dictated by the design (which can be intricate or complex) of the electrode patterns (e.g., first pattern or second pattern). 57. The device of any of the examples 1-56, further comprising a patch 2040 comprising each of the multilayer structures, wherein the patch is optionally covered with adhesive. 58. The device of any of the examples 1-57, wherein the elastomeric films comprise dielectric elastomers as described in [3]-[5] of the references section, including those listed on pages 20-26 or Table 2 in [5] (reproduced in Fig.21) or in Section 2. DIELECTRIC ELASTOMER MATERIALS of [4] (e.g. VHB elastomers, polyacrylate with Diels Alder bonds, bistable electroactive polymers). 56. The device of any of the examples 1-58, wherein the different binder layer 102a thickness creates the electric field gradient even if the elastomeric films 102 have the same thickness. 57. A method of making a DEA comprising: (a) depositing n-1 elastomeric films (e.g., PHDE) on a smooth substrate (e.g., glass) from which the films can be peeled; (b) depositing (e.g., casting) an nth elastomeric film (e.g.,PHDE) on any stiff but flexible material (e.g., PET); (c)depositing an electrode layer (e.g., CNT) on the elastomeric films on the substrate; (d) depositing a binder on the electrode layer; (e)attaching the elastomeric film (on the stiff but flexible material) to the binder. (f) curing the structure formed in steps (a)-(d); (g) peeling the structure from the substrate; and (h) repeating (c)-(g) with different thickness of the binder to obtain the DEA. 58. The method of example 56 used to make the device of any of the examples 1-56. References The following references are incorporated by reference herein. [1] Y. Shi et al., “A processable, high-performance dielectric elastomer and multilayering process,” Science, vol.377, no.6602, pp.228–232, Jul.2022, doi: 10.1126 / science.abn0099. [2] M. Gao et al., “Skin temperature-triggered, debonding-on-demand sticker for a self-powered mechanosensitive communication system,” Matter, vol.4, no.6, pp.1962–1974, 2021, doi: 10.1016 / j.matt.2021.03.003. [3] PCT International Patent Application Serial No. PCT / US2022 / 029446, PCT Publication Serial No WO2022 / 241 / 313 entitled a A PROCESSABLE, HIGH- PERFORMANCE DIELECTRIC ELASTOMER AND MULTILAYER DIELECTRIC ELASTOMER ACTUATOR [4] Dielectric Elastomer Artificial Muscle: Materials Innovations and Device Explorations Published as part of the Accounts of Chemical Research special issue “Wearable Bioelectronics: Chemistry, Materials, Devices, and Systems”. Yu Qiu, Elric Zhang, Roshan Plamthottam, and Qibing Pei. DOI: 10.1021 / acs.accounts.8b00516, Acc. Chem. Res.2019, 52, 316−325. [5] Advances in Dielectric Elastomers for Actuators and Artificial Muscles by Paul Brochu, Qibing Pei, Macromol. Rapid Commun.2010, 31, 10–36. Pages 20- 26. Tenth Example: Haptic Artificial Muscle Skin 1. Introduction Current extended reality (XR) technologies, such as virtual and augmented reality head mounted displays, primarily enhance human experiences through interactive visuals and sounds. The next frontier of XR, however, aims to redefine immersion by incorporating the sense of touch, which holds the potential to revolutionize various fields, including entertainment, communication, education, and healthcare (1). Central to next-generation XR are haptic actuators that are responsible for generating and transmitting tactile sensations from the virtual environment to the mechanoreceptors nestled within our skin’s dermis (2). While traditional haptic actuators have been integrated into XR interfaces like controllers (3), gloves (4), or shoes (5), their bulky form factors and restriction to specific body parts lack versatility, impede dexterity during XR interaction, and limit users’ immersive experience. Skin-integrated haptic interfaces, which resemble skin-like patches, present a promising alternative with flexible adaptation to various body parts, thereby reducing intrusiveness and enabling natural interaction with virtual environments (6–8). Existing skin-integrated haptics predominantly employ piezoelectric actuators (9) or magnetic motors (10) to create artificial sensory feedback in the form of mechanical vibrations, known as vibrotactile feedback. Nonetheless, the inherent rigidity of these actuators hinders the wearability of the XR devices. Moreover, due to their low strokes, these devices often operate at frequencies over 100 Hz to optimize human perception (6), which falls short in accurately replicating real-world experiences where sustained force and lower frequencies are needed. Additionally, they offer limited spatial resolution, typically up to 10 mm (11), posing challenges in delivering complex haptic feedback to smaller, more sensitive body parts, such as the fingertips. Soft transducers, such as magnetic-responsive soft actuators (12), shape memory polymer actuators (13), fluidic soft actuators (14), and dielectric elastomer actuators (DEAs) (15) are promising alternatives. DEAs are particularly appealing due to their fast response, broad bandwidth, large strains, high energy densities, and silent operation, comparable to natural muscles (16). A typical DEA uses a dielectric elastomer (DE) thin film with compliant electrodes coated on its opposing sides. It contracts in the thickness direction and expands in-plane when placed under a voltage bias (17). While in-plane actuation can stretch the skin to create tactile sensation (15), this mode of stimulus is only sensitive to Ruffini corpuscles, a mechanosensory organ with a relatively low density within the skin (18). On the other hand, skin indentation can optimally stimulate a broader range of mechanoreceptors, including Meissner corpuscles, Merkel cells, and Pacinian corpuscles, allowing replication of more complex physical interactions such as light touch, low- and high-frequency vibrations, sustained pressure, and weight perception (19). Therefore, to effectively impart realistic tactile sensations, DEAs must generate significant out-of-plane output to indent the skin. One way to achieve out-of-plane motions in DEAs is to create a pressure difference between the opposing surfaces of the DE film (20). This approach usually necessitates an external pressure source and bulky pneumatic components such as pumps, chamber, tubes, and / or valves, which also renders the device susceptible to air leakage. Another strategy involves the use of stiff materials, such as embossed plastics (21, 22) or rigid indenters (23, 24), beneath the DEAs to induce buckling actuation. These solutions often compromise wearability and comfort, especially after prolonged use, due to the introduction of rigid components, and can also adversely impact the performance (e.g., strain and / or force output) of the actuator. Embedding fluidic channels within DEAs to induce anisotropic deformation has been explored as an alternative (25), allowing for the fabrication of stretchable and conformal haptic interfaces (26). However, the resulting actuators have a maximum force output of 40 mN, potentially inadequate for areas of skin without high perception sensitivity. Additionally, the introduction of a liquid significantly complicates the fabrication process, further limiting its widespread implementation. 2. Structure and Operation of Haptic Device according to the example Fig. 22 illustrates a wearable haptic artificial muscle skin (HAMS) based on a millimeter-scale, multilayered DEA capable of producing significant out-of-plane deformation and indenting the skin for optimal haptic stimuli (Fig. 22A). The DEAs harnessed an electric field gradient mechanism within a thickness-varied multilayer dielectric elastomer (TVMDE) to achieve out-of-plane deformation without an external pressure bias or any inactive, rigid components. This enabled HAMS to maintain a fully soft structure that conforms to a user’s skin with optimal wearability and comfort. When seamlessly applied onto the user's body and connected to a VR headset, HAMS delivered an immersive XR experience with extended sensations that closely mimicked the tactile feedback of real-world interactions. The actuation principle can be described by Fig. 22B. In this example, the multilayer consists of three layers of DEs with graduated thicknesses. Under a DC voltage bias, thinner layers experience larger electric fields than thicker ones, causing them to exhibit larger actuation strains. The resulting disparity in actuation strains enables the actuator to buckle out of plane in the direction of the thinner layers and output a force having a strong vertical component. 3. Fabrication To ensure robust actuation, especially when individual layers are under different strain, strong interlayer adhesion is crucial. We developed a process to fabricate the TVMDE based on a processable high-performance dielectric elastomer (PHDE) and the corresponding multilayering process (27), as illustrated in fig. 27. This method ensures sufficient interlayer adhesion to prevent delamination during actuation. We began by preparing 40-µm-thick cured PHDE films, each coated with ultra-thin single- walled carbon nanotubes (SWNTs) acting as the compliant electrodes. The PHDE precursor was diluted in acetone and sprayed in various amounts onto the SWNT- coated PHDE films to form PHDE precursor layers of various thicknesses (see detailed concentrations and quantities of precursors sprayed in table S1 in Fig.50). The modified PHDE films are then stacked to form the TVMDE, with each precursor layer being cured immediately after the addition of each new PHDE layer. The cured precursor layer not only acts as a binder to significantly enhance the interlayer adhesion, as evidenced by a swelling test (fig.28), but also varies the total thickness of each PHDE layer in a scalable, controllable manner. For practical implementations that require large force output, TVMDE configurations may extend beyond three layers. Our scalable process enabled large-area fabrication and customization in dimensions, array sizes, and layer counts for TVMDE (fig. 29, see Materials and Methods for detailed fabrication process of TVMDE). This work focused on a 10-layer TVMDE with the following thickness configuration: the initial six layers each having 40 µm, followed by two layers of 45 µm, and concluding with two layers at 50 µm. Cross-sectional imaging using a scanning electron microscope (SEM) of an as-fabricated 10-layer TVMDE revealed the seamless integration of the precursor with the bulk layers, effectively modifying the layer thicknesses (fig. 30). Fig. 22C show the out-of-plane actuation of a 10-layer TVMDE with an active area (circular overlapping area of the SWNT electrodes) diameter of 4 mm. Finite element analysis (FEA) of this setup also validated the anticipated buckling behavior under a 3 kV voltage (fig. 31, see Materials and Methods for detailed simulation setup). 4. Experimental characterization Experimental measurements of the displacement and force output of the 10- layer TVMDEs were performed to test their effectiveness as haptic stimuli. The diameter of active area in the TVMDEs was varied from 3 mm to 7 mm. Displacement was assessed by placing each actuator beneath a laser displacement sensor while subjecting it to a 0.5 Hz square wave voltage for static actuation (fig.32A). Due to the transparency of SWNTs, a small reflective paint was applied at the center of each actuator's top surface to facilitate accurate sensor readings. Force output was measured by placing the actuators on a z-axis linear stage and contacting them with a force sensor to obtain minimal readings, typically below 0.3 mN (fig. 32B). The stage was then lowered until the sensor displayed zero, indicating no preload. The stage was further lowered for 30 µm, allowing TVMDE to buckle towards the probe. This setup approximated TVMDE’s operation on skin, which, with skin being soft and flexible, provided low resistance to actuation and allowed the actuator to buckle despite being in contact with it. As depicted in Fig. 23A and 23B, TVMDEs with larger diameters exhibited greater displacement and force output, as expected, due to the larger actuator geometry and active mass. This finding was consistent with the modeling results as well (Fig. 23C; see fig. 33 for additional simulated data). The displacement to diameter ratio (DDR) and specific force output, however, indicated that smaller actuators provided more efficient output (Fig. 23D). Furthermore, larger actuators decreased the spatial resolution of HAMS, required significantly more materials for their fabrication, and were more likely to contain defects that cause inferior performance or even failure. Considering these factors, and to maintain sufficient absolute haptic output, we selected 4-mm TVMDEs for the remainder of this study. Figure 34 shows the DDR and force output per unit area of this TVMDE, which compare favorably to other buckling actuators reported in literature (15, 22–24, 26, 28– 30). In addition, the thickness-gradient approach minimized stress concentrations on the elastomer films in both active and inactive states. The monolithic design allowed the TVMDE to have a prolonged lifetime and retain its performance over 200,000 cycles at a high voltage (Fig.23E). As shown in fig.35A, the TVMDE produced stable displacement over extensive continuous cycling. Two instances of drop-and-recover in the displacement profile were self-clearing events due to the fault‐tolerant properties of thin SWNT electrodes (31, 32). Furthermore, TVMDE actuators stored for 12 months in an ambient environment still operated with minimal degradation in performance (fig. 35B). TVMDEs also demonstrated resilience in humid environments, as evidenced by the negligible loss in displacement output after being immersed in water for over 48 hours (fig.35C). Fig. 36A and B showed the displacement and force output profiles during a 2- Hz square-wave actuation. At 3.5 kV, the 4-mm TVMDE retained around 50% of its displacement and force output at 25 Hz (Fig.23F). Through the versatile fabrication process, the TVMDE design can incorporate pixels to realize the HAMS device. This was achieved by sandwiching an array of the TVMDEs between a thin elastomeric layer coated with stretchable conductive traces and a skin adhesive that provided robust adhesion to the skin (Fig.24A, see fig.37 for assembly process schematics). The elastomer layer was a 40-µm PHDE film and the conductive paths were stencil-printed stretchable silver conductors. Electrical connections were established by puncturing the electrode leads on each actuator to reveal the interlayer SWNTs and subsequently filling the punctures with a conductive epoxy. This created both parallel connections between active DE layers and vertical interconnect accesses (VIAs) to the conductive path (Fig.24B). Fig.38 shows the array dimension and conductive path design of the HAMS for this study. A custom flexible flat cable (FFC) was fabricated to extend HAMS’s connection pads and provide robust connection to the external circuit (fig. 39). The skin adhesive was a copolymer of octadecyl acrylate (OA) and tetradecyl acrylate (TA) in a chemically crosslinked elastomer network (33), with a low modulus of 5 kPa at normal skin temperature and a high modulus of 67 MPa below 32°C (fig. 40). This allowed HAMS to be easily attached by pressing it on the skin and nondestructively detached upon cooling. The adhesive layer also acted as an insulation layer to prevent charge dissipating from the actuators to skin. The as-fabricated HAMS was a 600-μm thick elastomer patch that can adapt to multiple mechanical manipulations such as bending and stretching (fig.41). Apart from the color variations in the conductive materials, HAMS appeared skin-like, conforming seamlessly to the skin (Fig. 24C). In addition, HAMS formed a strong bond with the skin and maintained its adhesion strength through long hours of continuous wear and during activities that involve significant deformation of the skin. While HAMS having 10-layer, 4-mm diameter TVMDEs were the focus of this study, it is important to note that HAMS can also be configured with different TVMDE dimension, number of stacked DE layers, and / or array sizes tailored for different parts of the body. For example, HAMS integrated with a 2-by-2 array of 5-layer 2.5-mm diameter TVMDE can fit on the fingertip, which outputs a maximum force of over 80 mN at 3.5 kV (fig.42). 5. Control System To replicate complex, real-life tactile experiences, HAMS requires precise, individual control over each actuator element within the array. Additionally, producing meaningful deformation and force in DEAs necessitates applying an electric field exceeding 50 V / μm, or several kV across DE films that are merely tens of micrometers thick. While this poses safety considerations for a wearable device like HAMS, the associated current and power consumption remain low, due to the low capacitance of these actuators (34). To address these challenges, we employed a battery-powered, high-voltage power supply (HVPS) with HV switching using multiple channels of optoelectronic half-bridge circuit (35, 36). More details about this power supply can be found in fig. 43 and Materials and Methods. Our HVPS effectively actuated each element in HAMS at a current level less than 100 µA, with peak power consumption of less than 200 mW (fig.44-45). This control scheme allowed for HAMS's safe operation on skin, while providing individual addressing of the TVMDE in the array at a computer-programmable intensity and frequency (fig.46). Fig.24D shows that a 3-by- 3 HAMS can be programmed to display certain letters, either statically or dynamically. The threshold for static haptic perception, particularly on sensitive areas like the fingertips and palm, is reported to be as low as 10 µm for displacement and 1.5 mN for force (37). However, the thresholds can vary considerably due to factors such as age, gender, and the characteristics of the stimulus, including its type and sequence. While a single TVMDE can produce static displacement and force significantly exceeding these thresholds, perception tests were performed to assess the effectiveness of HAMS when providing more dynamic haptic stimulations. We initially evaluated HAMS's ability to produce distinguishable haptic stimuli of varying intensity and frequency involving 7 volunteers. A 3-by-3 HAMS was attached to the back of each participant’s left hand. In the intensity differentiation test, participants were asked to identify haptic feedback at low, medium, and high intensities, which corresponded to activation voltages of 2 kV, 2.25 kV, and 2.5 kV, respectively. An 'off' state was also included for control. The confusion matrix indicated high identification rates exceeding 82% for all intensity levels, with minimal confusion between adjacent intensities (Fig. 25A). The frequency test assessed each participant’s perception of haptic feedback across five frequencies from 0.5 to 10 Hz. Participants demonstrated a consistent ability to perceive frequency changes, with accuracy rates surpassing 85% for all tested frequencies (Fig. 25B). HAMS was then programmed to generate 9 distinct patterns to evaluate its effectiveness in delivering more complex, spatiotemporal feedback. These patterns, depicted in fig.48, include directional cues (right, left, down, and up) as well as more intricate movements like radial ripples and rotational feedback that could simulate potential interactive events in the virtual environment. To ensure that differences in subject responses were due solely to the distinctiveness of the tactile patterns, all patterns were programmed with identical frequencies and comprised the same number of steps, eliminating variations in the signal’s speed or rhythm. Almost all patterns showed correct identification rates of over 80%, except the radial pattern (pattern number 7) at 71.4% (Fig.25C). The slightly lower perception rate for the radial pattern may stem from its less intuitive representation of motion. Overall, the identification rates for three perception tests were all agreeably high, averaging over 90% (fig. 49). Importantly, in each test, the identification rate between the “off” and “on” states of the HAMS was 100%, indicating that the participants can consistently detect when HAMS is activated, regardless of the type of actuation. This confirms that TVMDE actuators have sufficiently high stroke and force output such that their actuation is perceived through the adhesive layer. The generated tactile feedback is clearly perceptible in varying intensities, frequencies, and sequences, enabling HAMS to replicate various dynamic and interactive experiences in the virtual environment. Fig.26A illustrates the use of HAMS for immersive experiences within an XR system. During these tests, the user wore a commercial head-mounted display (HMD) and a 3-by-3 HAMS on the palm. The HMD, interfaced with the XR system, provided visual and auditory information of the virtual scenes created by Unity Engine on a PC. The built-in hand tracking function in the HMD captured hand movements, while the scenes were scripted to detect collisions between the virtual hand and objects. Upon collision, the PC sent signals to the HVPS which generated specific haptic patterns on HAMS for realistic feedback. We demonstrated two dynamic scenarios: the perception of virtual rain and the manipulation of a virtual golf ball. In the rain scene, users were placed in a digitally rendered rainy setting, where they could feel the raindrops on their hand (Fig. 26B). Leveraging HAMS’s ability to modulate the intensity and frequency of the haptic feedback, the experience varied from the gentle and slow touch of light rain to the more pronounced and rapid sensation of a heavy downpour (Fig.26C). Users’ interaction with the environment also affected the dynamic feedback; for instance, moving the hand under a parasol ceased the haptic sensation of rain. The golf simulation offered another layer of interaction, where users virtually grasped and manipulated a golf ball. As the ball rolled across the hand’s surface, specific actuators on HAMS were activated, and a constant force was applied onto the hand to replicate the weight of the golf ball. The actuators mirrored the ball's movements and changes in position until the ball rolled away (Fig. 26). Unlike traditional haptic interfaces that rely on high- frequency vibrotactile actuation, HAMS could generate a substantial vertical displacement over a long duration to apply a constant pressure on skin, effectively simulating the weight of the golf ball and enhancing the immersive experience. This example demonstrated HAMS, a fully soft, skin-integrated haptic interface, comprising millimeter-scale TVMDE actuators that achieve large out-of-plane actuation. A 4-mm TVMDE can generate a displacement of up to 1.36 mm and a force of up to 0.21 N, while maintaining high performance with over 200,000 cycles of continuous operation. With these soft and stable actuators and a skin adhesive, HAMS can be seamlessly and robustly attached to the skin, providing complex haptic feedback with over 90% perception accuracy. The scalability and customizability of HAMS allow it to be applied to different skin surfaces and potentially cover the entire body. Additionally, HAMS eliminates the rigid components typically found in wearable haptic devices and provides additional sensations such as sustained pressure on the skin, enhancing users’ experience in XR environments. This work allows HAMS to potentially be used in applications such as XR entertainment and virtual training, as well as assistive technologies like displaying Braille letters and indoor navigation for people with visual impairments. 6. Materials and Methods The following reagents were used in the synthesis of PHDE resin and adhesive polymer precursors: urethane diacrylate (UDA, catalog name: CN9021) and isobornyl acrylate (IBOA, catalog name: SR506A) were purchased from Sartomer; butyl acrylate (BA), acrylic acid (AA), propoxylate neopentyl glycol diacrylate (PNPDA), benzophenone (BP), octadecyl acrylate (OA), and 2,2-dimethoxy-2- phenylacetophenone (DMPA) were obtained from Sigma Aldrich; tetradecyl acrylate (TA) was acquired from TCI America. a. Preparation of the PHDE precursor resin The preparation of the PHDE precursor was carried out by mixing the following reagents: UDA (70 wt%), PNPDA (10 wt%), IBOA (5 wt%), BA (13 wt%), AA (2.5 wt%), DMPA (1 wt%), and BP (0.5 wt%). The container holding the mixture was then immediately covered with aluminum foil and the mixture was stirred overnight. b. Fabrication of the TVMDE The fabrication of TVMDE began with the preparation of single layer PHDE films. Making an N-layer TVMDE requires one PHDE film on a 170-µm-thick PET substrate and N-1 films on glass. The selected substrates provided different adhesion and stiffness to allow continuous addition of layers and avoid delamination during fabrication. Each film was made by blade coating PHDE precursor solution onto glass or PET substrates, followed by UV curing in nitrogen on a UV conveyor equipped with a 2.5 W / cm2Fusion 300s type “h” UV curing bulb for two passes at a speed of 6 ft / min. Each film has a thickness of 40 µm, as controlled by the blade gap. All films were trimmed to ensure uniformity. SWNTs were then spray-coated onto glass / DE films with laser-cut masks to form patterned electrodes. Next, each glass / DE film was sprayed with specific amount and concentration of the diluted precursor solution to adjust thickness according to table S1. The precursor solution was diluted with acetone. Between layers that do not require thickness modification, i.e., the 40-µm layers, a thin layer of precursor solution was sprayed to act as a binder. The stacking process is shown in fig.27A. To initiate stacking, the PET / DE was aligned onto a glass / DE / SWNT / precursor, and the laminate was gently rolled to remove visible air bubble. The precursor layer was then UV cured in air on a UV conveyor equipped with 2.5 W / cm2Fusion 300s type “h” UV curing bulb for two passes at a speed of 6 ft / min. After UV curing, the glass was removed and the two-layer DE stack, which is now on PET, was aligned onto another glass / DE / CNT / precursor to add the next DE layer. These processes were repeated until the desired layer number was reached. Fig. 27B shows layer cross-sections during stacking of PET / DE and glass / DE / CNT / precursor. Although the precursor layer was sprayed on the glass / DE, it added thickness to the DE layer on PET substrate. c. Preparation of the TVMDE samples for testing Individual TVMDEs were cut out and interlayer SWNT electrode leads were exposed. Parallel connection of the layers in a TVMDE were achieved by painting a silver epoxy (Catalog name: 8331D, MG Chemicals) on the exposed electrode leads, as shown in fig. 27C. Electrical wires were then attached to the epoxy for connection to HV power. The silver epoxy was allowed to dry at room temperature for 1 hour. d. Swelling test The strong interlayer bonding of the TVMDE was assessed through a swelling test (fig. 28). A control sample consisting of 10 layers of 40-µm thick PHDE was laminated without any binder. Prior to testing, both the control and the TVMDE samples were well adhered and exhibited as a single film with an approximate area of 1 cm2each. After soaking in a tetrahydrofuran (THF) solution, the PHDE stack, which relied solely on van der Waals forces for bonding, delaminated completely within 1 minute. In contrast, the TVMDE maintained strong interlayer adhesion and continued to perform as a robust, unified film even after 24 hours of soaking in THF. e. Finite element analysis of the TVMDE i. A general constitutive model of a dielectric elastomer Based on previous studies on DEs (38-42), we used a general electromechanical constitutive model to capture the deformation of a DE under voltage. We considered a material particle labeled by a position vector ^^ in the stress-free reference configuration Ω^( ^^ ∈ Ω^) that moves to the position ^^ at time ^^ in the current configuration Ω^( ^^ ∈ Ω^). The deformation gradient was defined as ^^^^ൌ ^^ ^^^^ ^^, ^^^⁄^^ ^^^. Voltage ^^ was applied across the opposite surfaces of the DE. We simplified the model by assuming that no extrinsic electric charge is present and ^^ isconstant. The electric field in the undeformed configuration was defined as ^ഥ^ ൌ^ ^^⁄ ^^ ^ ^^, where ^^ is the thickness of the DE and ^^ is the unit vector normal to the in the reference configuration from positive charge to negative charge. considered an ideal DE (38, 39), whose free energy is the sum of the elastic energy due to the network deformation and the free energy due to polarizing the dielectric. The free energy density of a DE in the reference configuration can be expressed as: ^^^^ ^^, ^ഥ^^ ൌ ^^^^^ ^^^ ^ ^^ௗ^^^ ^^, ^ഥ^^. (1)The first term in Eq.1, ^^^^^ ^^, ^^^ ൌ െఓଶ ^^^∙ ^^ ^^ ^1 െூభିଷ^^^ െ ^^ ∙ ^^ ^^^ ^^^ ^ ^^(2) ଶ െ describes the entropic elasticity of the elastomer network, known as the Gent model, where ^^ is the shear modulus, ^^^is a fitting parameter, ^^^is the first invariant of ^^ ^^்defined as ^^^≔ ^^ ^^^ ^^ ^^்^, ^^ is the bulk modulus, and ^^ ൌ det ^ ^^^. The second term in Eq.1 is ^^ష^ ష^ௗ^^^ ^^, ^ഥ^^ ൌఌ^௧^^^ ^^ ^ഥ^^ ^^ ^^ ^ഥ^^^,(3) where ^^ is the permittivity. Considering the deformation of a DE as an equilibrium isothermal process, the thermodynamic condition requires the variation of the free energy of a DE over a small change should always equal the external work, ^ஐబ^^ ^^^^^ ^^ ൌ ^^ ^^. Here, we assumed no body force or traction force was applied on the material so that ^^ ^^ ൌ 0. Using thechain rule, we can get ^^ ^^^ ൌ ^^ ^^^⁄^^ ^^ : ^^ ^^ ^ ^^ ^^^⁄^^ ^ഥ^ : ^^ ^ഥ^. As the applied voltage ^^ isconstant, ^ഥ^ is constant and ^^ ^^^⁄ ^^ ^ഥ^ : ^^ ^ഥ^ ൌ 0. Then we can derive the governingequation ^^ ^^ ^^^ ^^^ ൌ 0, where the Cauchy stress ^^ ൌ ^^ି^^^ ^^^⁄ ^^ ^^ ^^்can be expressed as: ^^ ൌఓ^^^ ^^ ^்ఓ ^ ^^ ఓ(4) ^^ିூభାଷ ^^ െ^^^ ^ 2 ^^ െ 1 ^ଶെ^^^ ^^ ^ ^^ ^^ ^ ^^ െ where ^^ represents the electric field in the current configuration, i.e, ^^ ൌ ^^ି்^ഥ^. ii. Finite element simulation We further implemented the DE model into the commercial finite element software, ABAQUS, via a user element subroutine, UMAT. The material parameters were fitted based on the stress-strain data and the dielectric constant of PHDE (24): ^^ ൌ 0.7099 ^^ ^^ ^^, ^^^ ൌ 4.3822, ^^⁄ ^^ ൌ 1000, ^^ ൌ 4.7 ^^ െ (1)17 ^^ଶ / ^ ^^ ∙ ^^ ^^ଶ^,where the bulk modulus ^^ was set large enough to represent a nearly incompressible material. The model fitted well with the experimental stress-strain data as shown in fig.31A. To simulate the deformation of DE layers under a constant voltage across the thickness, we conducted static FEA in a model as shown in fig. 31B. Given the cylindrical shape of the actuator and the axisymmetric deformation, we used the 4-node bilinear axisymmetric quadrilateral hybrid element. We simulated the cases with diameters of 3, 4, 5, 6, and 7 mm in the active region (where voltage was applied) and a width of 3 mm in the inactive region (no voltage applied). The external edge of the inactive part was fixed. Different DE layers were modeled based on the geometry of the real actuators in the experiments. By varying the thickness of the DEs, different electrical field distributions were obtained, | ^ഥ^| ൌ ^^⁄ ^^ ; thinner layers corresponded to higher electric fields. The contours in fig. 31B and fig. 31C show the electrical field and displacement distributions of a case with the diameter of 4 mm in the active region under 3.5 kV. We calculated the maximum displacements under voltage for different geometry and compared them with the experimental results (fig.33). To calculate the force output, we created a rigid section with an initial gap of 30 µm away from the top surface of the actuator, consistent with the experimental setup, to calculate the reaction force (fig. 31Bii). As the voltage increased, the constrained expansion of the DE induced compressive stress, which can lead to mechanical instability of the structure. To overcome the divergence of the simulations due to the instability, we conducted dynamic explicit analysis under quasi-static loading, which gave the same results as static analysis but can go beyond the instability. The predicted force output as a function of the voltage agreed well with the experimental measurements (fig.33). f. Displacement and force measurement on TVMDE In the displacement tests, the laser displacement sensor (optoNCDT1420, Micro-Epsilon) was mounted around 15 mm above the actuators. A reflective dot with diameter of around 500 µm was carefully painted on the actuator using a blunt tip needle. Force output was measured by a force sensor (Model M7-012, Mark-10 Corporation), which was mounted on a motorized stand (Model ESM303, Mark-10 Corporation). An HV power amplifier (Trek 10 / 10B-HS, Advanced Energy) was used to generate square wave voltage signal for the displacement and force measurement. A data acquisition board (DAQ) (Model NI USB-6009, National Instruments) and a custom LabVIEW program were used to control the frequency and amplitude of the HV output. g. Lifetime characterization of TVMDE In the cyclic actuation test, a 4-mm, 10-layer TVMDE was positioned around 15 mm below the laser displacement sensor (optoNCDT1420, Micro-Epsilon). The actuator was then subject to a 20-Hz, 3.5-kV voltage until failure, and the displacement output was simultaneously recorded. To test the resistance to humid environment, three 4-mm, 10-layer TVMDEs were immersed in DI water for varying durations (0, 4, 12, 24, and 48 hour). After immersion, they were blow-dried before being actuated. h. Fabrication of the skin adhesive The precursor solution of the adhesive polymer was made by mixing UDA, OA, and TA in the ratio of 1:2:2, followed by adding 0.5 wt% of DMPA. The mixture was then sonicated for 30 min before injecting into a glass mold. The glass mold was made by gapping two pieces of water-repellent-coated glass slides with two 100-µm-thick polyester tape. The total tape thickness determined the final thickness of the adhesive. The precursor solution within the glass mold was then UV cured in air on a UV conveyor equipped with 2.5 W / cm2Fusion 300s type “h” UV curing bulb for one pass at a speed of 1 ft / min. i. Fabrication of the stretchable electrode layer The stretchable electrode layer consisted of a patterned stretchable silver conductor and a layer of PHDE as substrate. PHDE substrate was made by blade- casting the precursor onto an 80-µm-thick release liner (MBK Tape Solution). The release liner had a silicone coating that allowed easy removal of the liner when integrating into HAMS, as explained in the next section. The precursor solution coated on the liner was then UV cured in nitrogen on a UV curing conveyor equipped with 2.5 W / cm2Fusion 300s type “h” UV curing bulb for 2 passes at a speed of 6 ft / min. The thickness of the final film on the liner had a thickness of 40 µm. Stretchable silver paste (Catalog name: PE874, DUPONT™) was then printed on the PHDE through a laser- cut contact mask. The mask was then removed and the silver / DE / liner was heated at 130°C for 15 min. j. Assembly of a 3x3 HAMS Circular through-holes were created at the electrode leads on a 3x3 TVMDE array using a hollow metal punch with an inner diameter of 0.8 mm (fig. S11A). Then the array was laminated onto the silver / DE / liner by aligning the holes with the VIA contact sites (fig. S37B). The punctures were then filled with the silver epoxy to form VIAs. The array / silver / DE / liner was then put on a hotplate at 35°C and the skin adhesive was laminated on top. Finally, the bottom release liner was removed. k. Fabrication of the custom-made FFC and HAMS’s connection strategy An acrylic adhesive film (Catalog name: F9469PC, 3M) with a thickness of 58 µm was first cut out with the liner attached. Next, a layer of stretchable silver conductor was printed on the adhesive through a laser-cut mask. After removing the mask, the silver / adhesive / liner was heated at 130°C for 15 min. A row of male pin header connectors with a pitch of 2.54 mm was aligned with the silver paths on one end of the FFC. Electrical connection between the pins and the silver paths was secured by applying the silver epoxy. A non-conducting epoxy adhesive (5 Minute® Epoxy, Devcon) was applied at the contact points to provide electrical insulation and structural support. Then the FFC can be connected to the control circuit through the pins. The other side of the FFC was connected to the exposed FFC contact pads on HAMS. A thin layer of silver epoxy was applied in between to remove air gaps and to prevent high-voltage arcing. The exposed silver paths were covered by blade coating with the PHDE resin, followed by UV curing. Finally, the liner for the adhesive layer was removed. l. The HVPS The block diagram of the HVPS used in this study was shown in fig. S17. This HVPS used a DC / DC converter (Model A05P-5, XP Power) to transform the 3.7 V DC input into 4 kV, which was then directed to nine pairs of commercial miniature HV optocouplers (Model OPTO-150, HVM Technology) for switching. Each pair formed a half-bridge circuit responsible for the charging and discharging of individual actuators. A microcontroller (Teensy® 4.1) applied a digital pulse-width-modulated (PWM) signal to the LED in each optocoupler. By adjusting the duty cycle of the PWM signals, we can regulate each channel's output voltage, thereby varying the intensity of the haptic feedback produced. The output frequency was tuned by programming the on- and off- time of the optocouplers. m. Electrical characterization of the HVPS and TVMDE actuators The voltage output of the HVPS was recorded using high-resolution USB oscilloscopes (Model Handyscope HS4-5, TiePie engineering). Each oscilloscope can record up to four channels. Three oscilloscopes were connected and synchronized to allow electrical characterization of the 9-channel HVPS. The current and power consumption data was estimated using a shunt resistor method (fig. 39A), where a 1 MOhm resistor was connected in series with a TVMDE actuator. The voltages across the actuator and the resistor were simultaneously measured using two separate channels from the USB oscilloscope. The TVMDE actuator was charged for 500 ms and then discharged for 500 ms during each test at different actuation voltage, corresponding to an actuation cycle of 1 Hz. For each data point, the current was calculated by ^^ ൌ^ೃோ , and the instantaneous power can be calculated by ^^ ൌ ^^ ൈ ^^ , where VR is the voltage across the resistor, and VT is the voltage across the actuator. n. Haptic perception test The intensity, frequency, and pattern perception tests were performed on 7 healthy volunteers (4 female and 3 male individuals, with age from 18 to 40). During the test, the participants wore HAMS on their hands for haptic feedback and provided verbal response of the tactile sensation they received. HAMS was powered by the HVPS. All participants provided their consent before the test, and all experimental protocols for this human subject test were approved by the University of California, Los Angeles Institutional Review Board (UCLA IRB) (IRB#24-000170). o. XR system Oculus Quest 2 was selected for its high-resolution display (1080 × 1200) and integrated hand tracking. Virtual scenes were developed using Unity and custom scripts were written in C# to enable dynamic interaction between the virtual hand and the environment. HAMS was connected to the HVPS, and the microcontroller on the HVPS received serial command from the PC and activated HAMS accordingly. p. Actuator control in the XR demonstration scenes In the rain scene, when rain was detected on hand, the actuators received the command to produce a set pattern at set intensity and frequency. The light rain command charged each actuator to a voltage of around 1800 V for 500 ms, while the heavy rain command charged each actuator to a voltage of around 2500 V for 120 ms. In the ball scene, an invisible 3-by-3 grid was placed in the palm of the virtual hand. Each square within the grid corresponds to each actuator element in HAMS. When the ball rolled in the hand, it collided with exactly one square within the grid, and the corresponding actuator will then be charged to around 2800 V. Adjacent actuators were also programmed to actuate at lower voltages. q. Actuator data during XR demonstrations The voltages across the actuators in the rain scene and the ball scene were measured using the USB oscilloscope similar to what was mentioned in a previous section. To obtain the force data, a curve fitting was first performed to model the relationship between voltage and force data. The curve fitting used an exponential function and the force data as measured in Fig. 2B for 4-mm TVMDEs. Finally, force output was calculated from the measured voltage data using the fitted curve, and the force heatmaps were plotted. Below is the python script used for the curve fitting: import numpy as np from sci o timize im ort curve fit , en The following references are incorporated by reference herein. 1. H. Bai, S. Li, R. F. Shepherd, Elastomeric Haptic Devices for Virtual and Augmented Reality. Adv. Funct. Mater.31, 2009364 (2021). 2. K. R. Pyun, J. A. Rogers, S. H. Ko, Materials and devices for immersive virtual reality. Nat Rev Mater 7, 841–843 (2022). 3. B. C. M. Murray, B. N. Peele, P. Xu, J. Spjut, O. Shapira, D. Luebke, R. F. Shepherd, “A variable shape and variable stiffness controller for haptic virtual interactions” in 2018 IEEE International Conference on Soft Robotics (RoboSoft) (IEEE, Livorno, 2018; https: / / ieeexplore.ieee.org / document / 8404930 / ), pp.264–269. 4. M. Zhu, Z. Sun, Z. Zhang, Q. Shi, T. He, H. Liu, T. Chen, C. Lee, Haptic-feedback smart glove as a creative human-machine interface (HMI) for virtual / augmented reality applications. Sci. Adv.6, eaaz8693 (2020). 5. H. Son, H. Gil, S. Byeon, S.-Y. Kim, J. R. Kim, “RealWalk: Feeling Ground Surfaces While Walking in Virtual Reality” in Extended Abstracts of the 2018 CHI Conference on Human Factors in Computing Systems (ACM, Montreal QC Canada, 2018; https: / / dl.acm.org / doi / 10.1145 / 3170427.3186474), pp.1–4. 6. X. Yu, Z. Xie, Y. Yu, J. Lee, A. Vazquez-Guardado, H. Luan, J. Ruban, X. Ning, A. Akhtar, D. Li, B. Ji, Y. Liu, R. Sun, J. Cao, Q. Huo, Y. Zhong, C. Lee, S. Kim, P. Gutruf, C. Zhang, Y. Xue, Q. Guo, A. Chempakasseril, P. Tian, W. Lu, J. Jeong, Y. Yu, J. Cornman, C. Tan, B. Kim, K. Lee, X. Feng, Y. Huang, J. A. Rogers, Skin-integrated wireless haptic interfaces for virtual and augmented reality. Nature 575, 473–479 (2019). 7. Y. Huang, J. Zhou, P. Ke, X. Guo, C. K. Yiu, K. Yao, S. Cai, D. Li, Y. Zhou, J. Li, T. H. Wong, Y. Liu, L. Li, Y. Gao, X. Huang, H. Li, J. Li, B. Zhang, Z. Chen, H. Zheng, X. Yang, H. Gao, Z. Zhao, E. Song, H. Wu, Z. Wang, Z. Xie, K. Zhu, X. Yu, A skin-integrated multimodal haptic interface for immersive tactile feedback. Nat Electron, doi: 10.1038 / s41928-023-01074-z (2023). 8. Y. H. Jung, J.-Y. Yoo, A. Vázquez-Guardado, J.-H. Kim, J.-T. Kim, H. Luan, M. Park, J. Lim, H.-S. Shin, C.-J. Su, R. Schloen, J. Trueb, R. Avila, J.-K. Chang, D. S. Yang, Y. Park, H. Ryu, H.-J. Yoon, G. Lee, H. Jeong, J. U. Kim, A. Akhtar, J. Cornman, T. Kim, Y. Huang, J. A. Rogers, A wireless haptic interface for programmable patterns of touch across large areas of the skin. Nat Electron 5, 374– 385 (2022). 9. H. Jin, Y. Kim, W. Youm, Y. Min, S. Seo, C. Lim, C.-H. Hong, S. Kwon, G. Park, S. Park, H. J. Kim, Highly pixelated, untethered tactile interfaces for an ultra-flexible on-skin telehaptic system. npj Flex Electron 6, 82 (2022). 10. J.-H. Kim, A. Vázquez-Guardado, H. Luan, J.-T. Kim, D. S. Yang, H. Zhang, J.-K. Chang, S. Yoo, C. Park, Y. Wei, Z. Christiansen, S. Kim, R. Avila, J. U. Kim, Y. J. Lee, H.-S. Shin, M. Zhou, S. W. Jeon, J. M. Baek, Y. Lee, S. Y. Kim, J. Lim, M. Park, H. Jeong, S. M. Won, R. Chen, Y. Huang, Y. H. Jung, J.-Y. Yoo, J. A. Rogers, A wirelessly programmable, skin-integrated thermo-haptic stimulator system for virtual reality. Proc. Natl. Acad. Sci. U.S.A.121, e2404007121 (2024). 11. D. Li, J. Zhou, K. Yao, S. Liu, J. He, J. Su, Q. Qu, Y. Gao, Z. Song, C. Yiu, C. Sha, Z. Sun, B. Zhang, J. Li, L. Huang, C. Xu, T. H. Wong, X. Huang, J. Li, R. Ye, L. Wei, Z. Zhang, X. Guo, Y. Dai, Z. Xie, X. Yu, Touch IoT enabled by wireless self-sensing and haptic-reproducing electronic skin. Sci. Adv.8, eade2450 (2022). 12. Y. Wu, S. Zhang, Y. Yang, Z. Li, Y. Wei, Y. Ji, Locally controllable magnetic soft actuators with reprogrammable contraction-derived motions. Sci. Adv. 8, eabo6021 (2022). 13. D. Kim, B. Kim, B. Shin, D. Shin, C.-K. Lee, J.-S. Chung, J. Seo, Y.- T. Kim, G. Sung, W. Seo, S. Kim, S. Hong, S. Hwang, S. Han, D. Kang, H.-S. Lee, J.- S. Koh, Actuating compact wearable augmented reality devices by multifunctional artificial muscle. Nat Commun 13, 4155 (2022). 14. J. Barreiros, H. Claure, B. Peele, O. Shapira, J. Spjut, D. Luebke, M. Jung, R. Shepherd, Fluidic Elastomer Actuators for Haptic Interactions in Virtual Reality. IEEE Robot. Autom. Lett.4, 277–284 (2019). 15. X. Ji, X. Liu, V. Cacucciolo, Y. Civet, A. El Haitami, S. Cantin, Y. Perriard, H. Shea, Untethered Feel‐Through Haptics Using 18‐µm Thick Dielectric Elastomer Actuators. Adv. Funct. Mater.31, 2006639 (2021). 16. Y. Guo, Q. Qin, Z. Han, R. Plamthottam, M. Possinger, Q. Pei, Dielectric elastomer artificial muscle materials advancement and soft robotic applications. SmartMat, e1203 (2023). 17. R. Pelrine, R. Kornbluh, Q. Pei, J. Joseph, High-Speed Electrically Actuated Elastomers with Strain Greater Than 100%. Science 287, 836–839 (2000). 18. A. Handler, D. D. Ginty, The mechanosensory neurons of touch and their mechanisms of activation. Nat Rev Neurosci 22, 521–537 (2021). 19. S. Biswas, Y. Visell, Haptic Perception, Mechanics, and Material Technologies for Virtual Reality. Adv. Funct. Mater.31, 2008186 (2021). 20. 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, 285–288 (2012). 21. R. Vertechy, A. Frisoli, M. Bergamasco, F. Carpi, G. Frediani, D. De Rossi, Modeling and experimental validation of buckling dielectric elastomer actuators. Smart Mater. Struct.21, 094005 (2012). 22. I. Koo, K. Jung, J. Koo, J. Nam, Y. Lee, H. Choi, “Wearable Fingertip Tactile Display” in 2006 SICE-ICASE International Joint Conference (IEEE, Busan Exhibition & Convention Center-BEXCO, Busan, Korea, 2006; http: / / ieeexplore.ieee.org / document / 4108998 / ), pp.1911–1916. 23. D.-Y. Lee, S. H. Jeong, A. J. Cohen, D. M. Vogt, M. Kollosche, G. Lansberry, Y. Mengüç, A. Israr, D. R. Clarke, R. J. Wood, A Wearable Textile- Embedded Dielectric Elastomer Actuator Haptic Display. Soft Robotics 9, 1186–1197 (2022). 24. H. Phung, C. T. Nguyen, T. D. Nguyen, C. Lee, U. Kim, D. Lee, J. Nam, H. Moon, J. C. Koo, H. R. Choi, Tactile display with rigid coupling based on soft actuator. Meccanica 50, 2825–2837 (2015). 25. E. Acome, S. K. Mitchell, T. G. Morrissey, M. B. Emmett, C. Benjamin, M. King, M. Radakovitz, C. Keplinger, Hydraulically amplified self- healing electrostatic actuators with muscle-like performance. Science 359, 61–65 (2018). 26. G. Grasso, S. Rosset, H. Shea, Fully 3D‐Printed, Stretchable, and Conformable Haptic Interfaces. Adv Funct Materials, 2213821 (2023). 27. Y. Shi, E. Askounis, R. Plamthottam, T. Libby, Z. Peng, K. Youssef, J. Pu, R. Pelrine, Q. Pei, A processable, high-performance dielectric elastomer and multilayering process. Science 377, 228–232 (2022). 28. G. Frediani, H. Boys, M. Ghilardi, S. Poslad, J. J. C. Busfield, F. Carpi, A Soft Touch: Wearable Tactile Display of Softness Made of Electroactive Elastomers. Adv Materials Technologies 6, 2100016 (2021). 29. E. Leroy, R. Hinchet, H. Shea, Multimode Hydraulically Amplified Electrostatic Actuators for Wearable Haptics. Adv. Mater., 2002564 (2020). 30. A. K. Han, S. Ji, D. Wang, M. R. Cutkosky, Haptic Surface Display based on Miniature Dielectric Fluid Transducers. IEEE Robot. Autom. Lett.5, 4021– 4027 (2020). 31. W. Yuan, L. B. Hu, Z. B. Yu, T. Lam, J. Biggs, S. M. Ha, D. J. Xi, B. Chen, M. K. Senesky, G. Grüner, Q. Pei, Fault‐Tolerant Dielectric Elastomer Actuators using Single‐Walled Carbon Nanotube Electrodes. Advanced Materials 20, 621–625 (2008). 32. E. Hajiesmaili, D. R. Clarke, Dielectric elastomer actuators. Journal of Applied Physics 129, 151102 (2021). 33. M. Gao, H. Wu, R. Plamthottam, Z. Xie, Y. Liu, J. Hu, S. Wu, L. Wu, X. He, Q. Pei, Skin temperature-triggered, debonding-on-demand sticker for a self- powered mechanosensitive communication system. Matter 4, 1962–1974 (2021). 34. A. Minaminosono, H. Shigemune, T. Murakami, S. Maeda, Untethered rotational system with a stacked dielectric elastomer actuator. Smart Mater. Struct. 30, 065007 (2021). 35. S. Schlatter, P. Illenberger, S. Rosset, Peta-pico-Voltron: An open- source high voltage power supply. HardwareX 4, e00039 (2018). 36. S. K. Mitchell, T. Martin, C. Keplinger, A Pocket‐Sized Ten‐Channel High Voltage Power Supply for Soft Electrostatic Actuators. Adv Materials Technologies 7, 2101469 (2022). 37. C. Hatzfeld, T. A. Kern, Eds., Engineering Haptic Devices: A Beginner’s Guide (Springer London, London, 2014; https: / / link.springer.com / 10.1007 / 978-1-4471-6518-7)Springer Series on Touch and Haptic Systems. 38. X. Zhao, Z. Suo, Method to analyze programmable deformation of dielectric elastomer layers. Applied Physics Letters 93, 251902 (2008). 39. X. Zhao, W. Hong, Z. Suo, Electromechanical hysteresis and coexistent states in dielectric elastomers. Phys. Rev. B 76, 134113 (2007). 40. Z. Suo, X. Zhao, W. Greene, A nonlinear field theory of deformable dielectrics. Journal of the Mechanics and Physics of Solids 56, 467–486 (2008). 41. X. Zhao, Z. Suo, Theory of Dielectric Elastomers Capable of Giant Deformation of Actuation. Phys. Rev. Lett.104, 178302 (2010). 42. N. Goulbourne, E. Mockensturm, M. Frecker, A Nonlinear Model for Dielectric Elastomer Membranes. Journal of Applied Mechanics 72, 899–906 (2005). References for tenth example section 6 The following examples are incorporated by reference herein. 1. H. Bai, S. Li, R. F. Shepherd, Elastomeric Haptic Devices for Virtual and Augmented Reality. Adv. Funct. Mater.31, 2009364 (2021). 2. K. R. Pyun, J. A. Rogers, S. H. Ko, Materials and devices for immersive virtual reality. Nat Rev Mater 7, 841–843 (2022). 3. B. C. M. Murray, B. N. Peele, P. Xu, J. Spjut, O. Shapira, D. Luebke, R. F. Shepherd, “A variable shape and variable stiffness controller for haptic virtual interactions” in 2018 IEEE International Conference on Soft Robotics (RoboSoft) (IEEE, Livorno, 2018; https: / / ieeexplore.ieee.org / document / 8404930 / ), pp.264–269. 4. M. Zhu, Z. Sun, Z. Zhang, Q. Shi, T. He, H. Liu, T. Chen, C. Lee, Haptic-feedback smart glove as a creative human-machine interface (HMI) for virtual / augmented reality applications. Sci. Adv.6, eaaz8693 (2020). 5. H. Son, H. Gil, S. Byeon, S.-Y. Kim, J. R. Kim, “RealWalk: Feeling Ground Surfaces While Walking in Virtual Reality” in Extended Abstracts of the 2018 CHI Conference on Human Factors in Computing Systems (ACM, Montreal QC Canada, 2018; https: / / dl.acm.org / doi / 10.1145 / 3170427.3186474), pp.1–4. 6. X. Yu, Z. Xie, Y. Yu, J. Lee, A. Vazquez-Guardado, H. Luan, J. Ruban, X. Ning, A. Akhtar, D. Li, B. Ji, Y. Liu, R. Sun, J. Cao, Q. Huo, Y. Zhong, C. Lee, S. Kim, P. Gutruf, C. Zhang, Y. Xue, Q. Guo, A. Chempakasseril, P. Tian, W. Lu, J. Jeong, Y. Yu, J. Cornman, C. Tan, B. Kim, K. Lee, X. Feng, Y. Huang, J. A. Rogers, Skin-integrated wireless haptic interfaces for virtual and augmented reality. Nature 575, 473–479 (2019). 7. Y. Huang, J. Zhou, P. Ke, X. Guo, C. K. Yiu, K. Yao, S. Cai, D. Li, Y. Zhou, J. Li, T. H. Wong, Y. Liu, L. Li, Y. Gao, X. Huang, H. Li, J. Li, B. Zhang, Z. Chen, H. Zheng, X. Yang, H. Gao, Z. Zhao, E. Song, H. Wu, Z. Wang, Z. Xie, K. Zhu, X. Yu, A skin-integrated multimodal haptic interface for immersive tactile feedback. Nat Electron, doi: 10.1038 / s41928-023-01074-z (2023). 8. Y. H. Jung, J.-Y. Yoo, A. Vázquez-Guardado, J.-H. Kim, J.-T. Kim, H. Luan, M. Park, J. Lim, H.-S. Shin, C.-J. Su, R. Schloen, J. Trueb, R. Avila, J.-K. Chang, D. S. Yang, Y. Park, H. Ryu, H.-J. Yoon, G. Lee, H. Jeong, J. U. Kim, A. Akhtar, J. Cornman, T. Kim, Y. Huang, J. A. Rogers, A wireless haptic interface for programmable patterns of touch across large areas of the skin. Nat Electron 5, 374– 385 (2022). 9. H. Jin, Y. Kim, W. Youm, Y. Min, S. Seo, C. Lim, C.-H. Hong, S. Kwon, G. Park, S. Park, H. J. Kim, Highly pixelated, untethered tactile interfaces for an ultra-flexible on-skin telehaptic system. npj Flex Electron 6, 82 (2022). 10. J.-H. Kim, A. Vázquez-Guardado, H. Luan, J.-T. Kim, D. S. Yang, H. Zhang, J.-K. Chang, S. Yoo, C. Park, Y. Wei, Z. Christiansen, S. Kim, R. Avila, J. U. Kim, Y. J. Lee, H.-S. Shin, M. Zhou, S. W. Jeon, J. M. Baek, Y. Lee, S. Y. Kim, J. Lim, M. Park, H. Jeong, S. M. Won, R. Chen, Y. Huang, Y. H. Jung, J.-Y. Yoo, J. A. Rogers, A wirelessly programmable, skin-integrated thermo-haptic stimulator system for virtual reality. Proc. Natl. Acad. Sci. U.S.A.121, e2404007121 (2024). 11. D. Li, J. Zhou, K. Yao, S. Liu, J. He, J. Su, Q. Qu, Y. Gao, Z. Song, C. Yiu, C. Sha, Z. Sun, B. Zhang, J. Li, L. Huang, C. Xu, T. H. Wong, X. Huang, J. Li, R. Ye, L. Wei, Z. Zhang, X. Guo, Y. Dai, Z. Xie, X. Yu, Touch IoT enabled by wireless self-sensing and haptic-reproducing electronic skin. Sci. Adv.8, eade2450 (2022). 12. Y. Wu, S. Zhang, Y. Yang, Z. Li, Y. Wei, Y. Ji, Locally controllable magnetic soft actuators with reprogrammable contraction-derived motions. Sci. Adv. 8, eabo6021 (2022). 13. D. Kim, B. Kim, B. Shin, D. Shin, C.-K. Lee, J.-S. Chung, J. Seo, Y.- T. Kim, G. Sung, W. Seo, S. Kim, S. Hong, S. Hwang, S. Han, D. Kang, H.-S. Lee, J.- S. Koh, Actuating compact wearable augmented reality devices by multifunctional artificial muscle. Nat Commun 13, 4155 (2022). 14. J. Barreiros, H. Claure, B. Peele, O. Shapira, J. Spjut, D. Luebke, M. Jung, R. Shepherd, Fluidic Elastomer Actuators for Haptic Interactions in Virtual Reality. IEEE Robot. Autom. Lett.4, 277–284 (2019). 15. X. Ji, X. Liu, V. Cacucciolo, Y. Civet, A. El Haitami, S. Cantin, Y. Perriard, H. Shea, Untethered Feel‐Through Haptics Using 18‐µm Thick Dielectric Elastomer Actuators. Adv. Funct. Mater.31, 2006639 (2021). 16. Y. Guo, Q. Qin, Z. Han, R. Plamthottam, M. Possinger, Q. Pei, Dielectric elastomer artificial muscle materials advancement and soft robotic applications. SmartMat, e1203 (2023). 17. R. Pelrine, R. Kornbluh, Q. Pei, J. Joseph, High-Speed Electrically Actuated Elastomers with Strain Greater Than 100%. Science 287, 836–839 (2000). 18. A. Handler, D. D. Ginty, The mechanosensory neurons of touch and their mechanisms of activation. Nat Rev Neurosci 22, 521–537 (2021). 19. S. Biswas, Y. Visell, Haptic Perception, Mechanics, and Material Technologies for Virtual Reality. Adv. Funct. Mater.31, 2008186 (2021). 20. 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, 285–288 (2012). 21. R. Vertechy, A. Frisoli, M. Bergamasco, F. Carpi, G. Frediani, D. De Rossi, Modeling and experimental validation of buckling dielectric elastomer actuators. Smart Mater. Struct.21, 094005 (2012). 22. I. Koo, K. Jung, J. Koo, J. Nam, Y. Lee, H. Choi, “Wearable Fingertip Tactile Display” in 2006 SICE-ICASE International Joint Conference (IEEE, Busan Exhibition & Convention Center-BEXCO, Busan, Korea, 2006; http: / / ieeexplore.ieee.org / document / 4108998 / ), pp.1911–1916. 23. D.-Y. Lee, S. H. Jeong, A. J. Cohen, D. M. Vogt, M. Kollosche, G. Lansberry, Y. Mengüç, A. Israr, D. R. Clarke, R. J. Wood, A Wearable Textile- Embedded Dielectric Elastomer Actuator Haptic Display. Soft Robotics 9, 1186–1197 (2022). 24. H. Phung, C. T. Nguyen, T. D. Nguyen, C. Lee, U. Kim, D. Lee, J. Nam, H. Moon, J. C. Koo, H. R. Choi, Tactile display with rigid coupling based on soft actuator. Meccanica 50, 2825–2837 (2015). 25. E. Acome, S. K. Mitchell, T. G. Morrissey, M. B. Emmett, C. Benjamin, M. King, M. Radakovitz, C. Keplinger, Hydraulically amplified self- healing electrostatic actuators with muscle-like performance. Science 359, 61–65 (2018). 26. G. Grasso, S. Rosset, H. Shea, Fully 3D‐Printed, Stretchable, and Conformable Haptic Interfaces. Adv Funct Materials, 2213821 (2023). 27. Y. Shi, E. Askounis, R. Plamthottam, T. Libby, Z. Peng, K. Youssef, J. Pu, R. Pelrine, Q. Pei, A processable, high-performance dielectric elastomer and multilayering process. Science 377, 228–232 (2022). 28. G. Frediani, H. Boys, M. Ghilardi, S. Poslad, J. J. C. Busfield, F. Carpi, A Soft Touch: Wearable Tactile Display of Softness Made of Electroactive Elastomers. Adv Materials Technologies 6, 2100016 (2021). 29. E. Leroy, R. Hinchet, H. Shea, Multimode Hydraulically Amplified Electrostatic Actuators for Wearable Haptics. Adv. Mater., 2002564 (2020). 30. A. K. Han, S. Ji, D. Wang, M. R. Cutkosky, Haptic Surface Display based on Miniature Dielectric Fluid Transducers. IEEE Robot. Autom. Lett.5, 4021– 4027 (2020). 31. W. Yuan, L. B. Hu, Z. B. Yu, T. Lam, J. Biggs, S. M. Ha, D. J. Xi, B. Chen, M. K. Senesky, G. Grüner, Q. Pei, Fault‐Tolerant Dielectric Elastomer Actuators using Single‐Walled Carbon Nanotube Electrodes. Advanced Materials 20, 621–625 (2008). 32. E. Hajiesmaili, D. R. Clarke, Dielectric elastomer actuators. Journal of Applied Physics 129, 151102 (2021). 33. M. Gao, H. Wu, R. Plamthottam, Z. Xie, Y. Liu, J. Hu, S. Wu, L. Wu, X. He, Q. Pei, Skin temperature-triggered, debonding-on-demand sticker for a self- powered mechanosensitive communication system. Matter 4, 1962–1974 (2021). 34. A. Minaminosono, H. Shigemune, T. Murakami, S. Maeda, Untethered rotational system with a stacked dielectric elastomer actuator. Smart Mater. Struct. 30, 065007 (2021). 35. S. Schlatter, P. Illenberger, S. Rosset, Peta-pico-Voltron: An open- source high voltage power supply. HardwareX 4, e00039 (2018). 36. S. K. Mitchell, T. Martin, C. Keplinger, A Pocket‐Sized Ten‐Channel High Voltage Power Supply for Soft Electrostatic Actuators. Adv Materials Technologies 7, 2101469 (2022). 37. C. Hatzfeld, T. A. Kern, Eds., Engineering Haptic Devices: A Beginner’s Guide (Springer London, London, 2014; https: / / link.springer.com / 10.1007 / 978-1-4471-6518-7)Springer Series on Touch and Haptic Systems. 38. X. Zhao, Z. Suo, Method to analyze programmable deformation of dielectric elastomer layers. Applied Physics Letters 93, 251902 (2008). 39. X. Zhao, W. Hong, Z. Suo, Electromechanical hysteresis and coexistent states in dielectric elastomers. Phys. Rev. B 76, 134113 (2007). 40. Z. Suo, X. Zhao, W. Greene, A nonlinear field theory of deformable dielectrics. Journal of the Mechanics and Physics of Solids 56, 467–486 (2008). 41. X. Zhao, Z. Suo, Theory of Dielectric Elastomers Capable of Giant Deformation of Actuation. Phys. Rev. Lett.104, 178302 (2010). 42. N. Goulbourne, E. Mockensturm, M. Frecker, A Nonlinear Model for Dielectric Elastomer Membranes. Journal of Applied Mechanics 72, 899–906 (2005). Conclusion This concludes the description of the preferred embodiment of the present invention. The foregoing description of one or more embodiments of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto.

Claims

WHAT IS CLAIMED IS:

1. An out-of-plane dielectric elastomer actuator (DEA), comprising: a plurality of elastomeric films comprising a plurality of thicknesses wherein each of the elastomeric films include a first side and a second side; a plurality of electrode material layers deposited on at least one of a first side or a second side of each of the elastomeric films; and wherein the plurality of elastomeric films and the plurality of electrode material layers are assembled into a multilayer structure; and wherein the multilayer structure has a bottom side and a top side so that at least one of the thicknesses of the elastomeric films, the thicknesses of a binder material attached to each of the elastomeric films, or a Young’s modulus of the elastomeric films increase or decrease going from the bottom side to the top side so as to form at least one of a thickness gradient or a stiffness gradient, and such that when subjected to an applied electric field applied across the electrode material layers, the multilayer structure exhibits a non-planar deformation.

2. The DEA of claim 1, wherein the electrode material layers are arranged in a first pattern and a second pattern so that the electrode material layers in the first pattern are interdigitated with the electrode material layers in the second pattern .

3. The DEA of claim 2, whereina portion of the electrode material layers in the first pattern and a portion of the electrode material layers in second pattern overlap to form a dielectric capacitor structure.

4. The DEA of claim 3, further comprising the binder material deposited on at least one of the first side or the second side of each of the elastomeric films.

5. The DEA of claim 4, wherein the binder material is crosslinked to adhere the elastomeric films together.

6. The DEA of claim 1 , wherein the plurality of thicknesses range from 5 micrometers to 200 micrometers.

7. The DEA of claim 1 , wherein the plurality of defined thicknesses range from 10 micrometers to 50 micrometers.

8. The DEA ofclaim 1, wherein: the plurality of elastomeric films comprise a plurality of elastic moduli; and the multilayer structure has a bottom side and a top side so that the Young's modulus of the elastomeric films increases or decreases going from the bottom side to the top side so as to form the stiffness gradient leading to the out-of-plane (non- planar) deformation of the multilayer structure when the multilayer structure is subjected tothe applied electric field applied across the electrode material layers.

9. The DEA of claim 8 , wherein the plurality of elastic moduli range from10kPa to 10MPa10. The DEA of claim 8, wherein the plurality of elastic moduli range from 100kPa to 5MPa.

11. A device for providing haptic stimulation comprising the device of claim .

12. The device of claim 11, further comprising: an adhesive comprising a first surface opposite a second surface, wherein:the first surface is bonded to the top side of the multilayer structure and the second surface is for bonding to a surface on a user so that the haptic device transfers a perceptible force onto the surface on the user.

13. The device of claim 12 , wherein the applied electric field is at frequencies that induce the non-planar deformations at frequency ranges from static ^0 Hz^ up to 10kHz.

14. The device of claim 12 wherein the applied electric Field ranges from5MV / m to 200MV / m.

15. An array of the devices of claim 1, wherein the array has a size or dimension (length and / or width) from 0.2 mm to 10 mm.

16. The array of claim 15, wherein the devices are configured for attaching to one or more surfaces on the user.

17. The device of claim 1, wherein the elastomeric films comprise a crosslinked network comprising a poly(propylene oxide) unit on a network chain or a pendant group, wherein the pol(propylene oxide) unit comprises the structure -O- (C3H6O)n- and n is and integer greater than or equal to 1.

18. The device of claim 17, wherein the crosslinked network is formed by polymerization of a formulation comprising a difunctional monomer comprising a poly(propylene oxide) unit or a monofunctional monomer comprising a poly(propylene oxide) unit, wherein the poly(propylene oxide) unit constitutes or comprises 50 wt% or more in the formulation.

19. The device of claim 17 wherein the crosslinked network is formed by polymerization of a formulation comprising a difunctional monomer comprising a poly(propylene oxide) unit having a molecular weight at least 2000 g / mol and a difunctional monomer having a molecular weight less than 2000 g / mol.

20. The device of claims 19, wherein the formulation comprises at least one photoinitiator.

21. The device of claim 17, wherein the crosslinked network is formed by polymerization of a formulation comprising an oligomer comprising a urethane unit, a difunctional monomer comprising a poly(propylene oxide) unit, a monofunctional reactive diluent, and a photoinitiator.

22. The device of claim 21, wherein the monofunctional reactive diluent comprises a monomer comprising at least one of a poly(propylene oxide) unit, a butyl group, an isobornyl group, a carboxylic acid group, a 2-ethylhexyl group, or a mixture thereof.

23. The device of claim 21, wherein the oligomer comprising the urethane unit is a difunctional monomer having a molecular weight greater than 2000 g / mol.

24. The device of claim 17, wherein the crosslinked network is formed by a polymerization of a formulation comprising a polymerizable functional group comprising at least one of an acrylate, a methacrylate, or a mixture thereof.

25. The device of claim 18, wherein the difunctional monomer comprising the poly(propylene oxide) unit has a molecular weight less than 2000 g / mol.26 The device of claim 18, wherein the difunctional monomer comprising the poly(propylene oxide) unit comprises an oligo(propylene oxide) and two terminal polymerizable groups.

27. The device of claim 18, wherein the monofunctional monomer comprising the poly(propylene oxide) unit comprises an oligo(propylene oxide) with a molecular weight less than 500 g / mol.

28. The device of claim 1, wherein the electrode material layers comprise a conductive material comprising single walled carbon nanotubes, multi walled carbon nanotubes, carbon nanopowder, metal nanowires, metal nanoparticles, conductive polymer, liquid metal, conductive paste, conductive greases, conductive nanoparticles embedded in a polymer matrix, conductive nanowires embedded in a polymer matrix, or conductive powder embedded in a polymer matrix, or a mixture thereof.

29. The device of claim 1, wherein: the top side and the bottom side of the multilayer structure are covered with a material or the multilayer structure is supported by the material or the multiplayer structure is supported by a frame comprising the material.

30. The device of claim 1, comprising a conductive track passing through a via in a middle region of the multilayer structure, wherein the conductive track electrically contacts an edge of the electrode material layers in the middle region to apply a voltage, with respect to non-biased or differently biased edges of the electrode material layers, so as to generate the applied electric field.

31. The device of claim 30, comprising first conductive tracks connecting the electrode material layers in the middle region, second conductive tracksconnecting first outer surfaces of the electrode material layers and third conductive tracks connecting second outer surfaces of the electrode material layers.

32. An array of the devices of claim 31, wherein the conductive tracks electrically contact different ones of the multilayer structures.

33. The device of claim 2, comprising a first electrical contact electrically contacting the electrode material layers in the first pattern and a second electrical contact electrically contacting the electrode material layers in the second pattern, so that a voltage applied between the first electric contact and the second electrical contact generates the electric field.

34. The device of claim 33, wherein the first electrical contact is at a first end of the multilayer stack, the second electric contact is at a second end of the multilayer stack, the electrode material layers connected to the first end do not extend all the way to the second end, the electrode material layers connected to the second end do not extend all the way to the first end.

35. The device of claim 1, wherein an active region of maximum deformation, used for haptic communication, is in a middle of the multilayer structure or any position of the multilayer actuator structure as dictated by a design for positioning of the electrode material layers.

36. A patch comprising the device of claim 1.

37. A method of making a dielectric elastomer actuator (DEA), comprising: (a) depositing n-1 elastomeric films on a substrate from which the films can be peeled, where n is a positive integer;(b) depositing an nth one of the elastomeric films on any stiff but flexible material; (c)depositing an electrode layer on the elastomeric films on the substrate; (d) depositing a binder on the electrode layer; (e)attaching the nth one of the elastomeric films (on the stiff but flexible material) to the binder; (f) curing the structure formed in steps (a)-(d); (g) peeling the structure from the substrate; and (h) repeating (c)-(g) with different thickness of the binder to obtain the DEA.

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